Teaching Guide for Common Core Curriculum€¦ · KEY: Bold = 1ST Introduced Italicized = Spiraling Underlined = Essential REVISED 7.27.15 Pittsburg Unified School District Math 6

KEY: Bold = 1ST

Introduced Italicized = Spiraling Underlined = Essential REVISED 7.27.15

Pittsburg Unified School District

Math 6 CCSS Teaching Guide for Mathematics

Common Core Curriculum

2015-2016

KEY: Bold = Major Standards Underlined = Supporting Standards Gray = Additional Standards REVISED 7.27.15

MATH 6 Common Core State Standards

Benchmark 1 (30% of stds / 20 Q)

*27% when clustered


*65% when clustered


*80% taught (83% if clustered)

Quarter 4 Assessment

8/19 – 8/21 Intro (3 days) 8/24 – 9/15 Unit 1 (16 days) Rational Numbers & Absolute Value

6.NS.5 6.NS.6 a, b, c 6.NS.7 a, b, c, d 6.NS.8 6.G.3

9/16 – 10/7 Unit 2 (16 days) Fractions & Decimals

6.NS.1 6.NS.2 6.NS.3

---------------------------------------------------- 10/8 – 10/23

Benchmark #1 ----------------------------------------------------

10/23 Quarter 1 Ends (46 days /

35 instructional days)

10/26 – 11/20 Unit 3 (19 days) Ratio

6.RP.3c 6.RP.1 6.RP.3a

11/30 – 12/18 Unit 4 (15 days): Expressions

6.NS.4 6.EE.1 6.EE.2 a, b, c 6.EE.3 6.EE.4

1/4 – 1/22 Unit 5 (14 days) Equations and Inequalities

6.RP.3 a, b, c, d 6.EE.5 6.EE.6 6.EE.7 6.EE.8

---------------------------------------------------- 2/1 – 2/19

Benchmark #2 ----------------------------------------------------



1/25 - 3/3 Unit 6 (21 days) Rate

6.RP.1* 6 RP.2 6.RP.3a, b, d* 6.EE.9

3/4 – 3/23 Unit 7 (14 days) Surface Area & Volume

6.G.1 6.G.2 6.G.4

---------------------------------------------------- 4/4 – 4/15

Benchmark #3 ----------------------------------------------------

3/23 Quarter 3 Ends (45 days/


4/18 – 4/29 Unit 8 (10 days) Putting Mathematics to Work (review)

6.RP.3 a, b, d 6.NS.3 6.NS.8 6.EE.6 6.EE.7 6.EE.9 6.G.3

5/2 – 5-13 (5/27?) CAASPP Testing *1 week per subject/grade

5/2 - 5/27 Unit 9 (20 days/ 15 instructional days) Distributions & Variability

6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5 a, b, c, d

---------------------------------------------------- 5/31 – 6/6

Quarter 4 Assessment ----------------------------------------------------



*MATHEMATICAL PRACTICES should be embedded throughout instruction over the course of the school year.

MATHEMATICAL PRACTICES 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.

5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.


MATH 6 Common Core State Standards - YEARLY OVERVIEW


*27% when clustered


*65% when clustered UNIT 1 - Rational Numbers & Absolute Value

Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.5 - Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.6 - Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line;

recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.7 - Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number

line diagram. a. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.

c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

6.NS.8 - Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.G.3 - Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

UNIT 2 - FRACTIONS & DECIMALS Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.1 - Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2 - Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3 - Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

UNIT 3 - RATIO Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.RP.1 - Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

UNIT 4 - Expressions

6.NS.4 - Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2). Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.1 - Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.3 - Apply the properties of operations to generate equivalent expressions. 6.EE.4 - Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

UNIT 5 - Equations & Inequalities 6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.


b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?


d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Reason about and solve one-variable equations and inequalities 6.EE.5 - Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.7 - Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.8 - Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.



*80% taught (83% if clustered)

Quarter 4 Assessment

UNIT 6 - RATE Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.1 - Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.2 - Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.




Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.9 - Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

UNIT 7 - Surface Area & Volume Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1 - Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.G.2 - Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.4 - Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

UNIT 8 - Putting Mathematics to Work (review) 6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

c. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

d. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

e. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

6.NS.3 - Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.8 - Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.7 - Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

6.EE.9 - Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

6.G.3 - Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

UNIT 9 - Distribution & Variability Develop understanding of statistical variability.

6.SP.1 - Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

6.SP.2 - Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

6.SP.3 - Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Summarize and describe distributions.

6.SP.4 - Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.5 - Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of

measurement. c. Giving quantitative measures of center (median and/or mean) and variability (inter-quartile range and/or

mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.


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Unit 1 - Rational Numbers & Absolute Value (16 days) 6.NS.5; 6.NS.6 a, b, c; 6.NS.7 a, b, c, d; 6.NS.8; 6.G.3

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6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Students will be able to: represent and describe quantities in real

world situations using positive and negative numbers.

explain where zero fits into real world situation represented by integers.

Math 6 textbook pages

25-29 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

Students will be able to:

identify a rational number as a point on a number line.

identify the location of zero on a number line in relation to positive and negative numbers.

recognize opposite signs of numbers as locations on opposites sides of zero on a number line.


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6.NS.6 (cont.) b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.



label quadrants on a coordinate plane.

plot a point on the coordinate plane in any quadrant using ordered pairs.

recognize a reflection as being two ordered pairs that differ only in signs.

find and position integers on a horizontal and/or vertical

number line.

find and position rational numbers (fractions and decimals) on a horizontal and/or vertical number line.

find and position integers on a coordinate plane.

find and position rational numbers (fractions and decimals) on a coordinate plane.

Math 6 textbook pages

25-29

6.NS.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3° C > –7° C to express the fact that –3° C is warmer than –7° C.


Interpret statements of inequality as statements about relative position of two numbers on a number line diagram.

write statements of order for rational numbers in real- world context.

interpret statements of order for rational numbers in real-world context.

explain statements of order for rational numbers in real-world context.


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6.NS.7 (cont.)

c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than – 30 dollars represents a debt greater than 30 dollars.


define the absolute value of a rational number as its distance from 0 on a number line.

use absolute value to describe size or magnitude in a real-world situation. (Example: An ocean depth of -900 feet, write l-900l=900 to describe the distance below sea level.)

distinguish comparisons of absolute value from statements about order and apply to real world context.

Math 6 textbook

pages 25-29

6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.


solve real-world and mathematical problems by graphing points in all four quadrants.

find the distance between two points on the coordinate plane given only coordinates.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.


construct polygons in the coordinate plane given the coordinates for the vertices in real-world/ mathematical problems.

I can use given coordinates to find the length of a horizontal or vertical side joining points with the same first coordinates in real-world/mathematical problems. (If both the y-coordinates are the same (-3,2) and (4,2) then students recognize a horizontal line has been created and the distance between the coordinates is 7 units.)

Textbook Chapter 8


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Unit 2 - Fractions & Decimals (16 days) 6.NS.1; 6.NS.2; 6.NS.3

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Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.


interpret and compute quotients of fractions and mixed numbers

interpret and solve word problems involving division of fractions by fractions using visual fraction models.

interpret and solve word problems involving division of fractions by fractions using equations.

create word problems involving division of fractions by fractions.

Commoncoresheet.com

Textbook pages 129-133

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.


fluently divide multi-digit whole numbers using the standard algorithm with speed and accuracy.

Textbook Activity Page 121, 128

Textbook page 515

6.NS.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.


fluently add multi-digit decimals using the

standard algorithm with speed and accuracy

fluently subtract multi-digit decimals using the standard algorithm with speed and accuracy

fluently multiply multi-digit decimals using the standard algorithm with speed and accuracy

fluently divide multi-digit decimals using the standard algorithm with speed and accuracy

Textbook page 216

10/8 – 10/23 – Benchmark #1 Window (30% of standards assessed)

10/23 – Quarter 1 Ends


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Unit 3 – Ratios (19 days) 6.RP.3c; 6.RP.1; 6.RP.3a

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6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.



convert among fractions, decimals, and

percents.

solve problems finding the whole, given the part and the percent. (Example: % x of= is)

explain that a percent is a ratio of a number to 100.

Textbook Chapter 5

Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”


describe a ratio relationship by

comparing two quantities using ratio language.

write a ratio notation using a colon, the word “to”, and in fraction form.

write a ratio in simplest form.

analyze ratios to determine if they are equivalent.

6.RP.3



complete a table of equivalent ratios with whole number values including measurements.

create a function table and compare proportional quantities and plot those pairs of values on a coordinate plane.


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Unit 4 – Expressions (15 days) 6.NS.4; 6.EE.1; 6.EE.2; 6.EE.3; 6.EE.4

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6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2).


derive the greatest common factor of two whole numbers less than or equal to 100

derive the least common multiple of two whole numbers less than or equal to 12 identify the distributive property

apply the distributive property to express the sum of two whole numbers 1-100

Textbook pages 66-77

Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.


write numerical expressions involving whole-number exponents.

evaluate numerical expressions involving whole-number exponents.

solve order of operations that contain exponents.

Textbook Chapter 4

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient); view one or more parts of an expression as a single entity.

For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.


translate written phrases into algebraic expressions.

translate algebraic expressions into written phrases.

evaluate algebraic expressions using variables.

identify the parts of an expression using

mathematical terms. (sum, term, product, factor, quotient, coefficient)

identify the terms of an expression.

identify parts of an expression as a single entity, even if not a monomial


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c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.


evaluate expressions, substituting specific values for variables.

apply a formula to evaluate expressions using real world problems.

solve an expression with exponents. solve an expression with the Order of

Operations without parentheses.

Textbook Chapter 4

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.


identify properties of operations

(associative, commutative, distributive, identity, and zero).

apply the properties of operations to generate equivalent expressions.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.


justify that two expressions are equivalent regardless of which value is substituted.


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Unit 5 - Equations and Inequalities (14 days) 6.RP.3; 6.EE.5; 6.EE.6; 6.EE.7; 6.EE.8

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b. Solve unit rate problems including those involving unit pricing and constant speed.

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?






solve unit rate problems involving unit

pricing.

solve unit rate problems involving constant speed

convert among fractions, decimals, and percentages.

solve problems finding the whole, given the part and the percent. (Example: % x of= is)

explain that a percent is a ratio of a number to 100.

convert measurement units using ratios.

Textbook Chapter 5

Reason about and solve one-variable equations and inequalities

6.EE.5 Understand solving an equation or inequality as a process of answ ering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.


solve equations. solve inequalities. determine whether a given number

makes an equation or an inequality true using substitution.

Math 6 textbook Chapter 4

Math 7 textbook

Chapter 2


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Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.


use variables to represent unknown numbers.

write variable expressions when solving real-world/mathematical problems.

solve a variable expression using substitution in a real-world situation.


Math 7 textbook

Chapter 2

6.EE.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.


define inverse operation.

use inverse operation to solve one-variable equations.

write mathematical equations for real-world situations using nonnegative rational numbers.

solve mathematical equations for real-world situations using nonnegative rational numbers.

6.EE.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.


write an inequality based on a number line.

graph solutions to inequalities. represent possible solutions to

inequalities. justify that there are infinite solutions

to an inequality.

2/1 – 2/19 - Benchmark #2 Window (69% of standards assessed)

1/15 Quarter 2 Ends


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CC Standard Learning Objective Resources

Unit 6 – Rate (21 days) 6.RP.1*; 6 RP.2; 6.RP.3a, b, d*; 6.EE.9

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Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.1* Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”


describe a ratio relationship by comparing two quantities using ratio language.

write a ratio notation using a colon, the word “to”, and in fraction form.

write a ratio in simplest form.

analyze ratios to determine if they are equivalent.

Textbook Chapter 5

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”


can define a unit.

can define a rate.

can write a unit rate as a ratio.

can describe a unit rate using rate language.







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6.RP.3 (cont.)

b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.


solve unit rate problems involving unit pricing.



Textbook Chapter 5

Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.


define independent and dependent variables.

use variables to represent two different quantities in a real-world problem that change in relationship to one another.

complete a function table for a real-world situation that uses variables.

create a function table for a real-world situation that uses variables.

create a graph that represents two different quantities from a function table.

write equations for a given function table.

analyze the relationship between the dependent and independent variables.


Math 7 textbook

Chapter 2


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Unit 7 - Surface Area & Volume (14 days) 6.G.1; 6.G.2; 6.G.4

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Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.


discuss, develop, apply and justify formulas for triangles and parallelograms.

apply the techniques of composing and/or decomposing to find the area of triangles, special quadrilaterals and polygons to solve mathematical and real world situations. (complex figures).

Textbook Chapter 8

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

find the volume of a rectangular prism

using unit cubes. find the volume of a rectangular prism

using the formula V=l*w*h.

6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

construct a net of three dimensional figures made up of rectangles and triangles.

apply knowledge of calculating the area of rectangles and triangles to a net and combine the areas for each shape into one answer representing the surface area of a 3-d figure.

solve real world and mathematical problems involving surface area using nets.

4/4 – 4/15 - Benchmark #3 window (100% of standards assessed)

3/23 Quarter 3 Ends


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Unit 8 - Putting Mathematics to Work (review) (10 days) 6.RP.3a, b, d; 6.NS.3; 6.NS.8; 6.EE.6; 6.EE.7; 6.EE.9; 6.G.3

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b. Solve unit rate problems including those involving unit pricing and constant speed.

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?



complete a table of equivalent ratios with

whole number values including measurements.


solve unit rate problems involving unit pricing.



Textbook Chapter 5

6.NS.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.


fluently add multi-digit decimals using the standard algorithm with speed and accuracy

fluently subtract multi-digit decimals using the standard algorithm with speed and accuracy

fluently multiply multi-digit decimals using the standard algorithm with speed and accuracy

fluently divide multi-digit decimals using the standard algorithm with speed and accuracy

Textbook page 216


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solve real-world and mathematical problems by graphing points in all four quadrants.

find the distance between two points on the coordinate plane given only coordinates.

6.EE.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.


use variables to represent unknown

numbers. write variable expressions when

solving real-world/mathematical problems.

solve a variable expression using substitution in a real-world situation.

6.EE.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.


define inverse operation.

use inverse operation to solve one-variable equations.

write mathematical equations for real-world situations using nonnegative rational numbers.

solve mathematical equations for real-world situations using nonnegative rational numbers.


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6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.


define independent and dependent variables.

use variables to represent two different quantities in a real-world problem that change in relationship to one another.

complete a function table for a real-world situation that uses variables.

create a function table for a real-world situation that uses variables.

create a graph that represents two different quantities from a function table.

write equations for a given function table.

analyze the relationship between the dependent and independent variables.



construct polygons in the coordinate plane given the coordinates for the vertices in real-world/ mathematical problems.

use given coordinates to find the length of a horizontal or vertical side joining points with the same first coordinates in real-world/mathematical problems. (If both the y-coordinates are the same (-3,2) and (4,2) then students recognize a horizontal line has been created and the distance between the coordinates is 7 units.)

Textbook Chapter 8


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CAASPP Testing (1 week per subject/grade) 5/2 - 5/27



Unit 9 - Distributions & Variability 6.SP.1; 6.SP.2; 6.SP.3; 6.SP.4; 6.SP.5 a, b, c, d

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Develop understanding of statistical variability.

6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.


distinguish between a statistical and

non-statistical question. recognize that data can have

variability.

Chapter 10

6.SP.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Students will be able to: describe data distribution by its

center (median/mean). describe data distribution by its

spread (range). describe data distribution by its data

clusters, peaks, gaps, symmetry, and overall shape (line plot).

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.


calculate the range, median, mean, and mode of asset of data.

summarize a set of data using the measures of central tendencies.

describe the variability by examining graphs of data for spread and overall shape.


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Summarize and describe distributions.

6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Students will be able to: identify the components of dot plots,

histograms, and box plots. find the median quartile an

interquartile range of a set of data. display numerical data on a number

line. display numerical data on a scatter

plot. display numerical data in a histogram. display numerical data on a box-and-

whisker plot.

Chapter 10

6.SP.5 Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (inter-quartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.


organize and display data in tables and graphs.

summarize numerical data sets by reporting the number of observations in a data set or display.

describe the collected data, including

how it was measured and its units of measurement.

find and choose the appropriate measure of central tendencies to represent the data.

describe overall patterns on a variety of graphs.

describe the striking deviations (outliers) on a variety of graphs.


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6.SP.5 (cont.) d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.


choose the appropriate measures of

central tendency and variability and justify why this measure is appropriate in terms of the context.

Chapter 10

5/31 - 6/6 - Quarter 4 Assessment Window

6/8 Quarter 4 Ends


MATH 6 CCSS BLUEPRINT – PUSD 2015-2016

STANDARD Benchmark 1 Benchmark 2 Benchmark 3

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ration reasoning to solve problems.

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

X X

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

X

6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

X X


X X


X X


X X

THE NUMBER SYSTEM Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

X X X

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. X X X

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

X X X

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2).

X X


6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

X X X



6.NS.6

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

X X X

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

X X X


X X X

6.NS.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

X X X

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3° C > –7° C to express the fact that –3° C is warmer than –7° C.

X X X

c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

X X X

d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

X X X


X X X

EXPRESSIONS AND EQUATIONS Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. X X 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

a. Write expressions that record operations with numbers and with letters standing for numbers. For

example, express the calculation “Subtract y from 5” as 5 – y.

X X

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

X X



6.EE.2 (cont.)

c. Evaluate expressions at specific values of their variables. Include expressions that arise from

formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.

X X

6.EE.3 Apply the properties of operations to generate equivalent expressions. X X

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

X X

Reason about and solve one-variable equations and inequalities

6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

X X

6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

X X

6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

X X

6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

X X


6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

X

GEOMETRY Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing

into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

X

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

X




X X X

6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

X

STATISTICS AND PROBABILITY Develop understanding of statistical variability. 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question

and accounts for it in the answers. X

6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

X

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. X

Summarize and describe distributions. 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. X

6.SP.5 Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations. X

b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

X

c. Giving quantitative measures of center (median and/or mean) and variability (inter-quartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

X

d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

X

Documents

Teaching Guide for Common Core Curriculum€¦ · KEY: Bold = 1ST Introduced Italicized = Spiraling Underlined = Essential REVISED 7.27.15 Pittsburg Unified School District Math 6