Minnesota Standards Alignment 2007 Academic …doc.renlearn.com/KMNet/R0055396CDEC8882.pdfMinnesota Standards Alignment 2007 Academic Standards, produced by the State Department of

Minnesota Standards Alignment 2007 Academic Standards, produced by the State Department of Education

Kindergarten through Grades: 9-11

P.O. Box 8036 • Wisconsin Rapids, WI 54495-8036

Phone: (800) 338-4204 • Fax: (715) 424-4242

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Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending

registration in the United States and other countries.

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© 2012 by Renaissance Learning, Inc. All rights reserved. No portion of this document may be reproduced, by any process or technique, without the

express written consent of Renaissance Learning, Inc. Any standards referenced in this document are the property of their respective copyright holders.

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Minnesota Standards Alignment

Standards List with Aligned Product Skills

The Standards List with Aligned Product Skills Report is a standards-oriented document

showing the entire list of standards for the subject and grade and the product skills aligned to

those standards. This alignment report shows the breadth of standards coverage for the purpose

and focus of this product.

Note to Educator ................................................................................................... iii

Kindergarten ....................................................................................................... 1

Grade 1 ............................................................................................................ 4

Grade 2 ............................................................................................................ 9

Grade 3 ............................................................................................................ 15

Grade 4 ............................................................................................................ 23

Grade 5 ............................................................................................................ 30

Grade 6 ........ .................................................................................................... 41

Grade 7 ............................................................................................................ 53

Grade 8 .............. .............................................................................................. 66

Grades: 9-11 ....................................................................................................... 75

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Note to Educator:

Thank you for your interest in Renaissance Learning technology. At Renaissance

Learning, we recognize the impact that standards and assessment reform have on schools.

We share the concerns of educators and administrators that students perform well and

that teachers have the resources they need to support their efforts to address standards and

assessments.

Renaissance Learning provides alignment reports to customers to show how the skills

within each product align to the skills within academic standards. The alignment report

presents all of the academic math standards for a specific state/agency with the aligned

Renaissance Learning product skills indented below each standard.

Academic standards encompass the entire set of learning and expectations that teachers

are responsible for. Renaissance Learning recognizes that teachers are the key to using

products to address the entire set of standards. Renaissance Learning products are ideally

suited to support teachers and academic standards. The Renaissance Learning alignment

report supports teachers in this role by clearly identifying specific product skills that are

aligned to the multiple skills within the standards.

P.O. Box 8036

Wisconsin Rapids, WI 54495-8036

Phone: (800) 338-4204

Fax: (715) 424-4242

www.renlearn.com

iv

On the alignment report you will see the word “Core” next to some of the skills. Core

skills are the most critical mathematics skills for a student to learn at a grade level. They

are key building blocks in a student’s mathematics education. Students need to have

proficiency with core skills to be successful in math at their grade levels and to progress

in the grades that follow. Core skills are indicated on Renaissance Learning’s research-

based and empirically validated Core Progress math learning progression. Core Progress

Math identifies the continuum of concepts and skills needed for success in math. The

continuum begins with early numeracy and progresses to the level of mathematics

required for college and careers. All of the skills in the Core Progress Math contribute to

STAR Math Enterprise Assessment. Alignments for STAR Math Enterprise include

alignments to the Common Core State Standards (CCSS) Mathematics Standards.

In the alignment report, you will notice that most skills have a grade-level indicator at the

end of the text. In addition to these grade-level skills, the report includes skills that are

not grade specific and do not have a grade-level indicator. These skills are designated

Overall Product Skills. They are skills that all students gain through use of the product.

We hope this report answers your questions regarding the alignment of Renaissance

Learning technology and materials to standards. The complete alignment strategy

document is available. The Math document is number R39616. If you have any questions

about the alignment report, please feel free to call us at (800) 338-4204.

Sincerely,

Renaissance Learning

KindergartenMinnesotaAcademic Standards

STAR Math Enterprise

- 1 of 96 -6/22/2012

Numbers and Operations Identify two sets with equal numbers of up to 10 objects [Early Numeracy]

MN K.1.1.5 - Compare and order whole numbers, with and without objects, from 0 to 20. Example: Put the number cards 7, 3, 19 and 12 in numerical order.

Determine one more than or one less than a given number [Grade 1]

Core Skill

Numbers and Operations Add 1 to a set [Early Numeracy]

Subtract 1 from a set [Early Numeracy]

MN K.1.1.4 - Find a number that is 1 more or 1 less than a given number.

Count back by ones from a number less than 20 [Grade 1] Core Skill

Numbers and Operations Count on or count back with numbers 1 to 20 [Early Numeracy]

Count objects to 20 [Grade 1] Core Skill

Count back by ones from a number between 20 and 100 [Grade 1]

Count on by ones from a number less than 100 [Grade 1] Core Skill

MN K.1.1.3 - Count, with and without objects, forward and backward to at least 20.

Read a whole number from 31 to 100 [Grade 1]

Determine the word form of a whole number to 30 [Grade 1]

Numbers and Operations Count the number of any one type of object in a group of up to 10 mixed objects [Early Numeracy]

Read a whole number to 30 [Grade 1]


Determine the word form of a whole number from 31 to 100 [Grade 1]

MN K.1.1.2 - Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. Example: Represent the number of students taking hot lunch with tally marks.


Count the number of any one type of object in a group of up to 10 mixed objects [Early Numeracy]

Numbers and Operations Count 1-20 [Early Numeracy]

MN K.1.1.1 - Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. Example: Count students standing in a circle and count the same students after they take their seats. Recognize that this rearrangement does not change the total number, but may change the order in which students are counted.

MN K.1.1 - Understand the relationship between quantities and whole numbers up to 31.

MN K.1 - Number & Operation

Kindergarten



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Geometry and Measurement Identify a circle, a triangle, a square, or a rectangle [Grade 1] Core Skill

MN K.3.1.1 - Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres.

MN K.3.1 - Recognize and sort basic two- and three-dimensional shapes; use them to model real-world objects.

MN K.3 - Geometry & Measurement

Complete a sequence of numbers between 0 and 10 in ascending order [Early Numeracy]

Complete a sequence of numbers between 0 and 5 in ascending order [Early Numeracy]

Extend a pictorial growth pattern [Grade 1]

Extend a repeating picture pattern [Grade 1]

Algebra Complete a picture pattern [Early Numeracy]

MN K.2.1.1 - Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or x, xx, xxx.

MN K.2.1 - Recognize, create, complete, and extend patterns

MN K.2 - Algebra

Decompose a number into two numbers by using pictures [Early Numeracy]

Numbers and Operations Compose an equivalent number out of two numbers by using pictures [Early Numeracy]

MN K.1.2.2 - Compose and decompose numbers up to 10 with objects and pictures. Example: A group of 7 objects can be decomposed as 5 and 2 objects, or 2 and 3 and 2, or 6 and 1.

Subtract numbers with a minuend up to 10 using pictures [Early Numeracy]

Numbers and Operations Add numbers with a sum up to 20 using pictures [Early Numeracy]

MN K.1.2.1 - Use objects and draw pictures to find the sums and differences of numbers between 0 and 10.

MN K.1.2 - Use objects and pictures to represent situations involving combining and separating.

Compare sets of up to 20 objects using "more" or "fewer" [Early Numeracy]

Count up to 20 objects [Early Numeracy]

Determine the difference in number between two sets of objects [Early Numeracy]



- 3 of 96 -6/22/2012

Geometry and Measurement Compare objects using the vocabulary of measurement [Grade 1] Core Skill

Compare and order objects by attributes of height or length [Grade 1]

Core Skill

MN K.3.2.2 - Order 2 or 3 objects using measurable attributes, such as length and weight.

Compare sizes, weights, and volumes [Early Numeracy]

Compare the weights of two objects [Early Numeracy]

Geometry and Measurement Compare the sizes of two objects [Early Numeracy]

Compare the distances between a starting point and two different objects [Early Numeracy]

Compare objects using the vocabulary of measurement [Grade 1] Core Skill

MN K.3.2.1 - Use words to compare objects according to length, size, weight and position. Example 1: Use same, lighter, longer, above, between and next to. Example 2: Identify objects that are near your desk and objects that are in front of it. Explain why there may be some objects in both groups.

MN K.3.2 - Compare and order objects according to location and measurable attributes

Geometry and Measurement Determine the common attributes in a set of geometric shapes [Grade 1]

Core Skill

MN K.3.1.3 - Use basic shapes and spatial reasoning to model objects in the real-world. Example 1: A cylinder can be used to model a can of soup. Example 2: Find as many rectangles as you can in your classroom. Record the rectangles you found by making drawings.

Geometry and Measurement Sort objects according to one attribute [Early Numeracy]

Determine the common attributes in a set of geometric shapes [Grade 1]

Core Skill

MN K.3.1.2 - Sort objects using characteristics such as shape, size, color and thickness.

Grade 1MinnesotaAcademic Standards


- 4 of 96 -6/22/2012


Count on by ones from a number less than 100 [Grade 1] Core Skill

Numbers and Operations Count objects to 20 [Grade 1] Core Skill

Count back by ones from a number between 20 and 100 [Grade 1]

MN 1.1.1.3 - Count, with and without objects, forward and backward from any given number up to 120.

Model a number to 100 using tens and ones [Grade 1]

Locate a number to 20 on a number line [Grade 1] Core Skill

Identify a number to 20 represented by a point on a number line [Grade 1]

Core Skill

Recognize a number from a model of tens and ones to 100 [Grade 1]

Determine equivalent forms of a number, up to 10 [Grade 1] Core Skill

Determine the 2-digit number represented as tens and ones [Grade 1]

Core Skill

Represent a 2-digit number as tens and ones [Grade 1] Core Skill

Read a whole number from 31 to 100 [Grade 1]

Numbers and Operations Read a whole number to 30 [Grade 1]

Determine the word form of a whole number from 31 to 100 [Grade 1]

Determine the word form of a whole number to 30 [Grade 1]

MN 1.1.1.2 - Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.


Recognize a number from a model of tens and ones to 100 [Grade 1]

Numbers and Operations Model a number to 100 using tens and ones [Grade 1]


Core Skill

Determine the value of a digit in a 2-digit number [Grade 1] Core Skill

MN 1.1.1.1 - Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. Example: Recognize the numbers 21 to 29 as 2 tens and a particular number of ones.

MN 1.1.1 - Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones.

MN 1.1 - Number & Operation

Grade 1



- 5 of 96 -6/22/2012

Relate a number-line model to a basic addition fact [Grade 1]

Numbers and Operations Determine the missing portion in a partially screened (hidden) collection of up to 10 objects [Grade 1]

Core Skill

Relate a picture model to a basic addition fact [Grade 1]

Determine the basic addition fact shown by a picture model [Grade 1]

MN 1.1.2.1 - Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations.

MN 1.1.2 - Use a variety of models and strategies to solve addition and subtraction problems in real-world and mathematical contexts.

Data Analysis, Statistics, and Probability

Read a 2-category tally chart [Grade 1]

Use a bar graph to represent groups of objects [Grade 1]

Answer a question using information from a 2-category tally chart [Grade 1]

Read a bar graph [Grade 1]

Answer a question using information from a bar graph [Grade 1]

Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object) [Grade 1]

Use a bar graph with a y-axis scale by 2s to represent data [Grade 2]

Core Skill

MN 1.1.1.7 - Use counting and comparison skills to create and analyze bar graphs and tally charts. Example: Make a bar graph of students' birthday months and count to compare the number in each month.

Numbers and Operations Compare whole numbers to 100 using words [Grade 1] Core Skill

MN 1.1.1.6 - Use words to describe the relative size of numbers. Example: Use the words equal to, not equal to, more than, less than, fewer than, is about, and is nearly to describe numbers.

Order whole numbers to 100 in descending order [Grade 1]

Order whole numbers to 100 in ascending order [Grade 1] Core Skill

Numbers and Operations Determine one more than or one less than a given number [Grade 1]

Core Skill

Compare whole numbers to 100 using words [Grade 1] Core Skill

MN 1.1.1.5 - Compare and order whole numbers up to 100.

Numbers and Operations Determine ten more than or ten less than a given number [Grade 1]

Core Skill

MN 1.1.1.4 - Find a number that is 10 more or 10 less than a given number. Example: Using a hundred grid, find the number that is 10 more than 27.



- 6 of 96 -6/22/2012

Numbers and Operations Complete a skip pattern starting from a multiple of 2, 5, or 10 [Grade 2]

Core Skill

Complete a skip pattern of 2, 5, or 10 starting from any number [Grade 2]

Core Skill

MN 1.2.1.1 - Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. Example: Describe rules that can be used to extend the pattern 2, 4, 6, 8, __, __, __ and complete the pattern 33, 43, __, 63, __, 83 or 20, __, __, 17.

MN 1.2.1 - Recognize and create patterns; use rules to describe patterns.

MN 1.2 - Algebra

Apply the relationship between subtraction and counting back [Grade 1]

Numbers and Operations Count by 2s to 50 starting from a multiple of 2 [Grade 1] Core Skill

Complete a skip pattern starting from a multiple of 2, 5, or 10 [Grade 2]

Core Skill

Apply the relationship between addition and counting on [Grade 1]

Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively [Grade 1]

Core Skill


Core Skill

MN 1.1.2.3 - Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s.

Algebra Determine a missing addend in a basic addition-fact number sentence [Grade 1]

Core Skill

Determine the missing portion in a partially screened (hidden) collection of up to 10 objects [Grade 1]

Core Skill

Numbers and Operations Determine equivalent forms of a number, up to 10 [Grade 1] Core Skill

MN 1.1.2.2 - Compose and decompose numbers up to 12 with an emphasis on making ten. Example: Given 3 blocks, 7 more blocks are needed to make 10.

Determine the basic subtraction fact shown by a number-line model [Grade 1]

Determine the basic subtraction fact shown by a picture model [Grade 1]

Relate a picture model to a basic subtraction fact [Grade 1]

Determine the basic addition fact shown by a number-line model [Grade 1]

Relate a number-line model to a basic subtraction fact [Grade 1]

Algebra WP: Determine a basic addition- or subtraction-fact number sentence for a given situation [Grade 1]

Core Skill



- 7 of 96 -6/22/2012

Know basic subtraction facts to 20 minus 10 [Grade 1] Core Skill

Numbers and Operations Know basic addition facts to 10 plus 10 [Grade 1] Core Skill

MN 1.2.2.4 - Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Example: 5 + 3 = 8 could be used to represent a situation in which 5 red balloons are combined with 3 blue balloons to make 8 total balloons.

WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence [Grade 1]

Core Skill

Determine a missing subtrahend in a basic subtraction-fact number sentence [Grade 1]

Core Skill


Core Skill

MN 1.2.2.3 - Use number sense and models of addition and subtraction, such as objects and number lines, to identify the missing number in an equation such as: 2 + 4 = __; 3 + __ = 7; 5 = __ - 3.

Algebra Determine equivalent addition or subtraction expressions involving 1-digit numbers [Grade 1]


Know basic addition facts to 10 plus 10 [Grade 1] Core Skill

Numbers and Operations Determine equivalent forms of a number, up to 10 [Grade 1] Core Skill

MN 1.2.2.2 - Determine if equations involving addition and subtraction are true. Example: Determine if the following number sentences are true or false 7 = 7; 7 = 8 - 1; 5 + 2 = 2 + 5; 4 + 1 = 5 + 2.

WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence [Grade 1]

Core Skill


Core Skill


Core Skill

WP: Determine a basic addition- or subtraction-fact number sentence for a given situation [Grade 1]

Core Skill

MN 1.2.2.1 - Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Example: One way to represent the number of toys that a child has left after giving away 4 of 6 toys is to begin with a stack of 6 connecting cubes and then break off 4 cubes.

MN 1.2.2 - Use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

Algebra Extend a repeating picture pattern [Grade 1]

Determine the rule for an addition or subtraction number pattern [Grade 2]

Core Skill

Extend a pictorial growth pattern [Grade 1]

Extend a number pattern involving addition [Grade 2] Core Skill

Extend a number pattern involving subtraction [Grade 2] Core Skill



- 8 of 96 -6/22/2012

Determine the value of a collection of mixed coins [Grade 1]

Numbers and Operations Determine the value of a collection of like coins [Grade 1]

MN 1.3.2.3 - Identify pennies, nickels and dimes and find the value of a group of these coins, up to one dollar.

Geometry and Measurement Tell time to the hour [Grade 1] Core Skill

Tell time to the half hour [Grade 1] Core Skill

MN 1.3.2.2 - Tell time to the hour and half-hour.

Geometry and Measurement Estimate length in nonstandard units [Grade 1]

MN 1.3.2.1 - Measure the length of an object in terms of multiple copies of another object. Example: Measure a table by placing paper clips end-to-end and counting.

MN 1.3.2 - Use basic concepts of measurement in real-world and mathematical situations involving length, time and money.

Decompose a plane shape composed of three or more simpler shapes [Grade 2]


MN 1.3.1.2 - Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders. Example 1: Decompose a regular hexagon into 6 equilateral triangles; build prisms by stacking layers of cubes; compose an ice cream cone by combining a cone and half of a sphere. Example 2: Use a drawing program to find shapes that can be made with a rectangle and a triangle.

Determine the common attributes in a set of geometric shapes [Grade 1]

Core Skill


MN 1.3.1.1 - Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres. Example: Triangles have three sides and cubes have eight vertices (corners).

MN 1.3.1 - Describe characteristics of basic shapes. Use basic shapes to compose and decompose other objects in various contexts.

MN 1.3 - Geometry & Measurement


Core Skill



- 9 of 96 -6/22/2012

Represent a 3-digit number as hundreds, tens, and ones [Grade 2] Core Skill

Determine which digit is in a specified place in a 3-digit whole number [Grade 2]

Numbers and Operations Determine the value of a digit in a 3-digit number [Grade 2]

Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones [Grade 2]

Core Skill

Determine the 3-digit number represented as hundreds, tens, and ones [Grade 2]

Core Skill

MN 2.1.1.2 - Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. Example: Writing 853 is a shorter way of writing 8 hundreds + 5 tens + 3 ones.

Determine the 3-digit number represented as hundreds, tens, and ones [Grade 2]

Core Skill

Determine the word form of a whole number to 1,000 [Grade 2] Core Skill

Model a number using hundreds, tens, and ones to 1,000 [Grade 2]

Recognize a number from a model of hundreds, tens, and ones to 1,000 [Grade 2]



Core Skill

Read a whole number to 1,000 [Grade 2] Core Skill





Represent a 3-digit number as hundreds, tens, and ones [Grade 2] Core Skill

Numbers and Operations Identify a number to 20 represented by a point on a number line [Grade 1]

Core Skill

Determine a number pair that totals 100 [Grade 2] Core Skill

MN 2.1.1.1 - Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.

MN 2.1.1 - Compare and represent whole numbers up to 1000 with an emphasis on place value and equality.


Grade 2



- 10 of 96 -6/22/2012


Numbers and Operations Know basic addition facts to 10 plus 10 [Grade 1] Core Skill

MN 2.1.2.2 - Demonstrate fluency with basic addition facts and related subtraction facts.

Count objects grouped in tens and ones [Grade 1] Core Skill

Know basic addition facts to 10 plus 10 [Grade 1] Core Skill

Numbers and Operations Count on by ones from a number less than 100 [Grade 1] Core Skill



Core Skill


MN 2.1.2.1 - Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts. Example: Use the associative property to make ten when adding 5 + 8 = (3 + 2) + 8 = 3 + (2 + 8) = 3 + 10 = 13.

MN 2.1.2 - Demonstrate mastery of addition and subtraction basic facts; add and subtract one- and two-digit numbers in real-world and mathematical problems.

Compare whole numbers to 1,000 using words [Grade 2]

Compare whole numbers to 1,000 using the symbols <, >, and = [Grade 2]

Core Skill

Numbers and Operations Compare whole numbers to 100 using words [Grade 1] Core Skill

Order whole numbers to 100 in ascending order [Grade 1] Core Skill

Order whole numbers to 1,000 in descending order [Grade 2] Core Skill

Order whole numbers to 1,000 in ascending order [Grade 2] Core Skill

MN 2.1.1.5 - Compare and order whole numbers up to 1000.

Numbers and Operations Round a 2- to 4-digit whole number to its greatest place [Grade 3]

MN 2.1.1.4 - Round numbers up to the nearest 10 and 100 and round numbers down to the nearest 10 and 100. Example: If there are 17 students in the class and granola bars come 10 to a box, you need to buy 20 bars (2 boxes) in order to have enough bars for everyone.

Count on by 100s from any number [Grade 2] Core Skill

Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively [Grade 1]

Core Skill

Numbers and Operations Determine ten more than or ten less than a given number [Grade 1]

Core Skill

MN 2.1.1.3 - Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. Example: Find the number that is 10 less than 382 and the number that is 100 more than 382.



- 11 of 96 -6/22/2012

WP: Add or subtract two 2-digit numbers without regrouping [Grade 1]

Core Skill

Numbers and Operations WP: Add or subtract a 1- and 2-digit number without regrouping [Grade 1]

Core Skill

WP: Add or subtract numbers without regrouping [Grade 2] Core Skill

WP: Add or subtract up to 2-digit numbers with one regrouping [Grade 2]


Core Skill

MN 2.1.2.5 - Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits.

Determine a number pair that totals 100 [Grade 2] Core Skill

Subtract a 2-digit number from a 2-digit number without regrouping [Grade 1]

Core Skill

Add a 2-digit number to a 1-digit number with regrouping [Grade 2]

Numbers and Operations Add two 2-digit numbers without regrouping [Grade 1] Core Skill

Subtract a 1-digit number from a 2-digit number without regrouping [Grade 1]

Core Skill

Add three 2-digit numbers with one regrouping, sum less than 100 [Grade 2]

Subtract a 1- or 2-digit number from a 2-digit number with one regrouping [Grade 2]

Core Skill

Add two 2-digit numbers with regrouping [Grade 2] Core Skill

Add money values using cents or dollars with regrouping [Grade 2]

Subtract money values using cents or dollars with one regrouping [Grade 2]

MN 2.1.2.4 - Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Example: Using decomposition, 78 + 42, can be thought of as: 78 + 2 + 20 + 20 = 80 + 20 + 20 = 100 + 20 = 120 and using expanded notation, 34 - 21 can be thought of as: 30 + 4 - 20 - 1 = 30 - 20 + 4 - 1 = 10 + 3 = 13.

Estimate the difference of two 2-digit numbers [Grade 2]

Numbers and Operations Estimate the sum of two 2-digit numbers [Grade 2]

MN 2.1.2.3 - Estimate sums and differences up to 100. Example: Know that 23 + 48 is about 70.


Core Skill



- 12 of 96 -6/22/2012

MN 2.2.2 - Use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

Determine the rule for an addition or subtraction number pattern [Grade 2]

Core Skill

Algebra Determine an addition or subtraction number pattern given a rule [Grade 2]

Extend a number pattern involving subtraction [Grade 2] Core Skill

Extend a number pattern involving addition [Grade 2] Core Skill


Core Skill


Core Skill

Count on by 100s from any number [Grade 2] Core Skill

MN 2.2.1.1 - Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Example 1: Skip count by 5s beginning at 3 to create the pattern 3, 8, 13, 18, __. Example 2: Collecting 7 empty milk cartons each day for 5 days will generate the pattern 7, 14, 21, 28, 35, resulting in a total of 35 milk cartons.

MN 2.2.1 - Recognize, create, describe, and use patterns and rules to solve real-world and mathematical problems.

MN 2.2 - Algebra


Answer a question using information from a tally chart [Grade 2]







Core Skill

Answer a question using information from a bar graph with a y-axis scale by 2s [Grade 2]

Core Skill

MN 2.1.2.6 - Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts.



- 13 of 96 -6/22/2012

Decompose a plane shape composed of three or more simpler shapes [Grade 2]


Identify a parallelogram, a trapezoid, a pentagon, a hexagon, or an octagon [Grade 2]

MN 2.3.1.2 - Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. Example: Use a drawing program to show several ways that a rectangle can be decomposed into exactly three triangles.

Identify figures that are the same size and shape [Grade 2]

Geometry and Measurement Determine the common attributes in a set of geometric shapes [Grade 1]

Core Skill

MN 2.3.1.1 - Describe, compare, and classify two- and three-dimensional figures according to number and shape of faces, and the number of sides, edges and vertices (corners).

MN 2.3.1 - Identify, describe and compare basic shapes according to their geometric attributes.


WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers [Grade 2]

WP: Determine a basic addition- or subtraction-fact number sentence for a given situation [Grade 1]

Core Skill

Algebra WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence [Grade 1]

Core Skill

WP: Use an open sentence to represent a given situation [Grade 2]

MN 2.2.2.2 - Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Example: How many more players are needed if a soccer team requires 11 players and so far only 6 players have arrived? This situation can be represented by the number sentence 11 - 6 = p or by the number sentence 6 + p = 11.

Determine a missing subtrahend in a number sentence involving 2-digit numbers [Grade 2]

Determine a missing addend in a number sentence involving 2-digit numbers [Grade 2]


Core Skill


Core Skill

MN 2.2.2.1 - Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences. Example: One way to represent n + 16 = 19 is by comparing a stack of 16 connecting cubes to a stack of 19 connecting cubes; 24 = a + b can be represented by a situation involving a birthday party attended by a total of 24 boys and girls.



- 14 of 96 -6/22/2012

Convert money amounts in words to amounts in symbols [Grade 2]

Core Skill

Numbers and Operations Translate between a dollar sign and a cent sign [Grade 2] Core Skill

Determine cent amounts that total a dollar [Grade 2] Core Skill

MN 2.3.3.2 - Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Example: 50 cents can be made up of 2 quarters, or 4 dimes and 2 nickels, or many other combinations.

Geometry and Measurement Tell time to the quarter hour [Grade 2] Core Skill

MN 2.3.3.1 - Tell time to the quarter-hour and distinguish between a.m. and p.m.

MN 2.3.3 - Use time and money in real-world and mathematical situations.

Measure length in centimeters [Grade 2] Core Skill

Geometry and Measurement Measure length in inches [Grade 2] Core Skill

MN 2.3.2.2 - Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Example: Draw a line segment that is 3 inches long.

Measure length in inches [Grade 2] Core Skill

Geometry and Measurement Estimate length in nonstandard units [Grade 1]


MN 2.3.2.1 - Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Example: It will take more paper clips than whiteboard markers to measure the length of a table.

MN 2.3.2 - Understand length as a measurable attribute; use tools to measure length.

Name a 3-dimensional geometric shape [Grade 2]



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Estimate a sum or difference of whole numbers to 10,000 by rounding [Grade 3]

Numbers and Operations Round a 2- to 4-digit whole number to its greatest place [Grade 3]

MN 3.1.1.4 - Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. Example 1: 8726 rounded to the nearest 1000 is 9000, rounded to the nearest 100 is 8700, and rounded to the nearest 10 is 8730. Example 2: 473 - 291 is between 400 - 300 and 500 - 200, or between 100 and 300.

Numbers and Operations Count on by 100s from any number [Grade 2] Core Skill

MN 3.1.1.3 - Find 10,000 more or 10,000 less than a given five-digit number. Find 1000 more or 1000 less than a given four- or five-digit. Find 100 more or 100 less than a given four- or five-digit number.

Represent a 4- or 5-digit whole number in expanded form [Grade 3]

Core Skill

Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones [Grade 3]

Core Skill

Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones [Grade 3]

Core Skill

Determine the 4- or 5-digit whole number represented in expanded form [Grade 3]

Core Skill

Numbers and Operations Determine which digit is in a specified place in a 4- or 5-digit whole number [Grade 3]

Represent a 4-digit whole number as thousands, hundreds, tens, and ones [Grade 3]

Core Skill

MN 3.1.1.2 - Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. Example: Writing 54,873 is a shorter way of writing the following sums: 5 ten thousands + 4 thousands + 8 hundreds + 7 tens + 3 ones; 54 thousands + 8 hundreds + 7 tens + 3 ones.

Represent a 4-digit whole number as thousands, hundreds, tens, and ones [Grade 3]

Core Skill

Determine the word form of a 4- or 5-digit whole number [Grade 3]

Core Skill

Numbers and Operations Read a 4- or 5-digit whole number [Grade 3] Core Skill

Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones [Grade 3]

Core Skill

MN 3.1.1.1 - Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks.

MN 3.1.1 - Compare and represent whole numbers up to 100,000 with an emphasis on place value and equality.


Grade 3



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WP: Add or subtract numbers without regrouping [Grade 2] Core Skill

Numbers and Operations WP: Add or subtract two 2-digit numbers without regrouping [Grade 1]

Core Skill

MN 3.1.2.2 - Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. Example: The calculation 117 - 83 = 34 can be checked by adding 83 and 34.

Add three 2- to 3-digit whole numbers [Grade 3]

Subtract 3- and 4-digit whole numbers with regrouping [Grade 3] Core Skill

WP: Add or subtract 3- and 4-digit whole numbers with regrouping [Grade 3]

Core Skill

Add 3- and 4-digit whole numbers with regrouping [Grade 3] Core Skill

Add two 3-digit numbers with one regrouping [Grade 2] Core Skill

Numbers and Operations Add 2- and 3-digit numbers with no more than one regrouping [Grade 2]

Core Skill


Core Skill

Subtract a 3-digit number from a 3-digit number with one regrouping [Grade 2]

Core Skill


Core Skill

MN 3.1.2.1 - Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms.

MN 3.1.2 - Add and subtract multi-digit whole numbers; represent multiplication and division in various ways; solve real-world and mathematical problems using arithmetic.

Order 4- or 5-digit whole numbers in ascending or descending order [Grade 3]

Compare 4- or 5-digit whole numbers using the symbols <, >, and = [Grade 3]

Numbers and Operations Compare whole numbers to 1,000 using the symbols <, >, and = [Grade 2]

Core Skill

MN 3.1.1.5 - Compare and order whole numbers up to 100,000.

WP: Estimate a sum or difference of two 3- or 4-digit whole numbers using any method [Grade 3]

Core Skill

Estimate a sum of three 2- to 4-digit numbers using any method [Grade 3]

Round a 4- to 6-digit whole number to a specified place [Grade 4] Core Skill

Estimate a sum or difference of 2- to 4-digit whole numbers using any method [Grade 3]

Core Skill



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WP: Divide using basic facts to 100 ÷ 10 [Grade 3] Core Skill

Complete a multiplication and division fact family [Grade 3]

Know basic division facts for 11 and 12 [Grade 3]

WP: Multiply using basic facts to 10 x 10 [Grade 3] Core Skill

WP: Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient [Grade 4]

Core Skill

WP: Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotient [Grade 4]

Core Skill

WP: Multiply a multi-digit whole number by a 1-digit whole number [Grade 4]

Core Skill


Numbers and Operations Know basic multiplication facts to 10 x 10 [Grade 3] Core Skill

Know basic multiplication facts for 11 and 12 [Grade 3]

Know basic division facts to 100 ÷ 10 [Grade 3] Core Skill

MN 3.1.2.4 - Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems. Example 1: You have 27 people and 9 tables. If each table seats the same number of people, how many people will you put at each table? Example 2: If you have 27 people and tables that will hold 9 people, how many tables will you need?


Core Skill

WP: Divide objects into equal groups by sharing [Grade 2] Core Skill


Core Skill

Use a division sentence to represent objects divided into equal groups [Grade 3]

Core Skill

Use a multiplication sentence to represent an area or an array model [Grade 3]

Core Skill

MN 3.1.2.3 - Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.

WP: Add or subtract 3- and 4-digit whole numbers with regrouping [Grade 3]

Core Skill

WP: Add or subtract up to 2-digit numbers with one regrouping [Grade 2]



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MN 3.2.1 - Use single-operation input-output rules to represent patterns and relationships and to solve real-world and mathematical problems.

MN 3.2 - Algebra

Order unit fractions using pictorial models [Grade 2]

Numbers and Operations Compare unit fractions using pictorial models [Grade 2]

Order fractions using models [Grade 3] Core Skill

Compare fractions using models [Grade 3] Core Skill

MN 3.1.3.3 - Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator.

Numbers and Operations WP: Compare equal unit fractions of different-sized wholes [Grade 3]

MN 3.1.3.2 - Understand that the size of a fractional part is relative to the size of the whole. Example: One-half of a small pizza is smaller than one-half of a large pizza, but both represent one-half.

Identify a fraction represented by a point on a number line [Grade 3]

Core Skill

Determine a pictorial model of a fraction of a set of objects [Grade 3]

Core Skill

Numbers and Operations Determine a pictorial model of a fraction of a whole [Grade 3] Core Skill

Locate a fraction on a number line [Grade 3] Core Skill

Estimate fractions of a whole [Grade 3]

MN 3.1.3.1 - Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Example: Parts of a shape (3/4 of a pie), parts of a set (3 out of 4 people), and measurements (3/4 of an inch).

MN 3.1.3 - Understand meanings and uses of fractions in real-world and mathematical situations.

Apply the distributive property to multiply a multi-digit number by a 1-digit number [Grade 4]

Core Skill

Multiply a 2-digit whole number by a 1-digit number [Grade 3]

Multiply a 3- or 4-digit whole number by a 1-digit whole number [Grade 4]

Core Skill

Numbers and Operations WP: Multiply using basic facts to 10 x 10 [Grade 3] Core Skill

Multiply a 1-digit whole number by a multiple of 10 to 100 [Grade 3]

MN 3.1.2.5 - Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Example: 9 × 26 = 9 × (20 + 6) = 9 × 20 + 9 × 6 = 180 + 54 = 234.



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Recognize equivalent multiplication or division expressions involving basic facts [Grade 3]

WP: Determine a multiplication or division sentence for a given situation [Grade 3]

Core Skill



Know basic multiplication facts to 10 x 10 [Grade 3] Core Skill

Numbers and Operations Use a multiplication sentence to represent an area or an array model [Grade 3]

Core Skill

Use a division sentence to represent objects divided into equal groups [Grade 3]

Core Skill

Algebra Determine the missing multiplicand in a number sentence involving basic facts [Grade 3]

Determine the missing dividend or divisor in a number sentence involving basic facts [Grade 3]


MN 3.2.2.2 - Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Example 1: Find values of the unknowns that make each number sentence true 6 = p ÷ 9; 24 = a × b; 5 × 8 = 4 × t. Example 2: How many math teams are competing if there is a total of 45 students with 5 students on each team? This situation can be represented by 5 × n = 45 or 45/5 = n or 45/n = 5.

Overall Product Skills Demonstrate and develop understanding of mathematical concepts and ideas

MN 3.2.2.1 - Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Example: The number sentence 8 × m = 24 could be represented by the question "How much did each ticket to a play cost if 8 tickets totaled $24?".

MN 3.2.2 - Use number sentences involving multiplication and division basic facts and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

Generate a table of paired numbers based on a rule [Grade 4] Core Skill

WP: Find the missing number in a table of paired values [Grade 3]

Algebra Determine a rule for a table of related number pairs [Grade 3]

MN 3.2.1.1 - Create, describe, and apply single-operation input-output rules involving addition, subtraction and multiplication to solve problems in various contexts. Example: Describe the relationship between number of chairs and number of legs by the rule that the number of legs is four times the number of chairs.



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Calculate elapsed time within an hour, given two clocks, without regrouping [Grade 3]

Calculate elapsed time within an hour, given two clocks, with regrouping [Grade 3]

Geometry and Measurement Tell time to the quarter hour [Grade 2] Core Skill

Tell time to 5-minute intervals [Grade 2] Core Skill

Tell time to the minute [Grade 3] Core Skill

MN 3.3.3.1 - Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. Example: Your trip began at 9:50 a.m. and ended at 3:10 p.m. How long were you traveling?

MN 3.3.3 - Use time, money and temperature to solve real-world and mathematical problems.

Overall Product Skills Use strategies to derive solutions for problems

MN 3.3.2.3 - Measure distances around objects. Example: Measure the distance around a classroom, or measure a person's wrist size.

Geometry and Measurement Determine a method for finding the perimeter of a shape given the side lengths [Grade 3]

WP: Determine the perimeter of a rectangular shape given a grid with a reference unit [Grade 3]

WP: Determine the perimeter of a shape given a model showing all side lengths [Grade 3]

MN 3.3.2.2 - Find the perimeter of a polygon by adding the lengths of the sides.


Geometry and Measurement Measure length in inches [Grade 2] Core Skill

Measure length to the nearest half inch or quarter inch [Grade 3]

MN 3.3.2.1 - Use half units when measuring distances. Example: Measure a person's height to the nearest half inch.

MN 3.3.2 - Understand perimeter as a measurable attribute of real-world and mathematical objects. Use various tools to measure distances.


MN 3.3.1.2 - Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons.

Identify a shape that has parallel or perpendicular sides [Grade 4]

Geometry and Measurement Identify parallel, perpendicular, and intersecting lines [Grade 3]

MN 3.3.1.1 - Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids.

MN 3.3.1 - Use geometric attributes to describe and create shapes in various contexts.



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Core Skill

Answer a question using information from a pictograph (1 symbol = more than 1 object) [Grade 2]

Core Skill




Use a pictograph to represent data (1 symbol = more than 1 object) [Grade 2]

Core Skill

MN 3.4.1.1 - Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units.

MN 3.4.1 - Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays.

MN 3.4 - Data Analysis

Geometry and Measurement Read a thermometer in degrees Fahrenheit or Celsius [Grade 3]

MN 3.3.3.4 - Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius. Example: Read the temperature in a room with a thermometer that has both Fahrenheit and Celsius scales. Use the thermometer to compare Celsius and Fahrenheit readings.

Numbers and Operations Determine cent amounts that total a dollar [Grade 2] Core Skill

Add or subtract cent amounts to or from whole dollar amounts [Grade 3]

WP: Determine the amount of change from whole dollar amounts [Grade 3]

Core Skill

MN 3.3.3.3 - Make change up to one dollar in several different ways, including with as few coins as possible. Example: A chocolate bar costs $1.84. You pay for it with $2. Give two possible ways to make change.

Geometry and Measurement Convert hours to minutes or minutes to seconds [Grade 3]

MN 3.3.3.2 - Know relationships among units of time. Example: Know the number of minutes in an hour, days in a week and months in a year.

WP: Determine the start time given the end time on a clock and the elapsed time within an hour [Grade 3]

WP: Determine the end time given the start time and the elapsed time within an hour [Grade 3]

WP: Calculate elapsed time within an hour [Grade 3]

WP: Calculate elapsed time within an hour given two clocks [Grade 3]

WP: Determine the start time given the end time and the elapsed time within an hour [Grade 3]



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Read a line plot [Grade 3]

Use a line plot to represent data [Grade 3]

Use a bar graph with a scale interval of 5 or 10 to represent data [Grade 3]

Answer a question using information from a bar graph with a scale interval of 5 or 10 [Grade 3]


Core Skill

Answer a question using information from a line plot [Grade 3]

Answer a question using information from a frequency table [Grade 3]

Use a frequency table to represent data [Grade 3]



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WP: Estimate a product of two whole numbers using any method [Grade 4]

Core Skill

Estimate a product of whole numbers using any method [Grade 4] Core Skill

Numbers and Operations Estimate a product of whole numbers by rounding [Grade 4]

Estimate a quotient using any method [Grade 5] Core Skill

MN 4.1.1.4 - Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. Example: 53 × 38 is between 50 × 30 and 60 × 40, or between 1500 and 2400, and 411/73 is between 5 and 6.

Multiply a 2-digit whole number by a 2-digit whole number [Grade 4]

Core Skill

Multiply a 3-digit whole number by a 2-digit whole number [Grade 4]

Numbers and Operations Apply the distributive property to multiply a multi-digit number by a 1-digit number [Grade 4]

Core Skill


Core Skill

WP: Multiply a 2-digit whole number by a 2-digit whole number [Grade 4]

Core Skill


Multiply three 1- and 2-digit whole numbers [Grade 4]

WP: Multiply a multi-digit whole number by a 1-digit whole number [Grade 4]

Core Skill

MN 4.1.1.3 - Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

Numbers and Operations Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000 [Grade 4]

Core Skill

MN 4.1.1.2 - Use an understanding of place value to multiply a number by 10, 100 and 1000.

Numbers and Operations Know basic multiplication facts to 10 x 10 [Grade 3] Core Skill




MN 4.1.1.1 - Demonstrate fluency with multiplication and division facts.

MN 4.1.1 - Demonstrate mastery of multiplication and division basic facts; multiply multi-digit numbers; solve real-world and mathematical problems using arithmetic.


Grade 4



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Core Skill



Core Skill


Divide a multi-digit whole number by 10 or 100 with no remainder [Grade 4]

Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient [Grade 4]

Numbers and Operations Know basic division facts to 100 ÷ 10 [Grade 3] Core Skill


Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotient [Grade 4]

Core Skill

Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotient [Grade 4]

Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient [Grade 4]

MN 4.1.1.6 - Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Example: A group of 324 students are going to a museum in 6 buses. If each bus has the same number of students, how many students will be on each bus?

WP: Solve a 2-step problem involving whole numbers [Grade 5] Core Skill

WP: Solve a 2-step whole number problem using more than 1 operation [Grade 4]


Numbers and Operations WP: Subtract a 3-digit or greater whole number from a 5-digit or greater whole number [Grade 4]

WP: Solve a 2-step problem involving addition and/or subtraction of multi-digit whole numbers [Grade 4]

WP: Solve a multi-step problem involving whole numbers [Grade 6]

Core Skill

MN 4.1.1.5 - Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

WP: Estimate a quotient using any method [Grade 5] Core Skill



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WP: Subtract fractions with like denominators no greater than 10 and simplify the difference [Grade 4]

WP: Add fractions with like denominators no greater than 10 and simplify the sum [Grade 4]

WP: Add or subtract fractions with like denominators and simplify the sum or difference [Grade 5]

Core Skill

Subtract fractions with like denominators no greater than 10 using models [Grade 4]

Numbers and Operations Add fractions with like denominators no greater than 10 using models [Grade 4]

MN 4.1.2.3 - Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.

Order fractions on a number line [Grade 4]

Compare fractions on a number line [Grade 4]

Order fractions using models [Grade 3] Core Skill

Identify a mixed number represented by a model [Grade 4]

Identify a mixed number represented by a point on a number line [Grade 4]

Numbers and Operations Identify a fraction represented by a point on a number line [Grade 3]

Core Skill

Locate a fraction on a number line [Grade 3] Core Skill

Compare fractions using models [Grade 3] Core Skill

Identify an improper fraction represented by a point on a number line [Grade 4]

Locate an improper fraction on a number line [Grade 4]

Locate a mixed number on a number line [Grade 4]

Identify an improper fraction represented by a model of a mixed number [Grade 4]

MN 4.1.2.2 - Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Example: Locate 5/3 and 1 3/4 on a number line and give a comparison statement about these two fractions, such as "5/3 is less than 1 3/4.".

Numbers and Operations Identify equivalent fractions using models [Grade 3] Core Skill

MN 4.1.2.1 - Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions.

MN 4.1.2 - Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.



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Numbers and Operations Round a decimal number to a specified place through hundredths [Grade 4]

Core Skill

MN 4.1.2.7 - Round decimals to the nearest tenth. Example: The number 0.36 rounded to the nearest tenth is 0.4.

Determine the decimal number equivalent to a fraction model [Grade 4]

Core Skill

Determine the decimal number from a pictorial model of tenths or hundredths [Grade 4]

Core Skill

Numbers and Operations Read a decimal number through the hundredths place [Grade 4] Core Skill

Determine the fraction equivalent to a decimal number model [Grade 4]

Core Skill

Determine a fraction equivalent to a decimal, using a denominator of 10 or 100 [Grade 4]

Identify a pictorial model of tenths or hundredths of a decimal number [Grade 4]

Core Skill

Determine the decimal number equivalent to a fraction with a denominator of 10 or 100 [Grade 4]

MN 4.1.2.6 - Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Example: 1/2 = 0.5 = 0.50 and 7/4 = 1 3/4 = 1.75, which can also be written as one and three-fourths or one and seventy-five hundredths.

Compare decimal numbers of differing places to thousandths [Grade 5]

Core Skill

Order decimal numbers through the hundredths place [Grade 4] Core Skill

Numbers and Operations Compare decimal numbers through the hundredths place [Grade 4]

Core Skill

Order decimal numbers of differing places to thousandths in ascending or descending order [Grade 5]

Core Skill

MN 4.1.2.5 - Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.

Identify a pictorial model of tenths or hundredths of a decimal number [Grade 4]

Core Skill

Determine the decimal number from a pictorial model of tenths or hundredths [Grade 4]

Core Skill


Determine the word form of a decimal number through the hundredths place [Grade 4]

MN 4.1.2.4 - Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Example: Writing 362.45 is a shorter way of writing the sum: 3 hundreds + 6 tens + 2 ones + 4 tenths + 5 hundredths, which can also be written as: three hundred sixty-two and forty-five hundredths.



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MN 4.3.1 - Name, describe, classify and sketch polygons.


Solve a 1-step equation involving whole numbers [Grade 6] Core Skill

Algebra Determine the missing multiplicand in a number sentence involving basic facts [Grade 3]

WP: Determine a multiplication or division sentence for a given situation [Grade 3]

Core Skill

Determine the missing dividend or divisor in a number sentence involving basic facts [Grade 3]

MN 4.2.2.2 - Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Example 1: If $84 is to be shared equally among a group of children, the amount of money each child receives can be determined using the number sentence 84 ÷ n = d. Example 2: Find values of the unknowns that make each number sentence true: 12 × m = 36; s = 256 ÷ t.


MN 4.2.2.1 - Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. Example: The number sentence a × b = 60 can be represented by the situation in which chairs are being arranged in equal rows and the total number of chairs is 60.

MN 4.2.2 - Use number sentences involving multiplication, division and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

Determine the variable expression with one operation for a table of paired numbers [Grade 5]

Core Skill

Extend a number pattern in a table of related pairs [Grade 4]

WP: Determine the variable expression with one operation for a table of paired numbers [Grade 5]

Core Skill

Algebra Generate a table of paired numbers based on a rule [Grade 4] Core Skill

Determine a rule that relates two variables [Grade 4] Core Skill

MN 4.2.1.1 - Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Example 1: If the rule is "multiply by 3 and add 4," record the outputs for given inputs in a table. Example 2: A student is given these three arrangements of dots: Identify a pattern that is consistent with these figures, create an input-output rule that describes the pattern, and use the rule to find the number of dots in the 10th figure.

MN 4.2.1 - Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems.

MN 4.2 - Algebra



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Geometry and Measurement Determine the area of a rectangle given a picture showing the length and width [Grade 4]

WP: Determine the area of a rectangle [Grade 4] Core Skill

Determine the area of a rectangle given the length and width [Grade 4]

Core Skill

WP: Determine the area of a square or rectangle [Grade 5] Core Skill

WP: Determine the perimeter or the area of a complex shape [Grade 6]

Core Skill

MN 4.3.2.4 - Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.

Determine the area of a rectangle given the length and width [Grade 4]

Core Skill

WP: Determine the area of a rectangle [Grade 4] Core Skill

Geometry and Measurement Determine the area of a polygon on a grid [Grade 4] Core Skill


Estimate the area of an irregular polygon on a grid [Grade 4]

MN 4.3.2.3 - Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Example: How many copies of a square sheet of paper are needed to cover the classroom door? Measure the length and width of the door to the nearest inch and compute the area of the door.

Classify an angle given its measure [Grade 4] Core Skill

Geometry and Measurement Classify an angle given a picture [Grade 4] Core Skill

MN 4.3.2.2 - Compare angles according to size. Classify angles as acute, right and obtuse. Example: Compare different hockey sticks according to the angle between the blade and the shaft.

Geometry and Measurement Measure an angle to the nearest 5 degrees [Grade 5]

MN 4.3.2.1 - Measure angles in geometric figures and real-world objects with a protractor or angle ruler.

MN 4.3.2 - Understand angle and area as measurable attributes of real-world and mathematical objects. Use various tools to measure angles and areas.

Geometry and Measurement Classify a quadrilateral [Grade 4]

MN 4.3.1.2 - Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts.

Geometry and Measurement Classify a triangle by its sides [Grade 4]

MN 4.3.1.1 - Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts.



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Read a double-bar graph [Grade 4] Core Skill

Use a double-bar graph to represent data [Grade 4] Core Skill


Core Skill





Core Skill

Answer a question using information from a double-bar graph [Grade 4]

Core Skill

Answer a question using information from a table [Grade 4]

MN 4.4.1.1 - Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data.

MN 4.4.1 - Collect, organize, display and interpret data, including data collected over a period of time and data represented by fractions and decimals.


Identify mirror images [Grade 3]

Geometry and Measurement Identify congruent shapes [Grade 3]

Determine the result of a flip, a turn, or a slide [Grade 4] Core Skill

MN 4.3.3.4 - Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent.

Determine the result of a quarter or a half turn [Grade 4]

Geometry and Measurement Determine the result of a flip, a turn, or a slide [Grade 4] Core Skill

MN 4.3.3.3 - Apply rotations (turns) of 90° clockwise or counterclockwise.

Determine the result of a flip, a turn, or a slide [Grade 4] Core Skill

Geometry and Measurement Determine lines of symmetry [Grade 4] Core Skill

MN 4.3.3.2 - Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry.

Geometry and Measurement Determine the result of a flip, a turn, or a slide [Grade 4] Core Skill

MN 4.3.3.1 - Apply translations (slides) to figures.

MN 4.3.3 - Use translations, reflections and rotations to establish congruency and understand symmetries.



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WP: Divide a whole number and interpret the remainder [Grade 5]

Core Skill

Numbers and Operations Divide a multi-digit whole number by a 1-digit number and express the quotient as a mixed number [Grade 5]

MN 5.1.1.2 - Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Example: For example: If 77 amusement ride tickets are to be distributed equally among 4 children, each child will receive 19 tickets, and there will be one left over. If $77 is to be distributed equally among 4 children, each will receive $19.25, with nothing left over.

Numbers and Operations Divide a multi-digit whole number by multiples of 100 or 1,000 [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with no remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with a remainder and no zeros in the quotient [Grade 5]

Divide a multi-digit whole number by a 1-digit number, with a remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by a 1-digit number and express the quotient as a decimal [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with no remainder and no zeros in the quotient [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotient [Grade 5]

Core Skill

Divide a whole number by a 2-digit whole number resulting in a decimal quotient through thousandths [Grade 6]

Core Skill

Divide a multi-digit whole number by a 1-digit number, with no remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed number [Grade 5]

Core Skill

Divide a whole number by a 1-digit whole number resulting in a decimal quotient through thousandths [Grade 6]

Core Skill

MN 5.1.1.1 - Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Example: Dividing 153 by 7 can be used to convert the improper fraction 153/7 to the mixed number 21 6/7.

MN 5.1.1 - Divide multi-digit numbers; solve real-world and mathematical problems using arithmetic.


Grade 5



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Divide a multi-digit whole number by a 1-digit number, with no remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by multiples of 100 or 1,000 [Grade 5]

Divide a multi-digit whole number by a 1-digit number, with a remainder and at least one zero in the quotient [Grade 5]


Core Skill

WP: Multiply a 3- or 4-digit whole number by a 3-digit whole number [Grade 5]



Core Skill

Numbers and Operations WP: Multiply a multi-digit whole number by a 1-digit whole number [Grade 4]

Core Skill


MN 5.1.1.4 - Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Example: The calculation 117 ÷ 9 = 13 can be checked by multiplying 9 and 13.


Estimate a fraction sum using benchmark numbers 0, 1/2, and 1 [Grade 5]

Estimate a quotient using any method [Grade 5] Core Skill

Numbers and Operations WP: Estimate a product of two whole numbers using any method [Grade 4]

Core Skill

Estimate a quotient using compatible numbers [Grade 5]

Estimate a fraction difference using benchmark numbers 0, 1/2, and 1 [Grade 5]

Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified place [Grade 5]

Core Skill

WP: Estimate the sum or difference of two decimal numbers through thousandths using any method [Grade 5]

Core Skill

WP: Estimate a fraction sum or difference using benchmark numbers 0, 1/2, and 1 [Grade 5]

Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified place [Grade 5]

Core Skill

MN 5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.



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Order decimal numbers of differing places to thousandths in ascending or descending order [Grade 5]

Core Skill

Numbers and Operations Compare decimal numbers of differing places to thousandths [Grade 5]

Core Skill

MN 5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.

Determine the value of a digit in a decimal number to thousandths [Grade 5]

Determine a decimal number represented in expanded form [Grade 5]

Represent a decimal number in expanded form [Grade 5]


MN 5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Example: Possible names for the number 0.0037 are: 37 ten thousandths; 3 thousandths + 7 ten thousandths; a possible name for the number 1.5 is 15 tenths.

MN 5.1.2 - Read, write, represent and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.

Divide a multi-digit whole number by a 2-digit whole number, with no remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotient [Grade 5]

Core Skill

Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed number [Grade 5]

Core Skill

Divide a multi-digit whole number by a 2-digit whole number, with a remainder and no zeros in the quotient [Grade 5]

Divide a multi-digit whole number by a 1-digit number and express the quotient as a mixed number [Grade 5]

Divide a multi-digit whole number by a 1-digit number and express the quotient as a decimal [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with no remainder and no zeros in the quotient [Grade 5]

WP: Divide a whole number by a 1- or 2-digit whole number resulting in a decimal quotient [Grade 6]

Core Skill

WP: Solve a multi-step problem involving whole numbers [Grade 6]

Core Skill

WP: Solve a 2-step problem involving whole numbers [Grade 5] Core Skill

WP: Divide a whole number, with no remainder [Grade 5] Core Skill

WP: Divide a whole number and interpret the remainder [Grade 5]

Core Skill



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MN 5.1.3 - Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.

Numbers and Operations Round a decimal number to a specified place through hundredths [Grade 4]

Core Skill

Round a decimal number to a specified decimal place to thousandths [Grade 5]

MN 5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001. Example: Fifth grade students used a calculator to find the mean of the monthly allowance in their class. The calculator display shows 25.80645161. Round this number to the nearest cent.

Determine equivalent fractions not in simplest form [Grade 5] Core Skill

Numbers and Operations Determine the decimal number equivalent to a fraction model [Grade 4]

Core Skill

Convert an improper fraction to a mixed number [Grade 5] Core Skill

Convert a mixed number to an improper fraction [Grade 5] Core Skill

Determine the simplest form of a fraction [Grade 5]

Determine the fraction equivalent to a decimal number model [Grade 4]

Core Skill

Convert a fraction with a denominator that is a factor of 10, 100, or 1,000 to decimal notation [Grade 5]

Convert a decimal number through thousandths to a simplified fraction [Grade 5]

MN 5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. Example: When comparing 1.5 and 19/12 , note that 1.5 = 1 1/2 = 1 6/12 = 18/12, so 1.5 < 19/12.

Locate a decimal number to tenths on a number line [Grade 4] Core Skill

Compare decimal numbers through the hundredths place [Grade 4]

Core Skill

Numbers and Operations Locate a mixed number on a number line [Grade 4]

Identify a decimal number to tenths represented by a point on a number line [Grade 4]

Core Skill

Order decimal numbers through the hundredths place [Grade 4] Core Skill

Order fractions with unlike denominators in ascending or descending order [Grade 5]

Core Skill

Compare fractions with unlike denominators [Grade 5] Core Skill

MN 5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Example 1: Which is larger 1.25 or 6/5 ? Example 2: In order to work properly, a part must fit through a 0.24 inch wide space. If a part is 1/4 inch wide, will it fit?



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Numbers and Operations Add fractions with unlike denominators using a model and do not simplify the sum [Grade 5]

MN 5.1.3.2 - Model addition and subtraction of fractions and decimals using a variety of representations. Example: Represent 2/3 + 1/4 and 2/3 - 1/4 by drawing a rectangle divided into 4 columns and 3 rows and shading the appropriate parts or by using fraction circles or bars.

Subtract two decimal numbers of differing places to thousandths [Grade 5]

Core Skill

Subtract a decimal number from a whole number or a whole number from a decimal number [Grade 5]

Add decimal numbers and whole numbers [Grade 5] Core Skill

Subtract fractions with unlike denominators and do not simplify the difference [Grade 5]

Subtract fractions with like denominators greater than 10 and simplify the difference [Grade 5]

Subtract fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

Subtract fractions with unlike denominators that have factors in common and simplify the difference [Grade 5]

Core Skill

Add fractions with unlike denominators and do not simplify the sum [Grade 5]

Numbers and Operations Add fractions with like denominators greater than 10 and simplify the sum [Grade 5]

Add fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

Add fractions with unlike denominators that have factors in common and simplify the sum [Grade 5]

Core Skill

Add mixed numbers with like denominators and simplify the sum [Grade 5]

WP: Add or subtract mixed numbers with unlike denominators that have no factors in common [Grade 5]

Add three or more decimal numbers [Grade 5]

Add two decimal numbers of differing places to thousandths [Grade 5]

Core Skill

Add mixed numbers with unlike denominators and simplify the sum [Grade 5]

Subtract mixed numbers with like denominators and simplify the difference [Grade 5]

Subtract mixed numbers with unlike denominators and simplify the difference [Grade 5]

MN 5.1.3.1 - Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.



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WP: Add or subtract fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

WP: Add or subtract fractions with like denominators and simplify the sum or difference [Grade 5]

Core Skill

Subtract fractions with unlike denominators and do not simplify the difference [Grade 5]

Subtract fractions with like denominators greater than 10 and simplify the difference [Grade 5]

Subtract fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

Subtract fractions with unlike denominators that have factors in common and simplify the difference [Grade 5]

Core Skill

Numbers and Operations Add fractions with like denominators greater than 10 and simplify the sum [Grade 5]

Add fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

Add fractions with unlike denominators that have factors in common and simplify the sum [Grade 5]

Core Skill

Add fractions with unlike denominators and do not simplify the sum [Grade 5]

MN 5.1.3.4 - Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Example: Calculate the perimeter of the soccer field when the length is 109.7 meters and the width is 73.1 meters.

WP: Estimate a fraction sum or difference using benchmark numbers 0, 1/2, and 1 [Grade 5]

Estimate a fraction difference using benchmark numbers 0, 1/2, and 1 [Grade 5]

Numbers and Operations Estimate a fraction sum using benchmark numbers 0, 1/2, and 1 [Grade 5]


Core Skill


Core Skill


Core Skill

MN 5.1.3.3 - Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Example: Recognize that 12 2/3 - 3 3/4 is between 8 and 9 (since 2/5 < 3/4).

Subtract fractions with unlike denominators using a model and do not simplify the difference [Grade 5]



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Generate a table of paired numbers based on a variable expression with one operation [Grade 5]

Generate a table of paired numbers based on a variable expression with two operations [Grade 5]

WP: Extend a pattern to solve a problem [Grade 5]

Algebra Generate a table of paired numbers based on a rule [Grade 4] Core Skill

Determine a rule that relates two variables [Grade 4] Core Skill

Determine the variable expression with one operation for a table of paired numbers [Grade 5]

Core Skill

MN 5.2.1.1 - Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Example: An end-of-the-year party for 5th grade costs $100 to rent the room and $4.50 for each student. Know how to use a spreadsheet to create an input-output table that records the total cost of the party for any number of students between 90 and 150.

MN 5.2.1 - Recognize and represent patterns of change; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

MN 5.2 - Algebra

WP: Add or subtract mixed numbers with like denominators and simplify the sum or difference [Grade 5]

Core Skill

WP: Add or subtract mixed numbers with unlike denominators that have no factors in common [Grade 5]

Add two decimal numbers of differing places to thousandths [Grade 5]

Core Skill

Subtract mixed numbers with unlike denominators and simplify the difference [Grade 5]

Add mixed numbers with like denominators and simplify the sum [Grade 5]

Add mixed numbers with unlike denominators and simplify the sum [Grade 5]

Subtract mixed numbers with like denominators and simplify the difference [Grade 5]

Add three or more decimal numbers [Grade 5]

WP: Add or subtract decimal numbers through thousandths [Grade 5]

Core Skill

WP: Add or subtract a decimal number through thousandths and a whole number [Grade 5]

Core Skill

Subtract a decimal number from a whole number or a whole number from a decimal number [Grade 5]

Add decimal numbers and whole numbers [Grade 5] Core Skill

Subtract two decimal numbers of differing places to thousandths [Grade 5]

Core Skill



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WP: Use a 2-variable equation to represent a situation involving a direct proportion [Grade 6]

Core Skill

WP: Use a variable expression with one operation to represent a situation [Grade 5]

Use a verbal expression to represent a variable expression with one operation [Grade 5]

Algebra Use a variable expression with one operation to represent a verbal expression [Grade 5]

MN 5.2.3.2 - Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities. Example: 250 - 27 × a = b can be used to represent the number of sheets of paper remaining from a packet of 250 sheets when each student in a class of 27 is given a certain number of sheets.

Algebra Solve a 1-step equation involving whole numbers [Grade 6] Core Skill

MN 5.2.3.1 - Determine whether an equation or inequality involving a variable is true or false for a given value of the variable. Example: Determine whether the inequality 1.5 + x < 10 is true for x = 2.8, x = 8.1, or x = 9.2.

MN 5.2.3 - Understand and interpret equations and inequalities involving variables and whole numbers, and use them to represent and solve real-world and mathematical problems.

Numbers and Operations Apply the distributive property to multiply a multi-digit number by a 1-digit number [Grade 4]

Core Skill

MN 5.2.2.1 - Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Example: Purchase 5 pencils at 19 cents and 7 erasers at 19 cents. The numerical expression is 5 × 19 + 7 × 19 which is the same as (5 + 7) × 19.

MN 5.2.2 - Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving whole numbers.

Use a first quadrant graph to represent the values from a table generated in context [Grade 5]

Core Skill

Generate a table of paired numbers based on a variable expression with two operations [Grade 5]

Algebra Generate a table of paired numbers based on a variable expression with one operation [Grade 5]

Geometry and Measurement Determine the ordered pair of a point in the first quadrant [Grade 5]

MN 5.2.1.2 - Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.


Core Skill

WP: Generate a table of paired numbers based on a variable expression with one operation [Grade 5]

Core Skill



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Determine the area of a complex figure divided into basic shapes [Grade 5]

Use a formula to determine the area of a parallelogram [Grade 5]

Geometry and Measurement Determine the area of a rectangle given the length and width [Grade 4]

Core Skill

Use a formula to determine the area of a triangle [Grade 5] Core Skill

WP: Determine the area of a triangle [Grade 5] Core Skill

MN 5.3.2.1 - Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.

MN 5.3.2 - Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts.

Determine a net of a 3-dimensional shape [Grade 5]

Geometry and Measurement Determine the 3-dimensional shape that can be formed from a net [Grade 5]

MN 5.3.1.2 - Recognize and draw a net for a three-dimensional figure.

Geometry and Measurement Determine the number of faces, edges, and vertices in a 3-dimensional shape [Grade 5]

MN 5.3.1.1 - Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.

MN 5.3.1 - Describe, classify, and draw representations of three-dimensional figures.


WP: Evaluate a 2-variable expression with one operation using whole number values [Grade 5]

WP: Evaluate a 1-variable expression with one operation using a whole number value [Grade 5]

Evaluate a 2-variable expression, with two or three operations, using whole number substitution [Grade 6]

Core Skill

Algebra Evaluate a 1-variable expression, involving one operation, using whole number substitution [Grade 5]

Evaluate a 2-variable expression, involving one operation, using whole number substitution [Grade 5]

MN 5.2.3.3 - Evaluate expressions and solve equations involving variables when values for the variables are given. Example: Using the formula, A= lw, determine the area when the length is 5, and the width 6, and find the length when the area is 24 and the width is 4.

WP: Use a 1-variable 1-step equation to represent a situation [Grade 7]

Core Skill

WP: Use a 2-variable linear equation to represent a situation [Grade 6]

Core Skill



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Determine the mean of a set of whole number data [Grade 6]

Determine the range of a set of whole number data [Grade 5]

Determine the mean of a set of whole number data, whole number results [Grade 5]

Determine the median of an odd number of data values [Grade 5] Core Skill


Determine the range from a graph [Grade 5]

Determine the median of a set of whole number data [Grade 6]

MN 5.4.1.1 - Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data. Example: The set of numbers 1, 1, 4, 6 has mean 3. It can be leveled by taking one unit from the 4 and three units from the 6 and adding them to the 1s, making four 3s.

MN 5.4.1 - Display and interpret data; determine mean, median and range.


Determine the volume of a rectangular prism [Grade 5]

WP: Determine the volume of a rectangular prism given a diagram [Grade 5]

Geometry and Measurement Determine the volume of a rectangular prism given a diagram [Grade 5]

Core Skill

WP: Determine the volume of a rectangular prism [Grade 5] Core Skill

MN 5.3.2.4 - Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.

Geometry and Measurement Determine the volume of an object composed of rectangular prisms by counting units [Grade 5]

MN 5.3.2.3 - Understand that the volume of a three-dimensional figure can be found by counting the total number of same-size cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Example: Use cubes to find the volume of a small box.

Determine the surface area of a rectangular prism [Grade 5] Core Skill

Geometry and Measurement Determine the surface area of a cube or a rectangular prism given a net [Grade 5]

WP: Find the surface area of a rectangular prism [Grade 5] Core Skill

MN 5.3.2.2 - Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Example 1: Use a net or decompose the surface into rectangles. Example 2: Measure the volume of a cereal box by using a ruler to measure its height, width and length, or by filling it with cereal and then emptying the cereal into containers of known volume.

Determine the area of a complex shape [Grade 6] Core Skill




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Answer a question using information from a double-bar graph [Grade 4]

Core Skill

Answer a question using information from a line graph that does not start at zero or has a broken vertical scale [Grade 5]

Answer a question using information from a line graph [Grade 4] Core Skill

Use a double-bar graph to represent data [Grade 4] Core Skill

Read a double- or stacked-bar graph [Grade 5]

Use a line graph to represent data [Grade 4] Core Skill


Read a line graph [Grade 4] Core Skill

Use a double- or stacked-bar graph to represent data [Grade 5]

Answer a question using information from a double- or stacked-bar graph [Grade 5]

MN 5.4.1.2 - Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.



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Convert a decimal number to a percentage [Grade 6]

Convert a percentage to a decimal number [Grade 6]

Convert a fraction to a percentage [Grade 6]

Numbers and Operations Convert a mixed number to a decimal number [Grade 6]

Convert a decimal number to a mixed number [Grade 6]

Convert a fraction to a repeating decimal number [Grade 6]

WP: Calculate the percent of a whole number where the answer is a whole number [Grade 6]

Convert a decimal number in thousandths to a percentage [Grade 7]

Convert a percentage to a fraction [Grade 6]

Calculate a percent of a whole number where the answer is a whole number [Grade 6]

MN 6.1.1.4 - Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Example: If a woman making $25 an hour gets a 10% raise, she will make an additional $2.50 an hour, because $2.50 is 1/10 or 10% of $25.

Determine a percent where a ratio, not in 100ths, is given in words [Grade 6]

Core Skill

Numbers and Operations Relate an equivalent fraction and percent given a grid [Grade 5]

MN 6.1.1.3 - Understand that percent represents parts out of 100 and ratios to 100. Example: 75% corresponds to the ratio 75 to 100, which is equivalent to the ratio 3 to 4.

Compare numbers in decimal and fractional forms [Grade 6] Core Skill

Compare decimal numbers of differing places to thousandths [Grade 5]

Core Skill

Numbers and Operations Compare fractions with unlike denominators [Grade 5] Core Skill

Order numbers in decimal and fractional forms [Grade 6] Core Skill

MN 6.1.1.2 - Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Example: 1/2 > 0.36.

Geometry and Measurement Determine the ordered pair of a point in the first quadrant [Grade 5]

MN 6.1.1.1 - Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid.

MN 6.1.1 - Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.


Grade 6



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Numbers and Operations Convert a mixed number to an improper fraction [Grade 5] Core Skill

Convert a decimal number to a mixed number [Grade 6]

Convert an improper fraction to a mixed number [Grade 5] Core Skill

Convert a mixed number to a decimal number [Grade 6]

MN 6.1.1.7 - Convert between equivalent representations of positive rational numbers. Example: Express 10/7 as (7+3)/7 = 7/7 + 3/7 = 1 3/7.

Add fractions with unlike denominators and simplify the sum [Grade 6]

Subtract fractions with unlike denominators and simplify the difference [Grade 6]

Subtract a fraction from a whole number [Grade 6]

WP: Determine the least common multiple of two or more numbers [Grade 6]

Numbers and Operations Determine the least common multiple of two whole numbers [Grade 5]

Determine the greatest common factor of three numbers to 100 [Grade 6]

Determine the least common multiple of three numbers [Grade 6]

WP: Add or subtract fractions with unlike denominators and simplify the sum or difference [Grade 6]

Add and subtract three unlike-denominator fractions, mixed numbers, or fractions and mixed numbers, and simplify the answer [Grade 6]

WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference [Grade 6]

Subtract mixed numbers with unlike denominators or a mixed number and a fraction and simplify the difference [Grade 6]

Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum [Grade 6]

Subtract a mixed number from a whole number [Grade 6]

MN 6.1.1.6 - Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Example: Factor the numerator and denominator of a fraction to determine an equivalent fraction.

Apply divisibility rules for 3, 4, 6, and 9 [Grade 6]

Numbers and Operations Determine the prime factorization of a number between 50 and 200 [Grade 6]

MN 6.1.1.5 - Factor whole numbers; express a whole number as a product of prime factors with exponents. Example: 24= 2³ x 3.



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Numbers and Operations WP: Determine a ratio using whole numbers less than 50 [Grade 6]

WP: Determine a part given a ratio and the whole where the whole is less than 50 [Grade 6]

Core Skill

MN 6.1.2.4 - Use reasoning about multiplication and division to solve ratio and rate problems. Example: If 5 items cost $3.75, and all items are the same price, then 1 item costs 75 cents, so 12 items cost $9.00.

WP: Determine a unit rate [Grade 7] Core Skill

Numbers and Operations WP: Determine a unit rate with a whole number value [Grade 6] Core Skill

MN 6.1.2.3 - Determine the rate for ratios of quantities with different units. Example: 60 miles in 3 hours is equivalent to 20 miles in one hour (20 mph).

Numbers and Operations WP: Determine a part given a ratio and the whole where the whole is less than 50 [Grade 6]

Core Skill

WP: Determine a part given a ratio and another part where the whole is less than 50 [Grade 6]

WP: Determine the whole given a ratio and a part where the whole is less than 50 [Grade 6]

Core Skill

MN 6.1.2.2 - Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Example: If 5 cups of trail mix contains 2 cups of raisins, the ratio of raisins to trail mix is 2 to 5. This ratio corresponds to the fact that the raisins are 2/5 of the total, or 40% of the total. And if one trail mix consists of 2 parts peanuts to 3 parts raisins, and another consists of 4 parts peanuts to 8 parts raisins, then the first mixture has a higher concentration of peanuts.

WP: Determine a ratio using whole numbers less than 50 [Grade 6]

Numbers and Operations Determine equivalent fractions not in simplest form [Grade 5] Core Skill

Compare fractions with unlike denominators [Grade 5] Core Skill

MN 6.1.2.1 - Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Example: In a classroom with 15 boys and 10 girls, compare the numbers by subtracting (there are 5 more boys than girls) or by dividing (there are 1.5 times as many boys as girls). The comparison using division may be expressed as a ratio of boys to girls (3 to 2 or 3:2 or 1.5 to 1).

MN 6.1.2 - Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.


Convert a decimal number to a percentage [Grade 6]

Convert a fraction to a repeating decimal number [Grade 6]





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WP: Multiply or divide a fraction by a fraction [Grade 6] Core Skill

Divide a whole number by a fraction resulting in a fractional quotient [Grade 6]

Core Skill

WP: Multiply a decimal number through thousandths by a whole number [Grade 6]

Core Skill

Multiply a decimal number through thousandths by a whole number [Grade 6]

Core Skill

Divide a fraction by a fraction [Grade 6] Core Skill

Multiply a mixed number by a whole number [Grade 6] Core Skill

Divide a fraction by a whole number resulting in a fractional quotient [Grade 6]

Core Skill

Multiply a mixed number by a fraction [Grade 6] Core Skill

WP: Multiply a money expression by a decimal number [Grade 6]

Multiply a fraction by a fraction [Grade 6] Core Skill

Numbers and Operations Multiply a decimal number through thousandths by 10, 100, or 1,000 [Grade 5]

Core Skill

MN 6.1.3.1 - Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.

MN 6.1.3 - Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers.

WP: Use a unit rate, with a whole number or whole cent value, to solve a problem [Grade 6]

Core Skill

WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part given a ratio and another part where the whole is less than 50 [Grade 6]


Core Skill

WP: Determine a unit rate with a whole number value [Grade 6] Core Skill

WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Use a unit rate to solve a problem [Grade 7] Core Skill

WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill



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Relate division by a whole number power of ten to multiplication by the related decimal fraction power of ten [Grade 6]


Core Skill

Numbers and Operations Divide a fraction by a fraction [Grade 6] Core Skill

MN 6.1.3.2 - Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Example: Just as 12/4 = 3 means 12 = 3x4, 2/3 ÷ 4/5 = 5/6 means 5/6 x 4/5 = 2/3.

Divide a decimal number by 10, 100, or 1,000 [Grade 6] Core Skill

WP: Multiply two decimal numbers to thousandths [Grade 6] Core Skill

WP: Divide a decimal number through thousandths by a 1- or 2-digit whole number [Grade 6]

Core Skill

Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal places [Grade 6]

Core Skill

Multiply decimal numbers less than one in hundredths or thousandths [Grade 6]

Core Skill

Multiply decimal numbers to thousandths using basic facts [Grade 6]

Multiply decimal numbers greater than one where the product has 2 or 3 decimal places [Grade 6]

Core Skill

Multiply a decimal number greater than one by a decimal number to thousandths that has only 1 nonzero digit [Grade 6]

Multiply a decimal number greater than one, in tenths, by a decimal number in tenths [Grade 6]

WP: Divide a whole number by a decimal number through thousandths, rounded quotient if needed [Grade 6]

Core Skill

WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if needed [Grade 6]

Core Skill

Divide a whole number or a decimal number by 0.1, 0.01, or 0.001 [Grade 6]

Divide a decimal number by a decimal number through thousandths, rounded quotient if needed [Grade 6]

Core Skill

Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole number [Grade 6]

Core Skill

Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths [Grade 6]

Core Skill

Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed [Grade 6]

Core Skill



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WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference [Grade 6]



Subtract a mixed number from a whole number [Grade 6]

Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum [Grade 6]

Add and subtract three unlike-denominator fractions, mixed numbers, or fractions and mixed numbers, and simplify the answer [Grade 6]

Subtract mixed numbers with unlike denominators or a mixed number and a fraction and simplify the difference [Grade 6]

Multiply a mixed number by a mixed number [Grade 6] Core Skill

Numbers and Operations Add fractions with unlike denominators and simplify the sum [Grade 6]

WP: Add or subtract fractions with unlike denominators and simplify the sum or difference [Grade 6]

Subtract a fraction from a whole number [Grade 6]

Subtract fractions with unlike denominators and simplify the difference [Grade 6]

MN 6.1.3.4 - Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers.


Convert a percentage to a decimal number [Grade 6]

Numbers and Operations Convert a decimal number to a percentage [Grade 6]


WP: Calculate the percent of a whole number where the answer is a whole number [Grade 6]

Calculate a percent of a whole number where the answer is a whole number [Grade 6]

MN 6.1.3.3 - Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Example: If John has $45 and spends $15, what percent of his money did he keep?

Relate division by a decimal fraction power of ten to multiplication by the related whole number power of ten [Grade 6]


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Core Skill


Core Skill

Divide a whole number or a decimal number by 0.1, 0.01, or 0.001 [Grade 6]


Core Skill

WP: Multiply two decimal numbers to thousandths [Grade 6] Core Skill



Core Skill


Core Skill

Multiply a decimal number greater than one by a decimal number to thousandths that has only 1 nonzero digit [Grade 6]

WP: Multiply or divide two mixed numbers or a mixed number and a fraction [Grade 6]

Core Skill

WP: Multiply or divide a fraction by a fraction [Grade 6] Core Skill

Add three decimal numbers [Grade 6]

WP: Solve a 2-step problem involving fractions [Grade 6] Core Skill


Core Skill

Divide a fraction by a fraction [Grade 6] Core Skill

Divide a mixed number by a mixed number [Grade 6]

Divide a mixed number by a fraction [Grade 6]

WP: Multiply a money expression by a decimal number [Grade 6]


Core Skill

Multiply decimal numbers to thousandths using basic facts [Grade 6]

Multiply a decimal number greater than one, in tenths, by a decimal number in tenths [Grade 6]

WP: Add and subtract three decimal numbers [Grade 6]

Add and subtract three decimal numbers [Grade 6]


Core Skill

WP: Multiply a decimal number through thousandths by a whole number [Grade 6]

Core Skill



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Use a 2-variable equation to represent a relationship expressed in a table [Grade 6]

Core Skill

Use a 2-variable equation to construct an input-output table [Grade 6]

Core Skill

Algebra WP: Use a 2-variable equation to represent a situation involving a direct proportion [Grade 6]

Core Skill


Core Skill

MN 6.2.1.1 - Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Example: If a student earns $7 an hour in a job, the amount of money earned can be represented by a variable and is related to the number of hours worked, which also can be represented by a variable.

MN 6.2.1 - Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

MN 6.2 - Algebra


Core Skill


Core Skill

Numbers and Operations Estimate a quotient using any method [Grade 5] Core Skill



Core Skill

WP: Estimate the quotient of two decimals [Grade 6] Core Skill

WP: Estimate the product of two decimals [Grade 6] Core Skill

MN 6.1.3.5 - Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Example: The sum 1/3 + 0.25 can be estimated to be between 1/2 and 1, and this estimate can be used as a check on the result of a more detailed calculation.


Core Skill


Core Skill


Core Skill


Core Skill

WP: Solve a 2-step problem involving decimals [Grade 6] Core Skill



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Core Skill

MN 6.2.3.1 - Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Example: The number of miles m in a k kilometer race is represented by the equation m = 0.62 k.

MN 6.2.3 - Understand and interpret equations and inequalities involving variables and positive rational numbers. Use equations and inequalities to represent real-world and mathematical problems; use the idea of maintaining equality to solve equations. Interpret solutions in the original context.

Algebra Determine which property of addition or multiplication justifies a step in the simplification of an expression [Grade 6]

Numbers and Operations Evaluate a numerical expression of four or more operations, with parentheses, using order of operations [Grade 6]

Core Skill

MN 6.2.2.1 - Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Example 1: 32/15 x 5/6 = (32x5)/(15x6) = (2x16x5)/(3x5x3x2) = 16/9 x 2/2 x 5/5 = 16/9. Example 2: Use the distributive law to write: 1/2 + 1/3 (9/2 - 15/8) = 1/2 + 1/3 x 9/2 - 1/3 x 15/8 = 1/2 + 3/2 - 5/8 = 2 - 5/8 = 1 3/8.

MN 6.2.2 - Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers.

WP: Generate a table of paired numbers based on a variable expression with two operations [Grade 6]

Use a 2-variable equation to construct an input-output table [Grade 6]

Core Skill


Core Skill

Algebra Determine the variable expression with one operation for a table of paired numbers [Grade 5]

Core Skill

WP: Generate a table of paired numbers based on a variable expression with one operation [Grade 5]

Core Skill

Use a graph to determine the entries in an input-output table [Grade 6]

Use a first quadrant graph to represent the values in an input-output table [Grade 6]


Core Skill

MN 6.2.1.2 - Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Example: Describe the terms in the sequence of perfect squares t = 1, 4, 9, 16,... by using the rule t = n² for n = 1, 2, 3, 4,....


Core Skill



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MN 6.3.2 - Understand and use relationships between angles in geometric figures.

Geometry and Measurement Estimate the area of an irregular shape or a circle on a grid [Grade 7]

MN 6.3.1.3 - Estimate the perimeter and area of irregular figures on a grid when they cannot be decomposed into common figures and use correct units, such as cm and cm².

Geometry and Measurement WP: Determine the area of a square or rectangle [Grade 5] Core Skill

Determine the area of a trapezoid [Grade 7]

MN 6.3.1.2 - Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Example: The area of a kite is one-half the product of the lengths of the diagonals, and this can be justified by decomposing the kite into two triangles.

Determine the surface area of a rectangular prism [Grade 5] Core Skill

WP: Find the surface area of a rectangular prism [Grade 5] Core Skill

WP: Determine the volume of a rectangular prism [Grade 5] Core Skill

Geometry and Measurement Determine the volume of a rectangular prism [Grade 5]

Determine the volume of a prism with a right triangle base [Grade 6]

Determine the volume of a rectangular or a triangular prism [Grade 7]

Core Skill

Determine the surface area of a 3-dimensional shape made from cubes [Grade 6]

MN 6.3.1.1 - Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Example: The surface area of a triangular prism can be found by decomposing the surface into two triangles and three rectangles.

MN 6.3.1 - Calculate perimeter, area, surface area and volume of two- and three-dimensional figures to solve real-world and mathematical problems.


Algebra Solve a 1-step equation involving whole numbers [Grade 6] Core Skill

MN 6.2.3.2 - Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Example: A cellular phone company charges $0.12 per minute. If the bill was $11.40 in April, how many minutes were used?


Core Skill


Core Skill



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MN 6.4.1 - Use probabilities to solve real-world and mathematical problems; represent probabilities using fractions, decimals and percents.

MN 6.4 - Data Analysis & Probability

MN 6.3.3.2 - Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Example: Estimate the height of a house by comparing to a 6-foot man standing nearby.

WP: Multiply or divide metric measures of mass requiring unit conversion [Grade 6]

Geometry and Measurement WP: Add or subtract customary measures of capacity requiring unit conversion [Grade 6]

WP: Multiply or divide metric measures of capacity requiring unit conversion [Grade 6]

WP: Add or subtract metric measures of mass requiring unit conversion [Grade 6]

WP: Multiply or divide customary measures of weight requiring unit conversion [Grade 6]

WP: Add or subtract metric measures of capacity requiring unit conversion [Grade 6]

WP: Add or subtract customary measures of weight requiring unit conversion [Grade 6]

MN 6.3.3.1 - Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.

MN 6.3.3 - Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.

Geometry and Measurement Determine the missing angle measure in a quadrilateral given three other angle measures [Grade 7]

MN 6.3.2.3 - Develop and use formulas for the sums of the interior angles of polygons by decomposing them into triangles.

Geometry and Measurement Determine the missing angle measure in a triangle given two other angle measures [Grade 7]

MN 6.3.2.2 - Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180°. Use models of triangles to illustrate this fact. Example 1: Cut a triangle out of paper, tear off the corners and rearrange these corners to form a straight line. Example 2: Recognize that the measures of the two acute angles in a right triangle sum to 90°.

Geometry and Measurement Determine the measure of a missing angle using straight and right angle relationships [Grade 6]

MN 6.3.2.1 - Solve problems using the relationships between the angles formed by intersecting lines. Example 1: If two streets cross, forming four corners such that one of the corners forms an angle of 120°, determine the measures of the remaining three angles. Example 2: Recognize that pairs of interior and exterior angles in polygons have measures that sum to 180°.



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Make a prediction based on an experimental probability [Grade 6]


Determine an experimental probability given a list of results [Grade 6]

Make a prediction based on a theoretical probability [Grade 6]

MN 6.4.1.4 - Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown. Example: Repeatedly draw colored chips with replacement from a bag with an unknown mixture of chips, record relative frequencies, and use the results to make predictions about the contents of the bag.


Compare predictions from experimental and theoretical probability [Grade 6]

MN 6.4.1.3 - Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences. Example: Heads and tails are equally likely when flipping a fair coin, but if several different students flipped fair coins 10 times, it is likely that they will find a variety of relative frequencies of heads and tails.


Determine the probability of a single event [Grade 6]

MN 6.4.1.2 - Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood. Example: Each outcome for a balanced number cube has probability 1/6 , and the probability of rolling an even number is 1/2.


Determine the number of possible combinations of a set of objects [Grade 6]

MN 6.4.1.1 - Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations. Example: A 6 x 6 table with entries such as (1,1), (1,2), (1,3), ..., (6,6) can be used to represent the sample space for the experiment of simultaneously rolling two number cubes.



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Convert a decimal number to a percentage greater than 100% [Grade 7]

Convert a whole number greater than 10 to scientific notation [Grade 7]

Convert a whole number greater than 10 from scientific notation to standard form [Grade 7]

Numbers and Operations Represent a decimal number in expanded form using powers of ten [Grade 6]

Core Skill

Compare numbers in decimal and fractional forms [Grade 6] Core Skill

MN 7.1.1.5 - Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions. Example: -40/12 = -120/36 = -10/3 = -3.3 repeating.

Numbers and Operations Compare numbers in decimal and fractional forms [Grade 6] Core Skill

Order rational numbers (positive and negative) [Grade 7]

Compare rational numbers (positive and negative) [Grade 7]

MN 7.1.1.4 - Compare positive and negative rational numbers expressed in various forms using the symbols <, >, =, "less than or equal to", "greater than or equal to". Example: -1/2 < -0.36.

Determine the opposite of an integer [Grade 7]

Identify a positive or negative rational number represented by a point on a number line [Grade 7]

Locate a positive or negative rational number on a number line [Grade 7]

Numbers and Operations Identify or locate an integer on a number line [Grade 6]

MN 7.1.1.3 - Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.

Overall Product Skills Use technology to respond to questions

MN 7.1.1.2 - Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. Example: 125/30 gives 4.16666667 on a calculator. This answer is not exact. The exact answer can be expressed as 4 1/6, which is the same as 4.16 repeating. The calculator expression does not guarantee that the 6 is repeated, but that possibility should be anticipated.

Overall Product Skills Build comprehension of math vocabulary

MN 7.1.1.1 - Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.

MN 7.1.1 - Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.


Grade 7



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Core Skill


Core Skill




Core Skill


Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed [Grade 6]

Core Skill


Core Skill


Core Skill


Core Skill



Core Skill

Numbers and Operations Divide a whole number by a 2-digit whole number resulting in a decimal quotient through thousandths [Grade 6]

Core Skill

MN 7.1.2.1 - Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. Example: 3 to the 4th power x (1/2)² = 81/4.

MN 7.1.2 - Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.

Convert a mixed number to a percentage [Grade 7]

Convert a percentage to a decimal number in thousandths [Grade 7]


Convert a percentage to a mixed number [Grade 7]

Convert a percentage to a decimal number greater than 1 [Grade 7]

Convert a repeating decimal to a fraction or a mixed number [Grade 8]



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Core Skill


Core Skill

WP: Multiply or divide two mixed numbers or a mixed number and a fraction [Grade 6]

Core Skill

Numbers and Operations WP: Multiply or divide a fraction by a fraction [Grade 6] Core Skill


Core Skill

WP: Solve a 2-step problem involving fractions [Grade 6] Core Skill

MN 7.1.2.4 - Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.

Overall Product Skills Use technology to respond to questions

MN 7.1.2.3 - Understand that calculators and other computing technologies often truncate or round numbers. Example: A decimal that repeats or terminates after a large number of digits is truncated or rounded.


MN 7.1.2.2 - Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense. Example: Multiplying a distance by -1 can be thought of as representing that same distance in the opposite direction. Multiplying by -1 a second time reverses directions again, giving the distance in the original direction.

WP: Add and subtract using integers [Grade 7] Core Skill

Multiply integers [Grade 7] Core Skill

Divide integers [Grade 7] Core Skill

Subtract integers [Grade 7] Core Skill


Core Skill

WP: Answer a question involving a fraction and a decimal [Grade 7]

Add integers [Grade 7] Core Skill

WP: Multiply or divide integers [Grade 7] Core Skill

Multiply or divide signed decimals [Grade 8]

Determine the square of a fraction or a decimal [Grade 8]

Add or subtract signed decimals [Grade 8]

Add or subtract signed fractions or mixed numbers [Grade 8]

Multiply or divide signed fractions or mixed numbers [Grade 8]



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Core Skill


Core Skill


Core Skill


Core Skill


Core Skill

Numbers and Operations WP: Determine a part given a ratio and the whole where the whole is less than 50 [Grade 6]

Core Skill

MN 7.1.2.5 - Use proportional reasoning to solve problems involving ratios in various contexts. Example: A recipe calls for milk, flour and sugar in a ratio of 4:6:3 (this is how recipes are often given in large institutions, such as hospitals). How much flour and milk would be needed with 1 cup of sugar?

WP: Multiply or divide integers [Grade 7] Core Skill

Determine a percent of a number given a percent that is not a whole percent [Grade 8]

Core Skill

WP: Add and subtract using integers [Grade 7] Core Skill

WP: Answer a question involving a fraction and a decimal [Grade 7]

WP: Solve a 2-step problem involving decimals [Grade 6] Core Skill

WP: Solve a multi-step problem involving fractions or mixed numbers [Grade 7]

Core Skill

WP: Solve a multi-step problem involving decimal numbers [Grade 7]

Core Skill

Determine the percent one number is of another number [Grade 8] Core Skill

Solve a problem involving simple interest [Grade 8]

Solve a problem involving annually compounded interest [Grade 8]

WP: Find the result of two consecutive percentage changes applied to a given number [Grade 8]

WP: Determine a number given a part and a decimal percentage or a percentage more than 100% [Grade 8]

Core Skill

Determine a number given a part and a decimal percentage or a percentage more than 100% [Grade 8]

Core Skill

WP: Determine a given percent of a number [Grade 8] Core Skill

WP: Determine the percent one number is of another number [Grade 8]

Core Skill



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MN 7.2.2 - Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

Determine the graph of a 1-operation linear function [Grade 7] Core Skill

Use a graph to represent the ordered pairs in a function table [Grade 7]

Algebra WP: Use direct variation to solve a problem [Grade 7]

MN 7.2.1.2 - Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.

WP: Use direct variation to solve a problem [Grade 7]

Numbers and Operations WP: Determine the whole given a ratio and a part where the whole is less than 50 [Grade 6]

Core Skill


Core Skill

MN 7.2.1.1 - Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy=k or y= k/x). Example: The radius and circumference of a circle are proportional, whereas the length x and the width y of a rectangle with area 12 are inversely proportional, since xy = 12 or equivalently, y = 12/x.

MN 7.2.1 - Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.

MN 7.2 - Algebra

MN 7.1.2.6 - Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. Example: |- 3| represents the distance from - 3 to 0 on a number line or 3 units; the distance between 3 and 9/2 on the number line is |3 - 9/2| or 3/2.




Core Skill


Core Skill

Algebra Solve a proportion involving decimals [Grade 7] Core Skill

Geometry and Measurement Determine a measure of length, weight or mass, or capacity or volume using proportional relationships [Grade 8]

Core Skill

WP: Solve a proportion [Grade 7] Core Skill



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WP: Determine the percent of increase applied to a number [Grade 7]

Core Skill

WP: Determine the result of applying a percent of decrease to a value [Grade 7]

Core Skill

WP: Determine the result of applying a percent of increase to a value [Grade 7]

Core Skill

WP: Determine the percent a whole number is of another whole number, with a result less than 100% [Grade 7]

Core Skill

WP: Determine a whole number given a part and a percentage [Grade 7]

Core Skill

WP: Determine the percent of decrease applied to a number [Grade 7]

Core Skill


Core Skill


Core Skill

Numbers and Operations WP: Determine a percent of a whole number using less than 100% [Grade 7]

Core Skill

MN 7.2.2.2 - Solve multi-step problems involving proportional relationships in numerous contexts. Example 1: Distance-time, percent increase or decrease, discounts, tips, unit pricing, lengths in similar geometric figures, and unit conversion when a conversion factor is given, including conversion between different measurement systems. Example 2: How many kilometers are there in 26.2 miles?

WP: Use a 2-variable expression to represent a situation [Grade 7]

Use a table to represent a linear function [Grade 7]

Use a variable expression with two operations to represent a table of paired numbers [Grade 7]


Core Skill


Core Skill

WP: Interpret the meaning of the slope of a graphed line [Grade 8]

Core Skill

WP: Determine a linear graph that can represent a situation [Grade 8]

Use a graph to represent the ordered pairs in a function table [Grade 7]

Determine the slope of a line given its graph or a graph of a line with a given slope [Grade 8]

Core Skill

MN 7.2.2.1 - Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. Example: Larry drives 114 miles and uses 5 gallons of gasoline. Sue drives 300 miles and uses 11.5 gallons of gasoline. Use equations and graphs to compare fuel efficiency and to determine the costs of various trips.



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Determine the graph of the solution set of a 1-step linear inequality [Grade 7]

Determine the graph of an inequality on a number line [Grade 7]


Core Skill

WP: Use a 1-variable linear inequality to represent a situation [Grade 7]


Core Skill


Core Skill

MN 7.2.2.4 - Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers. Example 1: "Four-fifths is three greater than the opposite of a number" can be represented as 4/5 = -n + 3, and "height no bigger than half the radius" can be represented as h is less than or equal to r/2. Example 2: "x is at least -3 and less than 5" can be represented as -3 is less than or equal to x < 5, and also on a number line.

MN 7.2.2.3 - Use knowledge of proportions to assess the reasonableness of solutions. Example: Recognize that it would be unreasonable for a cashier to request $200 if you purchase a $225 item at 25% off.



Determine a number given a part and a decimal percentage or a percentage more than 100% [Grade 8]

Core Skill


Core Skill


Core Skill


Core Skill


Core Skill

WP: Determine a number given a part and a decimal percentage or a percentage more than 100% [Grade 8]

Core Skill

WP: Solve a problem involving a 1-variable, 2-step equation [Grade 8]

Core Skill

Geometry and Measurement WP: Solve a distance-rate-time problem that involves unit conversions [Grade 8]


WP: Find the result of two consecutive percentage changes applied to a given number [Grade 8]

Algebra WP: Solve a proportion [Grade 7] Core Skill



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Evaluate an algebraic expression involving whole number exponents [Grade 7]

Evaluate a 2-variable expression, with two or three operations, using integer substitution [Grade 7]

Core Skill


Evaluate a 2-variable expression with two or three operations substituting fractions or decimals [Grade 8]

WP: Evaluate a variable expression involving exponents [Grade 7]

WP: Evaluate a variable expression [Grade 7]

Algebra WP: Evaluate a 1- or 2-variable expression or formula using whole numbers [Grade 6]

Core Skill

Evaluate a rational expression involving variables with two or more terms in the numerator or denominator [Grade 7]

MN 7.2.3.2 - Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. Example: Evaluate the expression 1/3 (2x - 5)² at x = 5.

Numbers and Operations Evaluate an integer raised to a whole number power [Grade 8] Core Skill

Evaluate a numerical expression involving nested parentheses [Grade 8]

Algebra Simplify an algebraic expression by combining like terms [Grade 8]

Core Skill

Use the distributive property to simplify an algebraic expression [Grade 8]

MN 7.2.3.1 - Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws. Example: Combine like terms (use the distributive law) to write 3x - 7x + 1 = (3-7)x + 1 = -4x + 1.

MN 7.2.3 - Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.

WP: Use a 2-step linear inequality in one variable to represent a situation [Grade 8]

WP: Use a 2-variable equation with rational coefficients to represent a situation [Grade 8]

Core Skill

WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations [Grade 8]

Core Skill



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WP: Solve a proportion [Grade 7] Core Skill


Core Skill

Solve a proportion involving decimals [Grade 7] Core Skill

MN 7.2.4.2 - Solve equations resulting from proportional relationships in various contexts. Example 1: Given the side lengths of one triangle and one side length of a second triangle that is similar to the first, find the remaining side lengths of the second triangle. Example 2: Determine the price of 12 yards of ribbon if 5 yards of ribbon cost $1.85.


Core Skill


Core Skill


Core Skill


Core Skill


Core Skill


Core Skill

Solve a 1-step equation involving rational numbers [Grade 8] Core Skill


Core Skill

Solve a 2-step equation involving rational numbers [Grade 8] Core Skill

MN 7.2.4.1 - Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context. Example 1: Solve for w in the equation P = 2w + 2l when P = 3.5 and l = 0.4. Example 2: To post an Internet website, Mary must pay $300 for initial set up and a monthly fee of $12. She has $842 in savings, how long can she sustain her website?

MN 7.2.4 - Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.


Evaluate a numerical expression, with parentheses and exponents, using order of operations [Grade 7]

Numbers and Operations Evaluate an expression containing the fraction bar as the division sign [Grade 7]

MN 7.2.3.3 - Apply understanding of order of operations and grouping symbols when using calculators and other technologies. Example: Recognize the conventions of using a caret (^ raise to a power), asterisk (* multiply), pay careful attention to the use of nested parentheses.



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Geometry and Measurement Determine the scale for a drawing or map question [Grade 7]

MN 7.3.2.1 - Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors. Example: Corresponding angles in similar geometric figures have the same measure.

MN 7.3.2 - Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.

WP: Determine the volume of a cylinder [Grade 7]

Determine the surface area of a cylinder [Grade 7]

Geometry and Measurement Determine the volume of a cylinder [Grade 7]

MN 7.3.1.2 - Calculate the volume and surface area of cylinders and justify the formulas used. Example: Justify the formula for the surface area of a cylinder by decomposing the surface into two circles and a rectangle.

Determine the area of a circle using 3.14 for pi [Grade 7]

Determine the area of a circle using 22/7 for pi [Grade 7]

Determine the area of a circle in terms of pi [Grade 7]

Geometry and Measurement Determine the circumference of a circle in terms of pi [Grade 7]

Solve a problem involving the circumference of a circle [Grade 7] Core Skill

WP: Determine a length or an area involving a sector of a circle [Geometry]

Core Skill

Solve a problem given the area of a circle [Grade 7] Core Skill

WP: Determine the area of a circle using 3.14 for pi [Grade 7]

MN 7.3.1.1 - Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.

MN 7.3.1 - Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.


WP: Solve a problem involving similar shapes [Grade 7] Core Skill

Geometry and Measurement Determine a missing dimension given two similar shapes [Grade 7]

Core Skill

Determine a measure of length, weight or mass, or capacity or volume using proportional relationships [Grade 8]

Core Skill




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WP: Use the mean of a data set to solve a problem [Grade 7]

Compare the medians, the modes, or the ranges of the data in a double stem-and-leaf plot [Grade 8]

Determine the mean of a set of data [Grade 7]

Determine the median of a set of data [Grade 7]

Determine the median of a set of whole number data [Grade 6]


Determine the mean of a set of whole number data [Grade 6]

MN 7.4.1.1 - Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. Example: By looking at data from the past, Sandy calculated that the mean gas mileage for her car was 28 miles per gallon. She expects to travel 400 miles during the next week. Predict the approximate number of gallons that she will use.

MN 7.4.1 - Use mean, median and range to draw conclusions about data and make predictions.


Geometry and Measurement Determine the coordinates of a translated, a rotated, or a reflected shape on the Cartesian plane [Grade 7]

MN 7.3.2.4 - Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation. Example: The point (1, 2) moves to (-1, 2) after reflection about the y-axis.

Convert a rate from one unit to another with a change in both units [Grade 7]

Core Skill

Convert a rate from one unit to another with a change in one unit [Grade 7]

Core Skill

Geometry and Measurement WP: Solve a problem involving a map or scale drawing [Grade 7]

WP: Solve a problem involving scale [Grade 8]

MN 7.3.2.3 - Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. Example 1: 1 square foot equals 144 square inches. Example 2: In a map where 1 inch represents 50 miles, 1/2 inch represents 25 miles.

Determine the ratio of the perimeters or areas of similar shapes [Grade 8]

WP: Solve a problem involving a map or scale drawing [Grade 7]

WP: Solve a problem involving scale [Grade 8]

Geometry and Measurement Determine a missing dimension given two similar shapes [Grade 7]

Core Skill

WP: Solve a problem involving similar shapes [Grade 7] Core Skill

MN 7.3.2.2 - Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures. Example: If two similar rectangles have heights of 3 and 5, and the first rectangle has a base of length 7, the base of the second rectangle has length 35/3.



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Determine the probability for independent events [Grade 7]

Use a proportion to make an estimate, related to a population, based on a sample [Grade 7]

Core Skill


Determine the probability of a single event [Grade 6]

MN 7.4.3.2 - Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. Example: Determine probabilities for different outcomes in game spinners by finding fractions of the area of the spinner.


Use a histogram to represent data [Grade 7] Core Skill

MN 7.4.3.1 - Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities. Example: Use a spreadsheet function such as RANDBETWEEN(1, 10) to generate random whole numbers from 1 to 10, and display the results in a histogram.

MN 7.4.3 - Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.

Use a histogram to represent data [Grade 7] Core Skill

Use a circle graph to represent percentage data [Grade 7] Core Skill


Answer a question using information from a circle graph using percentage calculations [Grade 7]

Core Skill

Answer a question using information from a histogram [Grade 7] Core Skill

Use a circle graph to organize data [Grade 8]

MN 7.4.2.1 - Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

MN 7.4.2 - Display and interpret data in a variety of ways, including circle graphs and histograms.


Analyze the effect that changing elements in a data set has on the mean, the median, or the range [Grade 8]

MN 7.4.1.2 - Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact. Example: How does dropping the lowest test score affect a student's mean test score?

Determine the mean of the data in a frequency table or a bar graph [Grade 8]

Determine the median of the data in a frequency table or a bar graph [Grade 8]



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Determine the probability for dependent events [Grade 7]

Compare predictions from experimental and theoretical probability [Grade 6]


Make a prediction based on an experimental probability [Grade 6]

Make a prediction based on a theoretical probability [Grade 6]

MN 7.4.3.3 - Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities. Example: When rolling a number cube 600 times, one would predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.



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Numbers and Operations Evaluate an integer raised to a whole number power [Grade 8] Core Skill

MN 8.1.1.4 - Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions. Example: 3² x 3 to the -5 power = 3 to the -3 power (1/3)³ = 1/27.

Determine the square root of a whole number to the nearest tenth [Grade 8]

Numbers and Operations Approximate the location of a square root on a number line [Grade 8]

Core Skill

MN 8.1.1.3 - Determine rational approximations for solutions to problems involving real numbers. Example 1: A calculator can be used to determine that the square root of 7 is approximately 2.65. Example 2: To check that 1 5/12 is slightly bigger than the square root of 2, do the calculation (1 5/12)² = (17/12)² = 289/144 = 2 1/144. Example 3: Knowing that the square root of 10 is between 3 and 4, try squaring numbers like 3.5, 3.3, 3.1 to determine that 3.1 is a reasonable rational approximation of the square root of 10.

Approximate the location of a square root on a number line [Grade 8]

Core Skill

Compare rational numbers and/or irrational numbers in various forms [Grade 8]

Order rational numbers and irrational numbers [Grade 8]

Determine the square root of a perfect-square fraction or decimal [Grade 8]

Core Skill

Numbers and Operations Evaluate the positive square root of a perfect square [Grade 7]

Determine the two closest integers to a given square root [Grade 8]

Core Skill

Determine both square roots of a perfect square [Grade 8]

MN 8.1.1.2 - Compare real numbers; locate real numbers on a number line. Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers. Example 1: Put the following numbers in order from smallest to largest: 2, square root of 3, -4, -6.8, - the square root of 37. Example 2: The square root of 68 is an irrational number between 8 and 9.

Numbers and Operations Identify rational or irrational numbers [Grade 8]

MN 8.1.1.1 - Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number and an irrational number is irrational, and the product of a non-zero rational number and an irrational number is irrational. Example: Classify the following numbers as whole numbers, integers, rational numbers, irrational numbers, recognizing that some numbers belong in more than one category: 6/3, 3/6, 3.6 repeating, pi/2, - the square root of 4, the square root of 10, -6.7.

MN 8.1.1 - Read, write, compare, classify and represent real numbers, and use them to solve problems in various contexts.


Grade 8



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Evaluate a function written in function notation for a given value [Algebra 1]

Core Skill

Algebra Determine the independent or dependent variable in a given situation [Algebra 1]

MN 8.2.1.1 - Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as f(x), to represent such relationships. Example: The relationship between the area of a square and the side length can be expressed as f(x)=x². In this case, f(5)=25 , which represents the fact that a square of side length 5 units has area 25 units squared.

MN 8.2.1 - Understand the concept of function in real-world and mathematical situations, and distinguish between linear and non-linear functions.

MN 8.2 - Algebra

Convert a number less than 1 to scientific notation [Grade 8] Core Skill

Numbers and Operations Convert a whole number greater than 10 to scientific notation [Grade 7]

Convert a number less than 1 from scientific notation to standard form [Grade 8]

Core Skill

MN 8.1.1.5 - Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved. Example: (4.2 x 10 to the 4th power) x (8.25 x 10³)= 3.465 x 10 to the 8th power, but if these numbers represent physical measurements, the answer should be expressed as 3.5 x 10 to the 8th power because the first factor, 4.2 x 10 to the 4th power, only has two significant digits.

Algebra Evaluate a fraction raised to an integer power [Algebra 1]

Evaluate a numerical expression involving one or more exponents and multiple forms of rational numbers [Algebra 1]

Core Skill


Evaluate a zero or negative power of an integer [Grade 8]

Evaluate a numerical expression involving integer exponents and/or integer bases [Grade 8]

Core Skill

Apply the quotient of powers property to monomial numerical expressions [Algebra 1]

Apply the power of a power property to a monomial numerical expression [Algebra 1]

Apply the product of powers property to a monomial numerical expression [Algebra 1]



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Determine the graph of a line for a given table of values [Grade 8]

Determine the slope-intercept form or the standard form of a linear equation [Algebra 1]

Core Skill

Determine the graph of a line using given information [Algebra 1] Core Skill

Determine the table of values that represents a linear equation with rational coefficients in two variables [Grade 8]

Core Skill

Determine a linear equation in two variables that represents a table of values [Grade 8]

Core Skill


Algebra Determine the graph of a 1-operation linear function [Grade 7] Core Skill


Determine the graph of a linear equation given in slope-intercept, point-slope, or standard form [Algebra 1]

Core Skill

MN 8.2.2.1 - Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.

MN 8.2.2 - Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions and explain results in the original context.

MN 8.2.1.5 - Understand that a geometric sequence is a non-linear function that can be expressed in the form f(x)=ab to the x power, where x = 0, 1, 2, 3,.... Example: The geometric sequence 6, 12, 24, 48, ... , can be expressed in the form f(x) = 6(2 to the x power).

MN 8.2.1.4 - Understand that an arithmetic sequence is a linear function that can be expressed in the form f(x)=mx+b, where x = 0, 1, 2, 3,.... Example: The arithmetic sequence 3, 7, 11, 15, ..., can be expressed as f(x) = 4x + 3.

Determine whether a graph or a table represents a linear or nonlinear function [Algebra 1]

Algebra Determine if a function is linear or nonlinear [Algebra 1]

MN 8.2.1.3 - Understand that a function is linear if it can be expressed in the form f(x)=mx+b or if its graph is a straight line. Example: The function f(x)=x² is not a linear function because its graph contains the points (1,1), (-1,1) and (0,0), which are not on a straight line.


Core Skill



MN 8.2.1.2 - Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount. Example: Uncle Jim gave Emily $50 on the day she was born and $25 on each birthday after that. The function f(x)=50+25x represents the amount of money Jim has given after x years. The rate of change is $25 per year.



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WP: Evaluate a variable expression [Grade 7]

WP: Evaluate a variable expression involving exponents [Grade 7]

Evaluate an algebraic expression involving whole number exponents [Grade 7]

Algebra Evaluate a rational expression involving variables with two or more terms in the numerator or denominator [Grade 7]


MN 8.2.3.1 - Evaluate algebraic expressions, including expressions containing radicals and absolute values, at specified values of their variables. Example: Evaluate pi r²h when r = 3 and h = 0.5, and then use an approximation of pi, to obtain an approximate answer.

MN 8.2.3 - Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.

MN 8.2.2.5 - Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. Example: If a girl invests $100 at 10% annual interest, she will have 100(1.1 to the x power) dollars after x years.

MN 8.2.2.4 - Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. Example: If a girl starts with $100 in savings and adds $10 at the end of each month, she will have 100 + 10x dollars after x months.

Algebra Determine an equation of a line given the slope and y-intercept of the line [Algebra 1]

Core Skill

MN 8.2.2.3 - Identify how coefficient changes in the equation f(x) = mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects.


Core Skill

Determine the x- or y-intercept of a line given its graph [Grade 8] Core Skill

Algebra Determine the slope of a line given its graph or a graph of a line with a given slope [Grade 8]

Core Skill

WP: Interpret the meaning of the y-intercept of a graphed line [Grade 8]

Core Skill

MN 8.2.2.2 - Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

Determine an equation of a line given two points on the line [Algebra 1]

Core Skill

Determine an equation for a line given the slope of the line and a point on the line that is not the y-intercept [Algebra 1]

Core Skill

Determine an equation of a line given the slope and y-intercept of the line [Algebra 1]

Core Skill



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Rewrite an equation to solve for a specified variable [Algebra 1] Core Skill

Solve a 1-variable linear equation with the variable on both sides [Algebra 1]

Core Skill

Algebra Solve a 2-step equation involving rational numbers [Grade 8] Core Skill

Solve a 1-variable linear equation that requires simplification and has the variable on one side [Algebra 1]

MN 8.2.4.2 - Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used. Example 1: The equation 10x + 17 = 3x can be changed to 7x + 17 = 0, and then to 7x = -17 by adding/subtracting the same quantities to both sides. These changes do not change the solution of the equation. Example 2: Using the formula for the perimeter of a rectangle, solve for the base in terms of the height and perimeter.


Core Skill

WP: Determine a linear equation that can be used to solve a percent problem [Algebra 1]

Algebra WP: Use a 1-variable 1-step equation to represent a situation [Grade 7]

Core Skill


Core Skill

MN 8.2.4.1 - Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships. Example: For a cylinder with fixed radius of length 5, the surface area A = 2 pi(5)h + 2 pi(5)² = 10 pi h + 50 pi, is a linear function of the height h, but the surface area is not proportional to the height.

MN 8.2.4 - Represent real-world and mathematical situations using equations and inequalities involving linear expressions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.

Algebra Use the distributive property to simplify an algebraic expression [Grade 8]

MN 8.2.3.2 - Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra. Properties include the associative, commutative and distributive laws, and the order of operations, including grouping symbols.

Evaluate a multi-step numerical expression involving absolute value [Algebra 1]

Evaluate an algebraic expression involving negative integer exponents [Grade 8]

Evaluate a 2-variable expression with two or three operations substituting fractions or decimals [Grade 8]



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Algebra Solve a 1-variable absolute value equation [Algebra 1]

MN 8.2.4.6 - Represent relationships in various contexts with equations and inequalities involving the absolute value of a linear expression. Solve such equations and inequalities and graph the solutions on a number line. Example: A cylindrical machine part is manufactured with a radius of 2.1 cm, with a tolerance of 1/100 cm. The radius r satisfies the inequality |r - 2.1| is less than or equal to .01.

Solve a 1-variable compound inequality [Algebra 1]

Solve a 1-variable linear inequality with the variable on both sides [Algebra 1]

Core Skill

Determine the graph of the solutions to a 2-step linear inequality in one variable [Grade 8]

Core Skill

WP: Solve a problem involving a 2-step linear inequality in one variable [Grade 8]

Core Skill

Algebra Solve a 2-step linear inequality in one variable [Grade 8] Core Skill

Solve a 1-variable linear inequality with the variable on one side [Algebra 1]

MN 8.2.4.5 - Solve linear inequalities using properties of inequalities. Graph the solutions on a number line. Example: The inequality -3x < 6 is equivalent to x > -2 , which can be represented on the number line by shading in the interval to the right of -2.


Core Skill

Algebra WP: Use a 2-step linear inequality in one variable to represent a situation [Grade 8]

MN 8.2.4.4 - Use linear inequalities to represent relationships in various contexts. Example: A gas station charges $0.10 less per gallon of gasoline if a customer also gets a car wash. Without the car wash, gas costs $2.79 per gallon. The car wash is $8.95. What are the possible amounts (in gallons) of gasoline that you can buy if you also get a car wash and can spend at most $35?

Determine the slope of a line given two points on the line [Algebra 1]

Core Skill

Determine an equation of a line given the slope and y-intercept of the line [Algebra 1]

Core Skill

Algebra Determine the table of values that represents a linear equation with rational coefficients in two variables [Grade 8]

Core Skill

Determine the slope-intercept form or the standard form of a linear equation [Algebra 1]

Core Skill

Determine an equation of a line given two points on the line [Algebra 1]

Core Skill

Determine an equation for a line given the slope of the line and a point on the line that is not the y-intercept [Algebra 1]

Core Skill

MN 8.2.4.3 - Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line. Example: Determine an equation of the line through the points (-1,6) and (2/3, -3/4).



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Algebra Solve a quadratic equation by taking the square root [Algebra 1]

Numbers and Operations Evaluate the positive square root of a perfect square [Grade 7]

MN 8.2.4.9 - Use the relationship between square roots and squares of a number to solve problems. Example: If pi x² = 5, then |x| = the square root of (5/pi), or equivalently, x = the square root of (5/pi) or x = - the square root of (5/pi). If x is understood as the radius of a circle in this example, then the negative solution should be discarded and x = the square root of (5/pi).

Solve a system of linear equations in two variables using any method [Algebra 1]

Core Skill

Algebra Determine the number of solutions to a system of linear equations [Algebra 1]

MN 8.2.4.8 - Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.

Solve a system of linear equations in two variables by elimination [Algebra 1]

Solve a system of linear equations in two variables using any method [Algebra 1]

Core Skill

Solve a system of linear equations in two variables by substitution [Algebra 1]

Algebra Determine the graph of a linear equation given in slope-intercept, point-slope, or standard form [Algebra 1]

Core Skill

Solve a system of linear equations in two variables by graphing [Algebra 1]

WP: Determine a system of linear equations that represents a given situation [Algebra 1]

Core Skill

Solve a number problem that can be represented by a linear system of equations [Algebra 1]

WP: Solve a motion problem that can be represented by a system of linear equations [Algebra 1]

WP: Solve a mixture problem that can be represented by a system of linear equations [Algebra 1]

MN 8.2.4.7 - Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically. Example: Marty's cell phone company charges $15 per month plus $0.04 per minute for each call. Jeannine's company charges $0.25 per minute. Use a system of equations to determine the advantages of each plan based on the number of minutes used.

Determine the graph of a 1-variable absolute value inequality [Algebra 1]

Solve a 1-variable absolute value inequality [Algebra 1] Core Skill



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Geometry and Measurement Determine the location of a simple shape on the Cartesian plane given the coordinates of its vertices [Grade 7]

MN 8.3.2.2 - Analyze polygons on a coordinate system by determining the slopes of their sides. Example: Given the coordinates of four points, determine whether the corresponding quadrilateral is a parallelogram.

Overall Product Skills Use a software application

MN 8.3.2.1 - Understand and apply the relationships between the slopes of parallel lines and between the slopes of perpendicular lines. Dynamic graphing software may be used to examine these relationships.

MN 8.3.2 - Solve problems involving parallel and perpendicular lines on a coordinate system.

Overall Product Skills Use a software application

WP: Use the Pythagorean theorem to find a length or a distance [Grade 8]

Core Skill

Geometry and Measurement Determine the length of the hypotenuse of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

Determine the length of a leg of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

MN 8.3.1.3 - Informally justify the Pythagorean Theorem by using measurements, diagrams and computer software.

Geometry and Measurement Determine a distance on the Cartesian plane using the Pythagorean theorem [Grade 8]

MN 8.3.1.2 - Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system.

WP: Use the Pythagorean theorem to find a length or a distance [Grade 8]

Core Skill

Determine the length of a leg of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

Geometry and Measurement Determine the length of the hypotenuse of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

Determine if a triangle is a right triangle by using the Pythagorean theorem [Grade 8]

Determine a length in a complex figure using the Pythagorean theorem [Geometry]

Core Skill

MN 8.3.1.1 - Use the Pythagorean Theorem to solve problems involving right triangles. Example 1: Determine the perimeter of a right triangle, given the lengths of two of its sides. Example 2: Show that a triangle with side lengths 4, 5 and 6 is not a right triangle.

MN 8.3.1 - Solve problems involving right triangles using the Pythagorean Theorem and its converse.



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Answer a question using information from a scatter plot [Grade 8]

MN 8.4.1.3 - Assess the reasonableness of predictions using scatterplots by interpreting them in the original context. Example: A set of data may show that the number of women in the U.S. Senate is growing at a certain rate each election cycle. Is it reasonable to use this trend to predict the year in which the Senate will eventually include 1000 female Senators?



MN 8.4.1.2 - Use a line of best fit to make statements about approximate rate of change and to make predictions about values not in the original data set. Example: Given a scatterplot relating student heights to shoe sizes, predict the shoe size of a 5'4" student, even if the data does not contain information for a student of that height.

Approximate a trend line for a scatter plot [Grade 8]

Determine if a scatter plot shows a positive relationship, a negative relationship, or no relationship between the variables [Grade 8]


Use a scatter plot to organize data [Grade 8]


MN 8.4.1.1 - Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit.

MN 8.4.1 - Interpret data using scatterplots and approximate lines of best fit. Use lines of best fit to draw conclusions about data.


Algebra Determine an equation for a line given the slope of the line and a point on the line that is not the y-intercept [Algebra 1]

Core Skill

MN 8.3.2.3 - Given a line on a coordinate system and the coordinates of a point not on the line, find lines through that point that are parallel and perpendicular to the given line, symbolically and graphically.

Grades: 9-11MinnesotaAcademic Standards


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Relate changes in the values of a, b, and/or c to the graph of the equation y = a(x - b)^2 + c [Algebra 2]

Core Skill

Identify the vertex, axis of symmetry, or direction of the graph of a quadratic function [Algebra 2]

Core Skill

WP: Answer a question using the graph of a quadratic function [Algebra 1]

Core Skill

Algebra Determine the graph of a given quadratic function [Algebra 1] Core Skill

Convert a quadratic function between vertex and standard form of the equation [Algebra 2]

MN 9.2.1.5 - Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f(x) = ax² + bx + c, in the form f(x) = a(x - h)² + k , or in factored form.


Core Skill

Algebra WP: Determine a reasonable domain or range for a function in a given situation [Algebra 1]

Core Skill

MN 9.2.1.4 - Obtain information and draw conclusions from graphs of functions and other relations. Example: If a graph shows the relationship between the elapsed flight time of a golf ball at a given moment and its height at that same moment, identify the time interval during which the ball is at least 100 feet above the ground.

WP: Determine a reasonable domain or range for a function in a given situation [Algebra 1]

Core Skill

Algebra Determine the domain or range of a function [Algebra 1]

MN 9.2.1.3 - Find the domain of a function defined symbolically, graphically or in a real-world context. Example: The formula f(x) = pi x² can represent a function whose domain is all real numbers, but in the context of the area of a circle, the domain would be restricted to positive x.

Algebra Determine if a relation is a function [Algebra 1]

MN 9.2.1.2 - Distinguish between functions and other relations defined symbolically, graphically or in tabular form.

Algebra Evaluate a function written in function notation for a given value [Algebra 1]

Core Skill

MN 9.2.1.1 - Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain. Example: If f(x) = 1/(x²-3), find f(-4).

MN 9.2.1 - Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate.

MN 9.2 - Algebra

Grades: 9-11



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Core Skill


Core Skill

WP: Interpret the meaning of the y-intercept of a graphed line [Grade 8]

Core Skill

WP: Determine a reasonable domain or range for a function in a given situation [Algebra 1]

Core Skill


Core Skill

Algebra WP: Use a 2-variable equation with rational coefficients to represent a situation [Grade 8]

Core Skill

MN 9.2.2.1 - Represent and solve problems in various contexts using linear and quadratic functions. Example: Write a function that represents the area of a rectangular garden that can be surrounded with 32 feet of fencing, and use the function to determine the possible dimensions of such a garden if the area must be at least 50 square feet.

MN 9.2.2 - Recognize linear, quadratic, exponential and other common functions in real-world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.

Algebra Determine the equation of a function resulting from a translation and/or scaling of a given function [Algebra 2]

Core Skill

MN 9.2.1.9 - Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations. Example: Determine how the graph of f(x) = |x - h| + k changes as h and k change.

MN 9.2.1.8 - Make qualitative statements about the rate of change of a function, based on its graph or table of values. Example: The function f(x) = 3 to the x power increases for all x, but it increases faster when x > 2 than it does when x < 2.

Identify the asymptotes, growth or decay, or half-life of an exponential function [Algebra 2]

Algebra Identify the end behavior, asymptotes, excluded values, or behavior near excluded values of a rational function [Algebra 2]

Core Skill

MN 9.2.1.7 - Understand the concept of an asymptote and identify asymptotes for exponential functions and reciprocals of linear functions, using symbolic and graphical methods.

Determine approximate solutions to a polynomial equation [Algebra 2]

Identify the end behavior, the intercepts, or the zeros of a polynomial function [Algebra 2]

Core Skill

Algebra WP: Answer a question using the graph of a quadratic function [Algebra 1]

Core Skill

MN 9.2.1.6 - Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.



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Compare characteristics of two linear, two quadratic, or two exponential functions represented in different ways [Algebra 2]

Determine if the graph of a relation is modeled by a linear or quadratic function or represents exponential growth or decay [Algebra 2]

Determine an exponential function that represents a graph [Algebra 2]

Determine the graph of a linear equation given in slope-intercept, point-slope, or standard form [Algebra 1]

Core Skill

Determine an equation that represents a graphed line [Algebra 1] Core Skill


Determine the graph of a line using given information [Algebra 1] Core Skill

Determine the graph of a given quadratic function [Algebra 1] Core Skill

Determine the graph of an exponential function [Algebra 1]

MN 9.2.2.3 - Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.

WP: Determine an exponential function that represents a situation such as exponential growth or decay [Algebra 2]

Identify the asymptotes, growth or decay, or half-life of an exponential function [Algebra 2]

WP: Interpret an interest rate, rate of change, initial amount, frequency of compounding and other parameters of an exponential function [Algebra 2]

Core Skill

Algebra WP: Evaluate an exponential growth or an exponential decay function [Algebra 1]

Solve a problem involving exponential growth or exponential decay [Algebra 1]

MN 9.2.2.2 - Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.

WP: Solve a problem that can be modeled with a quadratic equation [Algebra 2]

WP: Use a given quadratic equation to solve a problem [Algebra 1]



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Apply properties of exponents to monomial algebraic expressions [Algebra 1]

Algebra Simplify an algebraic expression by combining like terms [Grade 8]

Core Skill

Determine an equivalent form of a variable expression involving exponents [Grade 8]

Apply the product of powers property to a monomial numerical expression [Algebra 1]

Simplify a polynomial expression by combining like terms [Algebra 1]

Simplify a monomial algebraic radical expression [Algebra 1] Core Skill

Add or subtract algebraic radical expressions [Algebra 1]

MN 9.2.3 - Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.

Algebra Determine the graph of a radical function [Algebra 1]

Determine the graph of a rational function [Algebra 1]

MN 9.2.2.6 - Sketch the graphs of common non-linear functions such as f(x)= the square root of x, f(x) = |x|, f(x)= 1/x, f(x) = x³, and translations of these functions, such as f(x) = the square root of (x-2) + 4. Know how to use graphing technology to graph these functions.

Algebra WP: Solve a problem that can be represented by a geometric sequence [Algebra 2]

Core Skill

WP: Solve a problem that can be represented by a finite geometric series [Algebra 2]

Core Skill

MN 9.2.2.5 - Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.

Determine the explicit formula for a geometric sequence [Algebra 2]

Algebra Determine the recursive formula for a geometric sequence [Algebra 2]

MN 9.2.2.4 - Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively. Example 1: A closed form formula for the terms t(sub n) in the geometric sequence 3, 6, 12, 24,... is t(sub n) = 3(2) to the (n-1) power, where n = 1, 2, 3,... , and this sequence can be expressed recursively by writing t(sub 1) = 3 and t(sub n) = 2t(sub n-1), for n is greater than or equal to 2. Example 2: The partial sums s(sub n) of the series 3 + 6 + 12 + 24 +... can be expressed recursively by writing s(sub 1) = 3 and s(sub n) = 3 + 2s(sub n-1), for n is greater than or equal to 2.



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Factor trinomials that result in factors of the form (ax +/- b)(cx +/- d) [Algebra 1]

Core Skill

Factor trinomials that result in factors of the form (ax +/- by)(cx +/- dy) [Algebra 1]

Algebra Factor the GCF from a polynomial expression [Algebra 1] Core Skill

Factor trinomials that result in factors of the form (x +/- a)(x +/- b) [Algebra 1]

Factor the difference of two squares [Algebra 1]

Factor a perfect-square trinomial [Algebra 1]

MN 9.2.3.3 - Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. Example: 9x to the 6th power - x to the 4th power = (3x³ - x²)(3x³ + x²).

Divide a polynomial expression by a monomial [Algebra 1] Core Skill

Divide a polynomial expression by a binomial [Algebra 1]

Add or subtract two rational expressions with unlike polynomial denominators [Algebra 1]

Core Skill

Multiply two binomials of the form (x +/- a)(x +/- b) [Algebra 1]

Multiply two binomials of the form (ax +/- b)(cx +/- d) [Algebra 1]

Core Skill

Multiply two binomials of the form (ax +/- by)(cx +/- dy) [Algebra 1]

Algebra Add polynomial expressions [Algebra 1] Core Skill

Subtract polynomial expressions [Algebra 1] Core Skill

Multiply a polynomial by a monomial [Algebra 1]

Multiply two nonlinear binomials [Algebra 1]

Multiply a trinomial by a binomial [Algebra 1]

Multiply rational expressions [Algebra 1] Core Skill

Square a binomial [Algebra 1]

MN 9.2.3.2 - Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.

Algebra Evaluate a function written in function notation for a given value [Algebra 1]

Core Skill

MN 9.2.3.1 - Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.

Simplify a rational expression involving polynomial terms [Algebra 1]

Core Skill

Divide monomial algebraic radical expressions [Algebra 1]

Multiply monomial algebraic radical expressions [Algebra 1]



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Apply the power of a quotient property to monomial algebraic expressions [Algebra 1]

Core Skill

Apply the quotient of powers property to monomial algebraic expressions [Algebra 1]

Core Skill

Apply the power of a product property to a monomial algebraic expression [Algebra 1]

Core Skill

Apply the power of a power property to a monomial algebraic expression [Algebra 1]

Core Skill

Apply the product of powers property to a monomial algebraic expression [Algebra 1]

Core Skill


Algebra Apply the product of powers property to a monomial numerical expression [Algebra 1]


MN 9.2.3.6 - Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions, including those involving nth roots. Example: The square root of 2 x the square root of 7 = 2 to the 1/2 power x 7 to the 1/2 power = 14 to the 1/2 power = the square root of 14. Rules for computing directly with radicals may also be used: the cubed root of 2 x the cubed root of x = the cubed root of 2x.

MN 9.2.3.5 - Check whether a given complex number is a solution of a quadratic equation by substituting it for the variable and evaluating the expression, using arithmetic with complex numbers. Example: The complex number (1+i)/2 is a solution of 2x² - 2x + 1 = 0, since 2((1+i)/2)² - 2((1+i)/2) + 1 = i-(1+i) + 1 = 0.

Multiply rational expressions [Algebra 1] Core Skill

Divide rational expressions [Algebra 1]

Algebra Factor the GCF from a polynomial expression [Algebra 1] Core Skill

Simplify a rational expression involving polynomial terms [Algebra 1]

Core Skill

Add or subtract two rational expressions with like denominators [Algebra 1]

Add or subtract two rational expressions with unlike polynomial denominators [Algebra 1]

Core Skill

Add or subtract two rational expressions with unlike monomial denominators [Algebra 1]

MN 9.2.3.4 - Add, subtract, multiply, divide and simplify algebraic fractions. Example: 1/(1-x) + x/(1+x) is equivalent to (1+2x-x²)/(1-x²).

Factor a polynomial that has a GCF and two linear binomial factors [Algebra 1]



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Core Skill

WP: Use a 2-step linear inequality in one variable to represent a situation [Grade 8]


Core Skill

Solve a 2-step linear inequality in one variable [Grade 8] Core Skill


Core Skill

Algebra WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations [Grade 8]

Core Skill



Core Skill

MN 9.2.4 - Represent real-world and mathematical situations using equations and inequalities involving linear, quadratic, exponential, and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.

MN 9.2.3.7 - Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables.

Add and/or subtract numerical radical expressions [Algebra 1]

Multiply a binomial numerical radical expression by a numerical radical expression [Algebra 1]

Rationalize the denominator of a numerical radical expression [Algebra 1]

Divide monomial numerical expressions involving radicals [Algebra 1]

Apply properties of exponents to monomial algebraic expressions [Algebra 1]

Simplify a monomial numerical expression involving the square root of a whole number [Algebra 1]

Core Skill

Multiply monomial numerical expressions involving radicals [Algebra 1]

Multiply monomial algebraic radical expressions [Algebra 1]

Divide monomial algebraic radical expressions [Algebra 1]

Add or subtract algebraic radical expressions [Algebra 1]

Simplify a monomial algebraic radical expression [Algebra 1] Core Skill

Rationalize the denominator of an algebraic radical expression [Algebra 1]



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WP: Solve a problem that can be modeled with a quadratic inequality [Algebra 2]


WP: Solve an exponential growth or decay problem [Algebra 2] Core Skill

WP: Determine a linear equation that can be used to solve a percent problem [Algebra 1]

Solve an exponential equation using the properties of exponents [Algebra 2]

Solve an exponential equation using logarithms [Algebra 2] Core Skill


Core Skill

WP: Determine possible solutions to a problem that can be represented by a system of linear inequalities [Algebra 1]

Solve a 1-variable linear inequality with the variable on both sides [Algebra 1]

Core Skill

Solve a quadratic equation by graphing the associated quadratic function [Algebra 1]

WP: Solve a mixture problem that can be represented by a system of linear equations [Algebra 1]


Core Skill

WP: Determine a system of linear inequalities that represents a given situation [Algebra 1]

WP: Solve a motion problem that can be represented by a system of linear equations [Algebra 1]

WP: Solve a problem that can be represented by a system of linear equations in three variables [Algebra 2]

Core Skill

Determine a quadratic function given the coordinates of two or three points [Algebra 2]

Core Skill

Solve a quadratic inequality in one variable [Algebra 2]

Solve a quadratic equation using the quadratic formula [Algebra 1]

Core Skill

Solve a quadratic equation by taking the square root [Algebra 1]

Solve a problem involving exponential growth or exponential decay [Algebra 1]

Solve a quadratic equation by factoring [Algebra 1] Core Skill



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Solve an exponential equation using the properties of exponents [Algebra 2]



Convert between a simple exponential equation and its corresponding logarithmic equation [Algebra 2]

Solve an exponential equation using logarithms [Algebra 2] Core Skill

Algebra Identify the asymptotes, growth or decay, or half-life of an exponential function [Algebra 2]

MN 9.2.4.2 - Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations.

Solve a quadratic equation using the quadratic formula [Algebra 1]

Core Skill

Determine a quadratic equation given its solutions [Algebra 2] Core Skill

Solve a quadratic inequality in one variable [Algebra 2]

Solve a quadratic equation by factoring [Algebra 1] Core Skill

Algebra Solve a quadratic equation by graphing the associated quadratic function [Algebra 1]

Solve a quadratic equation by taking the square root [Algebra 1]

Determine the solution(s) of an equation given in factored form [Algebra 1]

WP: Solve a problem that can be modeled with a quadratic inequality [Algebra 2]


Solve a quadratic equation with complex solutions [Algebra 2] Core Skill

Relate a quadratic inequality in two variables to its graph [Algebra 2]

Determine the graph of a quadratic inequality in one variable [Algebra 2]

MN 9.2.4.1 - Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities. Example: A diver jumps from a 20 meter platform with an upward velocity of 3 meters per second. In finding the time at which the diver hits the surface of the water, the resulting quadratic equation has a positive and a negative solution. The negative solution should be discarded because of the context.



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Algebra Solve a 1-variable absolute value inequality [Algebra 1] Core Skill

Determine the graph of a 2-variable absolute value inequality [Algebra 2]

MN 9.2.4.6 - Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically. Example: If a pipe is to be cut to a length of 5 meters accurate to within a tenth of its diameter, the relationship between the length x of the pipe and its diameter y satisfies the inequality |x - 5| is less than or equal to 0.1y.


Core Skill

WP: Solve a linear programming problem [Algebra 2]

Algebra Solve a 2-step linear inequality in one variable [Grade 8] Core Skill

MN 9.2.4.5 - Solve linear programming problems in two variables using graphical methods.

WP: Determine possible solutions to a problem that can be represented by a system of linear inequalities [Algebra 1]

WP: Determine a system of linear inequalities that represents a given situation [Algebra 1]

Algebra Determine the graph of the solution set of a system of linear inequalities in two variables [Algebra 1]

Determine the graph of the solution set of a system of three or more linear inequalities in two variables [Algebra 2]

Core Skill

WP: Solve a linear programming problem [Algebra 2]

MN 9.2.4.4 - Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines.

Solve a quadratic equation with complex solutions [Algebra 2] Core Skill

Algebra Convert the square root of a negative number to the form bi [Algebra 2]

MN 9.2.4.3 - Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.

Determine if the graph of a relation is modeled by a linear or quadratic function or represents exponential growth or decay [Algebra 2]

WP: Solve an exponential growth or decay problem [Algebra 2] Core Skill



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Determine the volume of a right pyramid or a right cone [Geometry]

Solve a problem involving the volume of a right pyramid or a right cone [Geometry]

Core Skill

WP: Determine the surface area of a pyramid or a cone [Grade 8]

Solve a problem involving the surface area of a cone or a pyramid that has a rectangle or right triangle as a base [Geometry]

Determine the volume of an oblique pyramid or an oblique cone [Geometry]

Determine the volume of a sphere or hemisphere [Geometry] Core Skill

WP: Determine the volume of a sphere or hemisphere [Geometry]

Determine the surface area of a sphere [Geometry] Core Skill

WP: Solve a problem involving the surface area of a sphere [Geometry]

Geometry and Measurement Determine the volume of a pyramid or a cone [Grade 8]

WP: Determine the volume of a pyramid or a cone [Grade 8]

Determine the surface area of a pyramid or a cone [Grade 8]

MN 9.3.1.1 - Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate. Example: Measure the height and radius of a cone and then use a formula to find its volume.

MN 9.3.1 - Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.


Algebra WP: Determine a reasonable domain or range for a function in a given situation [Algebra 1]

Core Skill

MN 9.2.4.8 - Assess the reasonableness of a solution in its given context and compare the solution to appropriate graphical or numerical estimates; interpret a solution in the original context.

Solve a radical equation that leads to a quadratic equation [Algebra 1]

Core Skill

Algebra Solve a radical equation that leads to a linear equation [Algebra 1] Core Skill

MN 9.2.4.7 - Solve equations that contain radical expressions. Recognize that extraneous solutions may arise when using symbolic methods. Example 1: The equation the square root of x-9 = 9 the square root of x may be solved by squaring both sides to obtain x - 9 = 81x, which has the solution x = -9/80. However, this is not a solution of the original equation, so it is an extraneous solution that should be discarded. The original equation has no solution in this case. Example 2: Solve the cubed root of (-x+1) = -5.



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Algebra WP: Determine the degree of accuracy of a computation [Algebra 2]

MN 9.3.1.5 - Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements. Example: Suppose the sides of a rectangle are measured to the nearest tenth of a centimeter at 2.6 cm and 9.8 cm. Because of measurement errors, the width could be as small as 2.55 cm or as large as 2.65 cm, with similar errors for the height. These errors affect calculations. For instance, the actual area of the rectangle could be smaller than 25 cm² or larger than 26 cm², even though 2.6 × 9.8 = 25.48.

Solve a problem involving the surface areas of similar solid figures [Geometry]

Determine the scale factor relating two similar polygons [Geometry]

Geometry and Measurement Determine the ratio of the perimeters or areas of similar shapes [Grade 8]

Solve a problem involving the volumes of similar solid figures [Geometry]

MN 9.3.1.4 - Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively.

Geometry and Measurement Convert a rate from one unit to another with a change in one unit [Grade 7]

Core Skill

Algebra WP: Solve a multi-step problem involving dimensional analysis [Algebra 2]

Convert a rate from one unit to another with a change in both units [Grade 7]

Core Skill

MN 9.3.1.3 - Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems. Example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 88 feet/second.

WP: Solve a problem involving the area of a complex shape formed by circles and polygons [Geometry]

Determine the surface area of a complex solid figure [Geometry]

Geometry and Measurement Determine the area of a quadrilateral [Geometry] Core Skill

Determine the area of a regular polygon [Geometry]

Solve a problem involving the surface area of a complex solid figure [Geometry]

WP: Solve a problem involving the volume of a complex solid figure [Geometry]

Determine the volume of a complex solid figure [Geometry]

MN 9.3.1.2 - Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures. Example: Find the volume of a regular hexagonal prism by decomposing it into six equal triangular prisms.



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Identify parallel lines using angle relationships [Geometry]

Determine the measure of an angle in a figure involving parallel and/or perpendicular lines [Geometry]

Geometry and Measurement Identify angle relationships formed by parallel lines cut by a transversal [Grade 8]

Determine the measure of an angle formed by parallel lines and one or more transversals [Geometry]

Core Skill

Determine if lines through points with given coordinates are parallel or perpendicular [Geometry]

MN 9.3.3.1 - Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results. Example: Prove that the perpendicular bisector of a line segment is the set of all points equidistant from the two endpoints, and use this fact to solve problems and justify other results.

MN 9.3.3 - Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.

Overall Product Skills Use technology for learning and assessment

MN 9.3.2.5 - Use technology tools to examine theorems, make and test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.

Overall Product Skills Develop use of various types of reasoning (inductive, deductive, etc.) as appropriate to the situation

MN 9.3.2.4 - Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations. Example: Prove that the sum of the interior angles of a pentagon is 540° using the fact that the sum of the interior angles of a triangle is 180°.

Overall Product Skills Develop use of various types of reasoning (inductive, deductive, etc.) as appropriate to the situation

MN 9.3.2.3 - Assess the validity of a logical argument and give counterexamples to disprove a statement.

Overall Product Skills Build comprehension of math vocabulary

MN 9.3.2.2 - Accurately interpret and use words and phrases such as "if...then," "if and only if," "all," and "not." Recognize the logical relationships between an "if...then" statement and its inverse, converse and contrapositive. Example: The statement "If you don't do your homework, you can't go to the dance" is not logically equivalent to its inverse "If you do your homework, you can go to the dance.".

MN 9.3.2.1 - Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.

MN 9.3.2 - Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.



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Solve for the length of a side of a triangle using the Pythagorean theorem [Geometry]

Determine if a triangle is a right triangle by using the Pythagorean theorem [Grade 8]

WP: Solve a problem involving a complex figure using the Pythagorean theorem [Geometry]

Determine a length in a complex figure using the Pythagorean theorem [Geometry]

Core Skill

Determine a distance on the Cartesian plane using the Pythagorean theorem [Grade 8]

Geometry and Measurement WP: Use the Pythagorean theorem to find a length or a distance [Grade 8]

Core Skill

MN 9.3.3.4 - Apply the Pythagorean Theorem and its converse to solve problems and logically justify results. Example: When building a wooden frame that is supposed to have a square corner, ensure that the corner is square by measuring lengths near the corner and applying the Pythagorean Theorem.

Geometry and Measurement Solve a problem using inequalities in a triangle [Geometry] Core Skill

Solve a problem involving two triangles by using the hinge theorem and other triangle inequality relationships [Geometry]

MN 9.3.3.3 - Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results. Example: Use the triangle inequality to prove that the perimeter of a quadrilateral is larger than the sum of the lengths of its diagonals.

Identify similar triangles using triangle similarity postulates or theorems [Geometry]

Core Skill

Determine the measure of an angle in a figure involving parallel and/or perpendicular lines [Geometry]

Geometry and Measurement Identify angle relationships formed by multiple lines and transversals [Geometry]

Determine the measure of an angle formed by parallel lines and one or more transversals [Geometry]

Core Skill

MN 9.3.3.2 - Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results. Example: Prove that two triangles formed by a pair of intersecting lines and a pair of parallel lines (an "X" trapped between two parallel lines) are similar.

Determine a length using parallel lines and proportional parts [Geometry]

Core Skill

Determine the coordinates of a point through which a line must pass in order to be parallel or perpendicular to a given line [Geometry]



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Identify similar triangles using triangle similarity postulates or theorems [Geometry]

Core Skill

Identify a triangle similarity postulate that justifies a similarity statement [Geometry]

Core Skill

Determine a length given the perimeters of similar triangles or the lengths of corresponding interior line segments [Geometry]

Determine a length in a triangle using a midsegment [Geometry]

WP: Determine a length using similarity [Geometry] Core Skill

Determine a length using similar triangles formed by the altitude to the hypotenuse of a right triangle [Geometry]

Determine a length using parallel lines and proportional parts [Geometry]

Core Skill

Determine the length of a side or the measure of an angle in similar triangles [Geometry]

Identify a triangle congruence postulate that justifies a congruence statement [Geometry]

Core Skill

Geometry and Measurement Determine the length of a side or the measure of an angle in congruent triangles [Geometry]

Identify congruent triangles using triangle congruence postulates or theorems [Geometry]

Core Skill

Determine the length of a side in one of two similar polygons [Geometry]

Solve a problem involving a point on the bisector of an angle [Geometry]

MN 9.3.3.6 - Know and apply properties of congruent and similar figures to solve problems and logically justify results. Example 1: Analyze lengths and areas in a figure formed by drawing a line segment from one side of a triangle to a second side, parallel to the third side. Example 2: Determine the height of a pine tree by comparing the length of its shadow to the length of the shadow of a person of known height. Example 3: When attempting to build two identical 4-sided frames, a person measured the lengths of corresponding sides and found that they matched. Can the person conclude that the shapes of the frames are congruent?

WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle [Geometry]

Solve a problem using multiple non-trigonometric right-triangle relationships [Geometry]

Geometry and Measurement Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle [Geometry]

Core Skill

MN 9.3.3.5 - Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results. Example 1: Use 30-60-90 triangles to analyze geometric figures involving equilateral triangles and hexagons. Example 2: Determine exact values of the trigonometric ratios in these special triangles using relationships among the side lengths.



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Determine the measure of an arc or an angle using the relationship between an inscribed angle and its intercepted arc [Geometry]

Core Skill

Determine the measure of an arc or an angle using properties of an inscribed triangle or quadrilateral [Geometry]

Determine a length using a perpendicular bisector of a chord [Geometry]

Determine a length using a line segment tangent to a circle and the radius that intersects the tangent [Geometry]

Core Skill

Determine a length using two intersecting tangents to a circle [Geometry]

Determine a length or an arc measure using the properties of congruent chords [Geometry]

Determine the length of a line segment, the measure of an angle, or the measure of an arc using a tangent to a circle [Geometry]

Core Skill

Geometry and Measurement Determine the measure of an arc or a central angle using the relationship between the arc and the central angle [Geometry]

Core Skill

Solve a problem involving the length of an arc [Geometry] Core Skill

MN 9.3.3.8 - Know and apply properties of a circle to solve problems and logically justify results. Example: Show that opposite angles of a quadrilateral inscribed in a circle are supplementary.

Determine a length or an angle measure using properties of trapezoids [Geometry]

Determine a length or an angle measure using properties of kites [Geometry]

Determine a length or an angle measure using properties of squares, rectangles, or rhombi [Geometry]

Geometry and Measurement Determine the measure of an angle or the sum of the angles in a polygon [Geometry]

Core Skill

Determine a length or an angle measure using general properties of parallelograms [Geometry]

Determine a length or an angle measure in a complex figure using properties of polygons [Geometry]

WP: Solve a problem involving the area of a quadrilateral [Geometry]

Determine a length given the area of a regular polygon [Geometry]

Determine a length given the area of a quadrilateral [Geometry] Core Skill

WP: Solve a problem using the properties of angles and/or sides of polygons [Geometry]

Core Skill

Determine the area of a quadrilateral [Geometry] Core Skill

MN 9.3.3.7 - Use properties of polygons-including quadrilaterals and regular polygons-to define them, classify them, solve problems and logically justify results. Example 1: Recognize that a rectangle is a special case of a trapezoid. Example 2: Give a concise and clear definition of a kite.



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WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio [Geometry]

Geometry and Measurement Determine the measure of an angle using a sine, cosine, or tangent ratio in a right triangle [Geometry]

MN 9.3.4.3 - Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.

WP: Determine a length in a right triangle using a sine, cosine, or tangent ratio [Geometry]

Approximate the area of a right triangle using trigonometry [Geometry]

Approximate the area of a regular polygon using trigonometry [Geometry]

Geometry and Measurement Determine a length using a sine, cosine, or tangent ratio in a right triangle [Geometry]

MN 9.3.4.2 - Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios. Example: Find the area of a triangle, given the measure of one of its acute angles and the lengths of the two sides that form that angle.

Geometry and Measurement Determine a sine, cosine, or tangent ratio in a right triangle [Geometry]

MN 9.3.4.1 - Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.

MN 9.3.4 - Solve real-world and mathematical geometric problems using algebraic methods.

Solve a problem involving intersecting chords, tangents, and/or secants of a circle [Geometry]

Determine the area of a sector of a circle [Geometry] Core Skill

Determine the measure of an arc or an angle formed by two tangents, two secants, or a tangent and a secant that intersect outside a circle [Geometry]

Determine a length using intersecting chords, two secants that intersect outside a circle, or a tangent and a secant that intersect outside a circle [Geometry]

Determine the measure of an arc or an angle formed by intersecting chords or a chord that intersects a tangent to a circle [Geometry]

Determine the area of a segment of a circle [Geometry]

WP: Determine a length or an area involving a sector of a circle [Geometry]

Core Skill

Determine the length of the radius or the diameter of a circle given the area of a sector [Geometry]

Core Skill



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Relate the coordinates of a preimage or an image to a dilation centered at the origin [Geometry]

Determine the coordinates of a preimage or an image given a reflection across a horizontal line, a vertical line, the line y = x, or the line y = -x [Geometry]

Geometry and Measurement Relate the coordinates of a preimage or an image to a translation described using mapping notation [Geometry]

Determine the coordinates of the image of a figure after two transformations of different types [Geometry]

Determine the coordinates of the image of a figure after two transformations of the same type [Geometry]

Determine the angle of rotational symmetry of a figure [Geometry]

MN 9.3.4.6 - Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid. Example: If the point (3,-2) is rotated 90° counterclockwise about the origin, it becomes the point (2,3).

Geometry and Measurement Determine the distance between two points [Geometry]

Determine an equation of a circle [Geometry]

Determine the radius, center, or diameter of a circle given an equation [Geometry]

MN 9.3.4.5 - Know the equation for the graph of a circle with radius r and center (h,k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean Theorem and properties of translations.

Determine the area of a right triangle or a rectangle given the coordinates of the vertices of the figure [Geometry]

Core Skill

Solve a problem involving the midpoint formula [Geometry]

Solve a problem involving the distance formula [Geometry] Core Skill

Determine the midpoint of a line segment given the coordinates of the endpoints [Geometry]

Core Skill

Geometry and Measurement Determine the distance between two points [Geometry]

Algebra Determine the slope of a line given two points on the line [Algebra 1]

Core Skill

Determine if lines through points with given coordinates are parallel or perpendicular [Geometry]

Determine the coordinates of a point through which a line must pass in order to be parallel or perpendicular to a given line [Geometry]

MN 9.3.4.4 - Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.



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Read a box-and-whisker plot [Grade 8]


Use a circle graph to organize data [Grade 8]

Determine the quartiles of a data set [Grade 8]

MN 9.4.1.1 - Describe a data set using data displays, including box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics.

MN 9.4.1 - Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships.


WP: Determine a length or an angle measure using triangle relationships [Geometry]

Core Skill

Solve a problem involving two triangles by using the hinge theorem and other triangle inequality relationships [Geometry]

Determine a length or an angle measure using general properties of parallelograms [Geometry]

Determine the length of a side or the measure of an angle in congruent triangles [Geometry]

Determine a length in a triangle using a median [Geometry]

Geometry and Measurement Determine the measure of an angle using the sum of the interior angles in a triangle [Geometry]

Solve a problem using inequalities in a triangle [Geometry] Core Skill

Solve for the length of a side of a triangle using the Pythagorean theorem [Geometry]

Determine the length of a side or the measure of an angle in similar triangles [Geometry]

Determine a length in a triangle using a midsegment [Geometry]

Determine a length using similar triangles formed by the altitude to the hypotenuse of a right triangle [Geometry]

Determine a length or an angle measure using properties of squares, rectangles, or rhombi [Geometry]

Determine a length or an angle measure using properties of kites [Geometry]

Determine a length or an angle measure using properties of trapezoids [Geometry]

MN 9.3.4.7 - Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.



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MN 9.4.2 - Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions.

MN 9.4.1.4 - Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve) and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve. Example 1: After performing several measurements of some attribute of an irregular physical object, it is appropriate to fit the data to a normal distribution and draw conclusions about measurement error. Example 2: When data involving two very different populations is combined, the resulting histogram may show two distinct peaks, and fitting the data to a normal distribution is not appropriate.

Approximate a trend line for a scatter plot [Grade 8]

Determine if a scatter plot shows a positive relationship, a negative relationship, or no relationship between the variables [Grade 8]


Use a scatter plot to organize data [Grade 8]


MN 9.4.1.3 - Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.


Analyze the effect that changing elements in a data set has on the mean, the median, or the range [Grade 8]

MN 9.4.1.2 - Analyze the effects on summary statistics of changes in data sets. Example 1: Understand how inserting or deleting a data point may affect the mean and standard deviation. Example 2: Understand how the median and interquartile range are affected when the entire data set is transformed by adding a constant to each data value or multiplying each data value by a constant.

Compare the medians, the modes, or the ranges of the data in a double stem-and-leaf plot [Grade 8]

Answer a question using information from two box-and-whisker plots [Grade 8]

Answer a question using information from a box-and-whisker plot [Grade 8]

Use a box-and-whisker plot to organize data [Grade 8]

Determine the median of the data in a frequency table or a bar graph [Grade 8]

Determine the mean of the data in a frequency table or a bar graph [Grade 8]



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Determine the probability of three or more dependent events [Grade 8]


Determine the probability of three or more independent events [Grade 8]

Determine the probability of an event consisting of mutually exclusive events [Grade 8]

MN 9.4.3.5 - Apply probability concepts such as intersections, unions and complements of events, and conditional probability and independence, to calculate probabilities and solve problems. Example: The probability of tossing at least one head when flipping a fair coin three times can be calculated by looking at the complement of this event (flipping three tails in a row).

MN 9.4.3.4 - Use random numbers generated by a calculator or a spreadsheet, or taken from a table, to perform probability simulations and to introduce fairness into decision making. Example: If a group of students needs to fairly select one of its members to lead a discussion, they can use a random number to determine the selection.

MN 9.4.3.3 - Understand that the Law of Large Numbers expresses a relationship between the probabilities in a probability model and the experimental probabilities found by performing simulations or experiments involving the model.

MN 9.4.3.2 - Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.

MN 9.4.3.1 - Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Example: If one girl and one boy are picked at random from a class with 20 girls and 15 boys, there are 20 × 15 = 300 different possibilities, so the probability that a particular girl is chosen together with a particular boy is 1/300.

MN 9.4.3 - Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.


Determine if a question is likely to produce a biased survey result [Grade 8]

MN 9.4.2.3 - Design simple experiments and explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.

MN 9.4.2.2 - Identify and explain misleading uses of data; recognize when arguments based on data confuse correlation and causation.

MN 9.4.2.1 - Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use spreadsheet tables and graphs or graphing technology to recognize and analyze distortions in data displays. Example: Displaying only part of a vertical axis can make differences in data appear deceptively large.



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MN 9.4.3.9 - Use the relationship between conditional probabilities and relative frequencies in contingency tables. Example: A table that displays percentages relating gender (male or female) and handedness (right-handed or left-handed) can be used to determine the conditional probability of being left-handed, given that the gender is male.


Make a prediction involving the probability of compound events [Grade 8]

MN 9.4.3.8 - Apply probability concepts to real-world situations to make informed decisions. Example 1: Explain why a hockey coach might decide near the end of the game to pull the goalie to add another forward position player if the team is behind. Example 2: Consider the role that probabilities play in health care decisions, such as deciding between having eye surgery and wearing glasses.

MN 9.4.3.7 - Understand and use simple probability formulas involving intersections, unions and complements of events. Example 1: If the probability of an event is p, then the probability of the complement of an event is 1 - p; the probability of the intersection of two independent events is the product of their probabilities. Example 2: The probability of the union of two events equals the sum of the probabilities of the two individual events minus the probability of the intersection of the events.


Use a Venn diagram to organize summarized data [Grade 8]

MN 9.4.3.6 - Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets.

Documents

Minnesota Standards Alignment 2007 Academic …doc.renlearn.com/KMNet/R0055396CDEC8882.pdfMinnesota Standards Alignment 2007 Academic Standards, produced by the State Department of