Chesterfield Elementary School Mathematics Curriculum

Chesterfield Elementary School Mathematics Curriculum

FIRST GRADE MATHEMATICS CURRICULUM

MODULE 1 Sums and Differences to 10

Recommended Pacing: 45 days

NJSLS Addressed: Represent and solve problems involving addition and subtraction.

● 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and subtraction. ● 1.OA.3 Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is

known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

● 1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. Add and subtract within 20.

● 1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). ● 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8

+ 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations. ● 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the

following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. ● 1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown

number that makes the equation true in each of the equations 8 + ? = 11, 5 = ☐ – 3, 6 + 6 = ☐. Math Practices:

● MP.2 Reason abstractly and quantitatively. ● MP.6 Attend to precision. ● MP.7 Look for and make use of structure. ● MP.8 Look for and express regularity in repeated reasoning.

Interdisciplinary Connections: ● SL.1.1. Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups. A. Follow

agreed-upon norms for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). B. Build on others’

Adopted January 2019


talk in conversations by responding to the comments of others through multiple exchanges. C. Ask questions to clear up any confusion about the topics and texts under discussion.

● SL.1.3. Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood. ● SL.1.5. Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings.

Technology Integration: ● 8.1.2.A.4 Demonstrate developmentally appropriate navigation skills in virtual environments (i.e. games, museums).

Essential Questions Enduring Understandings

● How do mathematical ideas interconnect and build on one another to produce a coherent whole?

● How can we compare and contrast numbers? ● How can counting, measuring, or labeling help to make sense of the

world around us? ● What makes a computational strategy both effective and efficient? ● How do operations affect numbers? ● How can change be best represented mathematically? ● How can patterns, relations, and functions be used as tools to best

describe and help explain real-life situations? ● How are different strategies be helpful when solving a problem? ● In what ways can operations (subtraction and addition) affect numbers?

● A quantity can be represented in various ways. ● Problem solving depends on choosing effective ways. ● Numeric fluency includes both the understanding of and the ability to

appropriately use numbers. ● One representation may sometimes be more helpful than another; and, used

together, multiple representations give a fuller understanding of a problem.. ● Many problems can be solved using adding and subtracting skills.

Student Objectives

Students will learn: ● Embedded Numbers and Decompositions ● Counting On from Embedded Numbers ● Addition Word Problems ● Strategies for Counting On ● The Commutative Property of Addition and the Equal Sign Development of Addition Fluency Within 10 ● Subtraction as an Unknown Addend Problem ● Subtraction Word Problems ● Decomposition Strategies for Subtraction ● Development of Subtraction Fluency Within 10



21st Century Life & Career Skills Standards

21st Century Practices

CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP8. Use critical thinking to make sense of problems and persevere in solving them. CRP9. Model integrity, ethical leadership and effective management. CRP12. Work productively in teams while using cultural global competence.

Materials: Personal White Boards ● Number bonds 1 heavy duty clear sheet protector ● Addition chart 1 piece of stiff red tag board 11" × 8 ¼" ● Rekenrek 1 piece of stiff white tag board 11" × 8 ¼" ● Counters 1 3" × 3" piece of dark synthetic cloth for an eraser (e.g., felt) ● Number path 1 low odor blue dry erase marker, fine point ● 5-Group cards ● Hide Zero cards

Assessment Evidence

Classroom Evidence: ● Exit Tickets ● Sprints ● Homework ● Teacher Observations ● Checklists ● Performance Tasks

Other Evidence: ● Report Cards ● Curriculum Based Assessment per Marking Period (Non-Graded) ● Cumulative Curriculum Based Assessments ● Mid-Module Assessment and Rubric ● End of Module Assessment with Rubric

Learning Plan

Learning Activities (may include, but are not limited to the following) Topic A: Embedded Numbers and Decompositions Lesson 1: Analyze and describe embedded numbers (to 10) using 5-groups and number bonds.



Lesson 2: Reason about embedded numbers in varied configurations using number bonds. Lesson 3: See and describe numbers of objects using 1 more within 5-group configurations. Topic B: Counting On from Embedded Numbers Lessons 4–5: Represent put together situations with number bonds. Count on from one embedded number or part to totals of 6 and 7, and generate all addition expressions for each total. Lessons 6–7: Represent put together situations with number bonds. Count on from one embedded number or part to totals of 8 and 9, and generate all expressions for each total. Lesson 8: Represent all the number pairs of 10 as number bonds from a given scenario, and generate all expressions equal to 10. Topic C: Addition Word Problems Lesson 9: Solve add to with result unknown and put together with result unknown math stories by drawing, writing equations, and making statements of the solution. Lesson 10: Solve put together with result unknown math stories by drawing and using 5-group cards. Lesson 11: Solve add to with change unknown math stories as a context for counting on by drawing, writing equations, and making statements of the solution. Lesson 12: Solve add to with change unknown math stories using 5-group cards. Lesson 13: Tell put together with result unknown, add to with result unknown, and add to with change unknown stories from equations. Topic D: Strategies for Counting On Lessons 14–15: Count on up to 3 more using numeral and 5-group cards and fingers to track the change. Lesson 16: Count on to find the unknown part in missing addend equations such as 6 + __ = 9. Answer, “How many more to make 6, 7, 8, 9, and 10?” Topic E: The Commutative Property of Addition and the Equal Sign Lessons 17–18: Understand the meaning of the equal sign by pairing equivalent expressions and constructing true number sentences. Lesson 19: Represent the same story scenario with addends repositioned (the commutative property). Lesson 20: Apply the commutative property to count on from a larger addend. Topic F: Development of Addition Fluency Within 10 Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Lesson 22: Look for and make use of repeated reasoning on the addition chart by solving and analyzing problems with common addends. Lesson 23: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. Lesson 24: Practice to build fluency with facts to 10. Topic G: Subtraction as an Unknown Addend Problem Lesson 25: Solve add to with change unknown math stories with addition, and relate to subtraction. Model with materials, and write corresponding number sentences. Lessons 26–27: Count on using the number path to find an unknown part. Topic H: Subtraction Word Problems Lesson 28: Solve take from with result unknown math stories with math drawings, true number sentences, and statements, using horizontal marks to cross off what is taken away. Lesson 29: Solve take apart with addend unknown math stories with math drawings, equations, and statements, circling the known part to find the unknown. Lesson 30: Solve add to with change unknown math stories with drawings, relating addition and subtraction. Lesson 31: Solve take from with change unknown math stories with drawings. Lesson 32: Solve put together/take apart with addend unknown math stories Topic I: Decomposition Strategies for Subtraction Lesson 33: Model 0 less and 1 less pictorially and as subtraction number sentences. Lesson 34: Model n – n and n – (n – 1) pictorially and as subtraction sentences. Lesson 35: Relate subtraction facts involving fives and doubles to corresponding decompositions.



Lesson 36: Relate subtraction from 10 to corresponding decompositions. Lesson 37: Relate subtraction from 9 to corresponding decompositions. Topic J: Development of Subtraction Fluency Within 10 Lesson 38: Look for and make use of repeated reasoning and structure, using the addition chart to solve subtraction problems. Lesson 39: Analyze the addition chart to create sets of related addition and subtraction facts.

Core Materials and Good Links: ● Eureka Math Program Materials ● Great Minds www.greatminds.net

o Great Minds Parent Resources o Homework Helpers NEW o Grade Roadmaps o Module Tip Sheets o Videos o FAQs o Additional Online Resources

● Zearn Math www.zearn.com ● Triple A Math www.aaamath.com ● ABC Ya Math Games www.abcya.com ● Buck Institute for Education www.bie.org ● Front Row www.Frontrow.com ● Lafayette Parrish School System www.lpssonline.com ● Barrington Public Schools www.bpsk-5math.weebly.com ● Ten Marks www.tenmarks.com ● IXL Fun Math Practice www.ixl.com ● Learn Zillion www.learnzillion.com ● Common Core Sheets www.commoncoresheets.com ● Youtube www.youtube.com ● Teacher Tube www.teachertube.com ● Real World Math (Google Earth) www.realworldmath.org ● Moby Math www.mobymax.com ● Kahn Academy Math www.kahnacademy.org ● Illuminations www.illuminations.nctm.org ● Math Playground www.mathplayground.com ● Sum Dog www.sumdog.com



English Language Learner - Retell content information in easier English

Use simple sentence structure (verb-subject-object)

Use high frequency words

Provide concrete examples of vocabulary words through the use of visuals

Model Think Alouds to increase student comprehension

Directly teach learning strategies

Provide small group instruction

Provide preferential seating

Provide models and manipulatives

Special Education

Seat student near model (student/teacher)

Seat student near instruction

Repeat major points of information

Provide visual cues (anchor charts, post-it reminders)

Reteach new vocabulary and key words

Provide sentence starters for discussion


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Vary the method of lesson presentation using multi-sensory techniques

Ask student to repeat/paraphrase context to check understanding

Simplify and repeat instructions

Vary instructional pace

Set time expectations for assignments

Provide clues such as clock faces indicating beginning and ending times

At-Risk Learners


Provide small group or individual instruction

Reinforce the use of compensatory strategies

Reinforce self-monitoring and self-reflecting strategies

Buddy in class to assist and clarify

Actively help students build connections and associations in order to access background

knowledge or previously taught information



Provide visual cues (posters, number lines, gestures, use of technology)

Gifted & Talented Learners

Allow student to skip mastered material

Provide student with alternate materials that are application based to extend thinking

Focus on higher DOK questions and tasks



FIRST GRADE MODULE 2

Introduction to Place Value Through Addition and Subtraction Within 20


NJSLS Addressed: Represent and solve problems involving addition and subtraction


● 1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and subtraction ● 1.OA.3 Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is

known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

● 1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. Add and subtract within 20

● 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Understand place value ● 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

● a. 10 can be thought of as a bundle of ten ones—called a “ten.” ● b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

Math Practices: ● MP.2 Reason abstractly and quantitatively. ● MP.4 Model with mathematics. ● MP.7 Look for and make use of structure. ● MP.8 Look for and make use of repeated reasoning.


agreed-upon norms for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). B. Build on others’ talk in conversations by responding to the comments of others through multiple exchanges. C. Ask questions to clear up any confusion about the topics and texts under discussion.






● How can counting help to make sense of the world around us? ● What makes a computational strategy both effective and efficient? ● How can change be best represented mathematically? ● How can patterns, relations, and functions be used as tools to best

describe and help explain real-life situations? ● In what ways can operations (subtraction and addition) affect

numbers? ● How can 10s be helpful when adding and subtracting?

● One representation may sometimes be more helpful than another; and, used together, multiple representations give a fuller understanding of a problem.

● A quantity can be represented in various ways. ● Problem solving depends on choosing effective ways. ● Numeric fluency includes both the understanding of and the ability to

appropriately use numbers.

Student Objectives

Students will learn: ● Counting On or Making Ten to Solve Result Unknown and Total Unknown Problems ● Counting On or Taking from Ten to Solve Result Unknown and Total Unknown Problems ● Strategies for Solving Change or Addend Unknown Problems ● Varied Problems with Decompositions of Teen Numbers as 1 Ten and Some Ones




Materials: ● 5-group formations: 5-groups (and 5-group cards), 5-group rows, 5-group column ● Hide Zero cards ● Number bonds ● Number path



● Rekenrek

Assessment Evidence



Learning Plan

Learning Activities (may include, but are not limited to the following) Topic A: Counting On or Making Ten to Solve Result Unknown and Total Unknown Problems Lesson 1: Solve word problems with three addends, two of which make ten. Lesson 2: Use the associative and commutative properties to make ten with three addends. Lessons 3–4: Make ten when one addend is 9. Lesson 5: Compare efficiency of counting on and making ten when one addend is 9. Lesson 6: Use the commutative property to make ten. Lessons 7–8: Make ten when one addend is 8. Lesson 9: Compare efficiency of counting on and making ten when one addend is 8. Lesson 10: Solve problems with addends of 7, 8, and 9. Lesson 11: Share and critique peer solution strategies for put together with total unknown word problems. Topic B: Counting On or Taking from Ten to Solve Result Unknown and Total Unknown Problems Lessons 12–13: Solve word problems with subtraction of 9 from 10. Lessons 14–15: Model subtraction of 9 from teen numbers. Lesson 16: Relate counting on to making ten and taking from ten. Lessons 17–18: Model subtraction of 8 from teen numbers. Lesson 19: Compare efficiency of counting on and taking from ten. Lesson 20: Subtract 7, 8, and 9 from teen numbers. Lesson 21: Share and critique peer solution strategies for take from with result unknown and take apart with addend unknown word problems from the teens. Topic C: Strategies for Solving Change or Addend Unknown Problems Lesson 22: Solve put together/take apart with addend unknown word problems, and relate counting on to the take from ten strategy. Lesson 23: Solve add to with change unknown problems, relating varied addition and subtraction strategies. Lesson 24: Strategize to solve take from with change unknown problems. Lesson 25: Strategize and apply understanding of the equal sign to solve equivalent expressions.



Topic D: Varied Problems with Decompositions of Teen Numbers as 1 Ten and Some Ones Lesson 26: Identify 1 ten as a unit by renaming representations of 10. Lesson 27: Solve addition and subtraction problems decomposing and composing teen numbers as 1 ten and some ones. Lesson 28: Solve addition problems using ten as a unit, and write two-step solutions. Lesson 29: Solve subtraction problems using ten as a unit, and write twostep solutions.




English Language Learner - At-Risk Learners



Retell content information in easier English









Special Education








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FIRST GRADE MODULE 3 Ordering and Comparing Length Measurements as Numbers




Measure lengths indirectly and by iterating length units. ● 1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. ● 1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand

that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Represent and interpret data. ● 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each

category, and how many more or less are in one category than in another. Math Practices:

● MP.2 Reason quantitatively and abstractly. ● MP.3 Construct viable arguments and critique the reasoning of others.. ● MP.6 Attend to precision. ● MP.7 Look for and make use of structure.






● How can measurements be used to solve problems? ● Measurements can be used to describe, compare, and make sense of phenomena. ● One representation may sometimes be more helpful than another; and, used




● How can different strategies be helpful when solving a problem? ● In what ways can operations (subtraction and addition) affect

numbers? ● How can I compare and contrast objects to understand

measurement? ● In what ways can collecting, organizing, and interpreting data be

helpful when answering questions about size, length, and quantity?

together, multiple representations give a fuller understanding of a problem. ● A quantity can be represented in various ways. Problem solving depends on

choosing effective ways. ● Many real world problems can be solved using addition and subtraction skills. ● Measurement helps to compare and contrast objects. ● Models, data and measurement tools help understanding of math applications.

Student Objectives

Students will learn: ● Indirect Comparison in Length Measurement ● Topic B: Standard Length Units ● Topic C: Non-Standard and Standard Length Units ● Topic D: Data Interpretation




Materials: ● Centimeter cubes ● Centimeter rulers (simply for the purpose of naming the centimeter) ● Non-standard units (toothpicks, small and large paper clips) ● String lengths of about 25 centimeters ● Tally marks

Assessment Evidence





Learning Plan

Learning Activities (may include, but are not limited to the following) Topic A: Indirect Comparison in Length Measurement Lesson 1: Compare length directly and consider the importance of aligning endpoints. Lesson 2: Compare length using indirect comparison by finding objects longer than, shorter than, and equal in length to that of a string. Lesson 3: Order three lengths using indirect comparison. Topic B: Standard Length Units Lesson 4: Express the length of an object using centimeter cubes as length units to measure with no gaps or overlaps. Lesson 5: Rename and measure with centimeter cubes, using their standard unit name of centimeters. Lesson 6: Order, measure, compare the length of objects before and after measuring with centimeter cubes, solving compare with difference unknown word problems. Topic C: Non-Standard and Standard Length Units Lesson 7: Measure the same objects from Topic B with different nonstandard units simultaneously to see the need to measure with a consistent unit. Lesson 8: Understand the need to use the same units when comparing measurements with others. Lesson 9: Answer compare with difference unknown problems about lengths of two different objects measured in centimeters. Topic D: Data Interpretation Lessons 10–11: Collect, sort, and organize data; then ask and answer questions about the number of data points. Lessons 12–13: Ask and answer varied word problem types about a data set with three categories.


o Great Minds Parent Resources o Homework Helpers NEW o Grade Roadmaps o Module Tip Sheets o Videos o FAQs



o Additional Online Resources ● Zearn Math www.zearn.com ● Triple A Math www.aaamath.com ● ABC Ya Math Games www.abcya.com ● Buck Institute for Education www.bie.org ● Front Row www.Frontrow.com ● Lafayette Parrish School System www.lpssonline.com ● Barrington Public Schools www.bpsk-5math.weebly.com ● Ten Marks www.tenmarks.com ● IXL Fun Math Practice www.ixl.com ● Learn Zillion www.learnzillion.com ● Common Core Sheets www.commoncoresheets.com ● Youtube www.youtube.com ● Teacher Tube www.teachertube.com ● Real World Math (Google Earth) www.realworldmath.org ● Moby Math www.mobymax.com ● Kahn Academy Math www.kahnacademy.org ● Illuminations www.illuminations.nctm.org ● Math Playground www.mathplayground.com ● Sum Dog www.sumdog.com










Special Education





At-Risk Learners




















504







FIRST GRADE MODULE 4 Place Value, Comparison, Addition and Subtraction to 40


NJSLS Addressed: Represent and solve problems involving addition and subtraction

● 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (See CCLS Glossary, Table 1.)

Extend the counting sequence ● 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Understand place value ● 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

● a. 10 can be thought of as a bundle of ten ones—called a “ten.” ● b. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

● 1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Use place value understanding and properties of operations to add and subtract

● 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.



● 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. ● 1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and

strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used

Math Practices: ● MP.3 Construct viable arguments and critique the reasoning of others. ● MP.5 Use appropriate tools strategically. ● MP.6 Attend to precision. ts. ● MP.7 Look for and make use of structure.






● How can we compare and contrast numbers? ● What makes a computational strategy both effective and efficient? ● How can patterns, relations, and functions be used as tools to best

describe and help explain real-life situations? ● What are efficient ways to count? ● How does counting by tens and ones help you count larger

numbers? (Skip Counting) ● What is place value? ● How does a digit’s position affect its value? ● How can numbers be expressed and compared? ● In what ways can numbers be composed and decomposed?

● A quantity can be represented in various ways. Problem solving depends on choosing effective ways.

● Numeric fluency includes both the understanding of and the ability to appropriately use numbers.

● The base 10 numbers are recorded using digits 0 – 9, groups of ten, and place value.

Student Objectives

Students will learn: ● Tens and Ones ● Comparison of Pairs of Two-Digit Numbers



● Addition and Subtraction of Tens ● Addition of Tens or Ones to a Two-Digit Number ● Varied Problem Types Within 20 ● Addition of Tens and Ones to a Two-Digit Number




Materials: ● Arrow notation Comparison symbols: >, <, = Dime ● Hide Zero cards Hundred chart Number bond ● Penny Place value chart en Rekenrek ● Tape diagram

Assessment Evidence



Learning Plan

Learning Activities (may include, but are not limited to the following) Topic A: Tens and Ones

Lesson 1: Compare the efficiency of counting by ones and counting by tens.



Lesson 2: Use the place value chart to record and name tens and ones within a two-digit number. Lesson 3: Interpret two-digit numbers as either tens and some ones or as all ones. Lesson 4: Write and interpret two-digit numbers as addition sentences that combine tens and ones. Lesson 5: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit number. Lesson 6: Use dimes and pennies as representations of tens and ones. Topic B: Comparison of Pairs of Two-Digit Numbers

Lesson 7: Compare two quantities, and identify the greater or lesser of the two given numerals. Lesson 8: Compare quantities and numerals from left to right. Lessons 9–10: Use the symbols >, =, and < to compare quantities and numerals. Topic C: Addition and Subtraction of Tens

Lesson 11: Add and subtract tens from a multiple of 10. Lesson 12: Add tens to a two-digit number. Topic D: Addition of Tens or Ones to a Two-Digit Number

Lessons 13–14: Use counting on and the make ten strategy when adding across a ten. Lesson 15: Use single-digit sums to support solutions for analogous sums to 40. Lessons 16–17: Add ones and ones or tens and tens. Lesson 18: Share and critique peer strategies for adding two-digit numbers. Topic E: Varied Problem Types Within 20

Lesson 19: Use tape diagrams as representations to solve put together/take apart with total unknown and add to with result unknown word problems. Lessons 20–21: Recognize and make use of part–whole relationships within tape diagrams when solving a variety of problem types. Lesson 22: Write word problems of varied types. Topic F: Addition of Tens and Ones to a Two-Digit Number

Lesson 23: Interpret two-digit numbers as tens and ones, including cases with more than 9 ones. Lessons 24–25: Add a pair of two-digit numbers when the ones digits have a sum less than or equal to 10. Lessons 26–27: Add a pair of two-digit numbers when the ones digits have a sum greater than 10. Lessons 28–29: Add a pair of two-digit numbers with varied sums in the ones.


o Great Minds Parent Resources o Homework Helpers NEW o Grade Roadmaps



o Module Tip Sheets o Videos o FAQs o Additional Online Resources











Special Education



At-Risk Learners




















504









FIRST GRADE MODULE 5 Identifying, Composing, and Partitioning Shapes


NJSLS Addressed: Tell and write time and money.1

● 1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks. Recognize and identify coins, their names, and their values. Reason with shapes and their attributes.

● 1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

● 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)

● 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Math Practices: ● MP.1 Make sense of problems and persevere in solving them. ● MP.6 Attend to precision.



● MP.7 Look for and make use of structure. Interdisciplinary Connections:

● SL.1.1. Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups. A. Follow agreed-upon norms for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). B. Build on others’ talk in conversations by responding to the comments of others through multiple exchanges. C. Ask questions to clear up any confusion about the topics and texts under discussion.




● How do geometric relationships help us solve problems and/or make sense of phenomena?

● How can measurements be used to solve problems? ● How can attributes be used to classify data/objects? ● How can plane and solid shapes be described? ● What are the characteristics (attributes) of a shape? ● How can circles, squares, and rectangles be divided (partitioned) into

equal parts? ● How are numbers used to show fractions? ● How are portioned shapes used to show fractions?

● Geometric properties can be used to construct geometric figures. ● Geometric relationships provide a means to make sense of a variety of

phenomena. ● Everyday objects have a variety of attributes, each of which can be

measured in many ways. ● Grouping by attributes (classification) can be used to answer mathematical

questions. ● Geometric language is important to identify features of shapes.

Student Objectives

Students will learn: ● Attributes of Shapes ● Part–Whole Relationships Within Composite Shapes ● Halves and Quarters of Rectangles and Circles ● Application of Halves to Tell Time



CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason.



CRP6. Demonstrate creativity and innovation. CRP8. Use critical thinking to make sense of problems and persevere in solving them. CRP9. Model integrity, ethical leadership and effective management. CRP12. Work productively in teams while using cultural global competence.

Materials: ● Pattern blocks, Square tiles, Straws ● Student clocks, preferably with gears that can provide the appropriate hour-hand alignment ● Three-dimensional shape models (commercially produced or commonly found examples) including cube, cone, cylinder, rectangular prism, and sphere

Assessment Evidence



Learning Plan

Learning Activities (may include, but are not limited to the following) Topic A: Attributes of Shapes Lesson 1: Classify shapes based on defining attributes using examples, variants, and non-examples. Lesson 2: Find and name two-dimensional shapes including trapezoid, rhombus, and a square as a special rectangle, based on defining attributes of sides and corners. Lesson 3: Find and name three-dimensional shapes including cone and rectangular prism, based on defining attributes of faces and points Topic B: Part–Whole Relationships Within Composite Shapes Lesson 4: Create composite shapes from two-dimensional shapes. Lesson 5: Compose a new shape from composite shapes. Lesson 6: Create a composite shape from three-dimensional shapes and describe the composite shape using shape names and positions. Topic C: Halves and Quarters of Rectangles and Circles Lesson 7: Name and count shapes as parts of a whole, recognizing relative sizes of the parts. Lessons 8–9: Partition shapes and identify halves and quarters of circles and rectangles. Topic D: Application of Halves to Tell Time



Lesson 10: Construct a paper clock by partitioning a circle and tell time to the hour. Lessons 11–13: Recognize halves within a circular clock face and tell time to the half-hour.


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FIRST GRADE MODULE 6 Place Value, Comparison, Addition and Subtraction to 100




Extend the counting sequence. ● 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.



● Understand place value. ● 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following special cases: ● 10 can be thought of as a bundle of ten ones—called a “ten.” ● The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). ● 1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Use place value understanding and properties of operations to add and subtract. ● 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete

models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

● 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. ● 1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings

and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Tell and write time and money.1 ● 1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks. Recognize and identify coins, their names, and their values.

Math Practices: ● MP.1 Make sense of problems and persevere in solving them.. ● MP.3 Construct viable arguments and critique the reasoning of others. ● MP.4 Model with mathematics. ● MP.5 Use appropriate tools strategically.







● What makes a computational strategy both effective and efficient? ● What are efficient ways to count? ● How does counting by tens and ones help you count larger

● One representation may sometimes be more helpful than another; and, used together, multiple representations give a fuller understanding of a problem.

● A quantity can be represented in various ways. Problem solving depends on choosing effective ways.

● Numeric fluency includes both the understanding of and the ability to



numbers? (Skip Counting, Bundles, 10 Frames) ● What is place value? ● How does a digit’s position affect its value? ● How can numbers be expressed and compared? ● In what ways can numbers be composed and decomposed? ● What is measured when we are telling time?

appropriately use numbers. ● Computational fluency includes understanding not only the meaning, but also

the appropriate use of numerical operations. ● Telling time is an essential life skill.

Student Objectives

Students will learn: ● Comparison Word Problems ● Numbers to 120 ● Addition to 100 Using Place Value Understanding ● Varied Place Value Strategies for Addition to 100 ● Coins and Their Values ● Varied Problem Types Within 20 ● Culminating Experiences




Materials: ● 100-bead Rekenrek ● Tape diagram

Assessment Evidence

Classroom Evidence: ● Exit Tickets ● Sprints

Other Evidence: ● Report Cards ● Curriculum Based Assessment per Marking Period (Non-Graded)



● Homework ● Teacher Observations ● Checklists ● Performance Tasks

● Cumulative Curriculum Based Assessments ● Mid-Module Assessment and Rubric ● End of Module Assessment with Rubric

Learning Plan

Learning Activities (may include, but are not limited to the following) Topic A: Comparison Word Problems Lesson 1: Solve compare with difference unknown problem types. Lesson 2: Solve compare with bigger or smaller unknown problem types. Topic B: Numbers to 120 Lesson 3: Use the place value chart to record and name tens and ones within a two-digit number up to 100. Lesson 4: Write and interpret two-digit numbers to 100 as addition sentences that combine tens and ones. Lesson 5: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit number within 100. Lesson 6: Use the symbols >, =, and < to compare quantities and numerals to 100. Lesson 7: Count and write numbers to 120. Use Hide Zero cards to relate numbers 0 to 20 to 100 to 120. Lesson 8: Count to 120 in unit form using only tens and ones. Represent numbers to 120 as tens and ones on the place value chart. Lesson 9: Represent up to 120 objects with a written numeral. Topic C: Addition to 100 Using Place Value Understanding Lesson 10: Add and subtract multiples of 10 from multiples of 10 to 100, including dimes. Lesson 11: Add a multiple of 10 to any two-digit number within 100. Lesson 12: Add a pair of two-digit numbers when the ones digits have a sum less than or equal to 10. Lessons 13–14: Add a pair of two-digit numbers when the ones digits have a sum greater than 10 using decomposition. Lesson 15: Add a pair of two-digit numbers when the ones digits have a sum greater than 10 with drawing. Record the total below. Lessons 16–17: Add a pair of two-digit numbers when the ones digits have a sum greater than 10 with drawing. Record the new ten below. Topic D: Varied Place Value Strategies for Addition to 100 Lesson 18: Add a pair of two-digit numbers with varied sums in the ones, and compare the results of different recording methods. Lesson 19: Solve and share strategies for adding two-digit numbers with varied sums. Topic E: Coins and Their Values Lesson 20: Identify pennies, nickels, and dimes by their image, name, or value. Decompose the values of nickels and dimes using pennies and nickels. Lesson 21: Identify quarters by their image, name, or value. Decompose the value of a quarter using pennies, nickels, and dimes. Lesson 22: Identify varied coins by their image, name, or value. Add one cent to the value of any coin. Lesson 23: Count on using pennies from any single coin. Lesson 24: Use dimes and pennies as representations of numbers to 120. Topic F: Varied Problem Types Within 20 Lessons 25–26: Solve compare with bigger or smaller unknown problem types. Lesson 27: Share and critique peer strategies for solving problems of varied types.











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FIRST GRADE MATH VOCABULARY

Modules Vocabulary

1 ● Count on (count up from one addend to the total) ● Track (use different objects to track the count on from one addend to the total) ● Expression (e.g., 2 + 1 or 5 – 3) ● Addend (one of the numbers being added) ● Doubles (e.g., 3 + 3 or 4 + 4) ● Doubles plus 1 (e.g., 3 + 4 or 4 + 5) ● Part (e.g., “What is the unknown part? 3 + ___ = 8”) ● Total and whole (use interchangeably instead of sum; e.g., “What is the total when we add 3 and 5?”) ● Label (using letters or words on a math drawing to indicate the referents from the story’s context) ● Addition, equal, and subtraction signs ● Equation and number sentence (used interchangeably throughout the module) ● Number bond (graphic showing part–part–whole) ● Equal sign (=) ● 5-groups (as pictured in the dot cards below), 2 rows of 5 ● Sum ● Unit ● Mental Math ● True ● False ● Unknown

2 ● A ten (a group, or unit, consisting of 10 items) ● Ones (individual units, 10 of which become a ten) ● 5-groups ● Add ● Equals ● Number bonds ● Partners to ten ● Subtract, Subtraction ● Difference ● Teen numbers ● Combinations



3 ● Centimeter (standard length unit within the metric system)

● Centimeter cube (pictured to the right, also used as a length unit in this module) ● Centimeter ruler (measurement tool using length units of centimeters) ● Data (collected information) ● Inch ● Endpoint (the end of an object, referenced when aligning for measurement purposes) ● Height (measurement of vertical distance of an object) ● Length unit (measuring the length of an object with equal-sized units) ● Poll (survey) ● Table or graph (organized charts visually representing data) ● 4Less than ● Longer than/taller than ● More than ● Shorter than ● Tally marks

4 ● (greater than) ● < (less than) ● Place value (quantity represented by a digit in a particular place within a number) ● = (equal) ● Numerals ● Ones ● Tens ● Digits ● Two-digit number

5 ● Attributes (characteristics of an object such as color or number of sides) ● Composite shapes (shapes composed of two or more shapes) ● Digital clock ● Face (two-dimensional surface of a three-dimensional solid) ● Fourth of (shapes), fourths (1 out of 4 equal parts) ● Half-hour (interval of time lasting 30 minutes) ● Half of, halves (1 out of 2 equal parts) ● Half past (expression for 30 minutes past a given hour) ● Hour (unit for measuring time, equivalent to 60 minutes or 1/24 of a day) ● Hour hand (component on clock tracking hours) ● Minute (unit for measuring time, equivalent to 60 seconds or 1/60 of an hour) ● Minute hand (component on clock tracking minutes) ● O’clock (used to indicate time to a precise hour, with no additional minutes) ● Quarter of (shapes) (1 out of 4 equal parts) ● Three-dimensional shapes:



● Cone ● Rectangular prism ● Right rectangular prism ● Two-dimensional shapes: ● Half-circle ● Quarter-circle ● Rhombus (flat figure enclosed by four straight sides of the same length wherein two pairs of opposite sides are parallel) ● Trapezoid (a quadrilateral in which at least one pair of opposite sides is parallel )

1

● Clock ● Shape names (two-dimensional and three-dimensional) from Kindergarten: ● Circle ● Cube ● Cylinder ● Hexagon (flat figure enclosed by six straight sides) ● Rectangle (flat figure enclosed by four straight sides and four right angles) ● Sphere ● Square (rectangle with four sides of the same length) ● Triangle (flat figure enclosed by three straight sides)

6 ● Dime ● Nickel ● Penny ● Quarter ● <, >, = (less than, greater than, equal to)

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FIRST GRADE MATERIALS LISTFIRST GRADE MATERIALS LIST

Module 1Module 1

Lesson

Teacher manipulatives

Individual manipulatives 1 Ten frame Ten frame, 9 beads or classroom objects, number bond, white board 2 Dot cards of 6-9 (template), stopwatch or timer Dot cards of 6-9 , white board, number bond dash 5 (template), marker

3* Rekenrek, 5 group cards, stopwatch or timer, Sentence frame 1 more (template 1)

Number bond dash 5, marker, 5-group mat (template 2), bag with 9 linking cubes of the same color, 1 linking cube of another color, white board

4 Chart to record decompositions of 6 Sprint, Rekenrek, bag of 10 two-color beans/chips, 6 apple picture card (template) 5 Stopwatch or timer; number bond on the white board,

markers, chart to record decompositions of 7 Per set of partners: 6 two color chips, 1 shake those disks 6 board (template); number bond dash (template), marker, 5 group cards (template), 7 children picture card (template), scissors, glue stick, a sheet of blank paper for student debrief

6 Stopwatch or timer, 8 animals picture card (template), ways to make 8 (template)

7 counters and a die per partner; number bond dash 7 (template), marker; 5 group cards 0-8 (template), 8 animals picture card (template), black number sentence and number bond (template), personal white board, ways to make 8 (template)

7 Stopwatch or timer, 9 books picture card (template), 5 group cards (template), chart to record decompositions of 9

Per set of partners: 8 two-color chips, white boards with shake those disks 8 board (template); number bond dash 8 (template), marker; bag of 10 linking cubes: 5 of each of 2 colors, white board, number bond and expression

8 Stopwatch or timer, chart to record decompositions of 10, 10 children on the playground card (template), linking cubes in two colors

Per set of partners: 9 counters, 1 die; number bond dash 9 (template), marker; pipe cleaners, 10 beads (5 of one color, 5 of another color)

9 5 group cards (template), 10 counters, container, Stopwatch or timer

Number bond dash 10 (template), marker, white board, number bond and two blank equations (template)

10 7 children picture card (template), 10 children on the playground card (template)

Per set of partners: white board, target practice (template), 6 counters, 1 die, 5 group cards (template), number bond and two blank equations (template), 10 children on the playground card (template) per pair

11 Stopwatch or timer, mystery box (shoe box with question mark on it), counting bears, enlarged blank number sentence and number bond, number sentence cards (template) and 2x2 sticky notes labeled with question mark

Number bond dash 6 (template), marker, white board, blank number sentence and number bond (template), yellow colored pencil or a crayon, set of bear counters, paper bag labeled with question marks on the front per pair

12 5 group cards (template), stopwatch or timer, mystery box, counting bears, enlarged blank number sentence and number bond

Number bond dash 6 (template), marker, white board, blank number sentence and number bond, 5 group cards including blank, number sentence cards with sticky notes labeled with question marks per pair



13 5 group cards Per group: 1 set of single-sided 5 group cards, 1 set single-sided numeral cards (template),

number sentence cards (template) with sticky notes labeled with a question mark per, white board, blank number sentence and number bond (template)

14 Pictures of crayons and hot dogs (template) 5 group cards (template), white board 15 5 group cards (template), number sentence cards (template) per pair with sticky note

covering the total, white board

16 5 group cards, mystery box, enlarged blank number sentence and number bond, set of 7 beans from shake those disks

7 two-color chips per set of partners, white board, shake those disks 7 board (template), blank number sentence and number bond, 5 group cards, number sentence cards, sticky notes with question marks

17 7 pennies, 1 can, stopwatch or timer Number bond dash 7 (template), marker, bag of 20 linking cubes (10 red, 10 yellow), white board

18 Stopwatch or timer 5 group cards (0-7 only), Number bond dash 7 (Lesson 6 Fluency Template), marker to correct work, 5-group cards (Lesson 5 Template 1), personal white board, true and false number sentence cards (Template), red and green markers per pair

19 5-group cards 1–5 only (Lesson 5 Template 1) Personal white board, bag of 7 counters (4 red, 3 white) 20 10 linking cubes (5 cubes one color, 5 cubes another color) per pair, white boards,

Expression cards (Template 1), equal signs (Template 2) per pair

21 5-group cards (1–6) (Lesson 5 Template 1), addition chart (Template), colored pencils (yellow, orange

Per set of partners: personal white board, target practice (Lesson 10 Fluency Template), 8 counters, 1 die, Personal white board

22 8 pennies, 1 can, Stopwatch or timer, Addition chart with sums to 10 (Lesson 21 Template), cover paper

Number bond dash 8 (Lesson 7 Fluency Template 2), marker to correct work

23 Stopwatch or timer, Addition chart with sums to 10 to project or post (Lesson 21 Template), cover paper, markers (three different colors)

5-group cards (0–8 only) (Lesson 5 Template 1), Number bond dash 8 (Lesson 7 Fluency Template 2), marker to correct work, Addition chart with sums to 10 (Lesson 21 Template), pencils (three different colors)

24 Friendly Fact Go Around: Addition Strategies Review (Fluency Template), Friendly Fact Go Around (Fluency Template), Related Fact Ladder (Template 1), 10 expression cards (Template 2)

5–12 expression cards per pair

25 9 counters, container, Stopwatch or timer, 10 bear counters, number bond and number sentences (Template)

(S) Race to the Top (Fluency Template), crayons (or pencil), 1 die (replace 6 with 0) per pair, Number Bond Dash 9 (Lesson 8 Fluency Template), marker to correct work, Personal white board, number bond and number sentences (Template), 10 bear counters

26 5-group cards (0–9) (Lesson 5 Template 1), Stopwatch or timer, Giant number path

5-group cards (Lesson 5 Template 1), 1 counter, Number bond dash 9 (Lesson 8 Fluency Template), marker to correct work, Personal white board, number path (Template)

27 2 number paths (projected or charted) Die (with 6 replaced by 0), personal white board, number path (Lesson 26 Template) 28 White board 29 1 set numeral side only 5 group cards (template) per pair, counters (if needed), white board



30 Stopwatch or timer, books of different sizes Number bond dash 10 (template), marker to correct work, white board, number path,

highlighter 31 15 pennies, 1 can, stopwatch/ timer, different book sizes Number bond dash 10, marker, white board, yellow highlighter

32 10 white linking cubes 5 group cards (0-10) with 1 extra 5 card per pair, white board

33 Rekenrek, number bracelet of 10, white board or easel Number bracelet of 10 beads made with 5 red and 5 white beads, white board

34 number bracelet of 10, white board or easel Number bracelet of 10 beads made with 5 red and 5 white beads, white board 35 Number bracelet of 10 beads made with 5 red and 5 white beads, white board

36 5-group cards, number bracelet of 10, white board or easel Number bracelet, white board

37 5-group cards, number bracelet of 10 Number bracelet of 10 beads made with 5 red and 5 white beads, white board

38 Rekenrek, addition chart, subtraction expression cards addition chart, subtraction expression cards per group, yellow crayon, white board

39 Addition chart addition chart, subtraction expression cards per group, white board


Documents

Chesterfield Elementary School Mathematics Curriculum