KNOX COUNTY SCHOOLS CURRICULUM & INSTRUCTION ......Multiplicative identity property of 1- a x 1 = 1...

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KNOX COUNTY SCHOOLS CURRICULUM & INSTRUCTION DEPARTMENT

CURRICULUM FRAMEWORK

Mathematics – Grade 3

Table of Contents Module 1: Operations and Algebraic Thinking, Part 1 (Approx. 8 weeks) Module 2: Number and Operations in Base Ten (Approx. 3 weeks) Module 3: Operations and Algebraic Thinking, Part 2 (Approx. 3 weeks) Module 4: Number and Operations- Fractions (Approx. 6 weeks) Module 5: Measurement and Data (Approx. 11 weeks) Module 6: Geometry (Approx. 3 weeks) Mathematical Practices: Literacy Skills for Mathematical Proficiency: MP.1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies. MP.2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary. MP.3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas. MP.4. Model with mathematics. 4. Write mathematical arguments. MP.5. Use appropriate tools strategically. MP.6 Attend to precision. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning.

*Major Content standards are indicated with shading.

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Resources that can be used throughout the year:

KCS Math Department Website http://knoxschools.org/site/Default.aspx?PageID=2932 TN Department of Education Math Standards https://www.tn.gov/education/article/mathematics-standards Achieve the Core Coherence Map http://achievethecore.org/page/1118/coherence-map Mathematics Common Core Bookmarks http://commoncore.tcoe.org/search/1/Resources/ac841232-cced-4c8e-

8ab2-667dfee99c9a Engage New York and Eureka Math https://www.engageny.org/ and

https://greatminds.org/store/products/eureka-basic-curriculum Georgia Department Math Units https://www.georgiastandards.org/Georgia-Standards/Pages/Math-K-

5.aspx Howard County Open Canvas Course (Go to Year-at-a-Glance) https://hcpss.instructure.com/courses/97

Illustrative Math https://www.illustrativemathematics.org/ North Carolina Public Schools Tasks http://3-5cctask.ncdpi.wikispaces.net/ Grade Levels, Resources, Routines for K-5 http://www.dusd.net/cgi/ Number Talk Powerpoints https://elementarynumbertalks.wordpress.com/ EduToolbox Task Arcs Click on “Tennessee Tools” at the bottom. Go to Mathematics > Instructional Resources and select the task arc for your grade level.

edutoolbox.org Some of the task arcs are locked and you will need to sign in to access them. In order to get a login, when prompted, select “Create New Account”. You will need to use the TNCore login credentials to verify your permission: Username- tneducation Password- fastestimproving You will then receive an email with a link to set up your profile.

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Module 1: Operations and Algebraic Thinking, Part 1 Suggested Time: Approx. 8 weeks TEACHER CONTENT KNOWLEDGE Module Overview: Students build on their understanding of addition and subtraction to develop an understanding of the meanings of multiplication and division of whole numbers. Students use increasingly sophisticated strategies, such as using order and grouping or breaking apart numbers to multiply easier, based on properties of operations to fluently solve multiplication and division problems within 100. Students represents expressions using various objects, pictures, words, and symbols in order to develop their understanding of properties. They change the order of numbers to determine that the order of numbers does not make a difference in multiplication (but does in division). Given three factors, they investigate changing the order of how they multiply numbers to determine that changing the order does not change the product. They also decompose numbers to build fluency with multiplication and division. ● Associative property of addition- (a + b) + c= a + (b + c) ● Commutative property of addition- a + b = b + a ● Additive identity property of 0- a + 0 = 0 + a = a ● Associative property of multiplication- (a x b) x c = a x (b x c) ● Commutative property of multiplication- a x b = b x a ● Multiplicative identity property of 1- a x 1 = 1 x a = a ● Distributive property of multiplication over addition- a x (b + c) = a x b + a x c

Students interpret multiplication as finding an unknown product in situations involving the strategies below. They use these interpretations to represent and solve contextual problems with unknowns in all positions. ● equal-sized groups ● arrays ● area models ● measurement models

Students interpret division as finding an unknown factor in situations involving the strategies below. They use these interpretations to represent and solve contextual problems with unknowns in all positions. Understand division as the inverse relationship of a multiplication problem. ● the unknown number of groups ● the unknown group size

They build number sense by investigating numerical representations, such as addition or multiplication tables for the purpose of identifying arithmetic patterns. Multiplication and division are new concepts in 3rd grade. Reaching fluency with these operations within 100 represents a major portion of students’ work.

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Pre-Requisite Skills and Knowledge: Understand the meaning and concept of equal groups, use repeated addition, write an equation to express the total in an array or equal groups as a sum of equal addends, understand multiplication of whole numbers as finding the total number of objects, use multiplication or division equations to represent and solve a word problem, understand multiplication of whole numbers, build arrays to show repeated addition and multiplication, understand the meaning of multiplication and division, connect multiplication and division, use addition, subtraction, multiplication and division, complete an addition table and multiplication table, recognize patterns in tables, know the difference between even and odd numbers For example, in 2nd grade: Students partition a rectangle into rows and columns of same-size squares and count to find the total number of squares. (2.G.2) Partition the rectangle into 2 rows and 4 columns. How many small squares did you make?

Vocabulary: equation, multiply, factor, product, array, division, divide, dividend, divisor, quotient, fact family, pattern, rule, even number, odd number, rows, columns, partition, shares, simple, unknown, commutative, associative, distributive, unknown factor, inverse operation, fluently, reasonableness, operation, decompose, multiples, arithmetic patterns, properties of operations Fluency Practice Daily First three weeks of practice: Review 2nd grade fluency of the following standards.

• 2.NBT.A.1 Know that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 can be represented in multiple ways as 7 hundreds, 0 tens, and 6 ones; 706 ones; or 70 tens and 6 ones).

• 2.NBT.A.2- Count within 1000. Skip count within 1000 by 2’s, 5’s, 10’s, and 100’s. Starting from any number in it’s skip counting sequence.

• 2.OA.C.3- Determine whether a group of objects (up to 20) has an odd or even number of members by pairing objects or counting them by 2’s.

• 2.MC.C.7- Tell and write time in quarter hours and to the nearest five minutes (in a.m. and p.m) using analog and digital clocks. Next three weeks of practice:

● Incorporate skip counting by 3’s, 4’s, 6’s, 7’s, 8’s, and 9’s. (skip counting will help prepare students for using repeated addition to multiply)

Starting with Lesson 6:

● 3.OA.C.7- Fluently multiply and divide within 100. By the end of 3rd grade know from memory all products of two one-digit numbers and related division facts.

Optional Resource:

● Choral Counting (See Illustrative Math 2.NBT Choral Counting) ● Number Talks (see table on Pg. 2)

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Standards Question Stems and Prompts Teacher Friendly Notes Activities/ Resources

Represent and solve problems involving multiplication and division. 3.OA.A.1 Interpret the factors and products in whole number multiplication equations (e.g., 4 x 7 is 4 groups of 7 objects with a total of 28 objects or 4 strings measuring 7 inches each with a total of 28 inches.) 3.OA.A.2 Interpret the dividend, divisor, and quotient in whole number division equations (e.g., 28 ÷ 7 can be interpreted as 28 objects divided into 7 equal groups with 4 objects in each group or 28 objects divided so there are 7 objects in each of the 4 equal groups).

How is multiplying like adding? Why do the groups have to be equal when you multiply? How can you use an array to help you think about both multiplication and division? 3.OA.A.1 If you have 3 rows and there is 6 in each row, how many do you have? How many do you have when you have __ rows and ___ in each row? A group of____students collected a total of ___pages of a notebook for recycling. If they each collected the same amount, how many pages did each student collect? 3.OA.A.2 How do you know what number to begin with when you divide objects or numbers? How is dividing objects like separating objects? If you have ___ objects and ____ baskets. How many would each basket receive if the objects were shared equally? Which multiplication fact can help you with this division problem?

The following videos are a great place to start before teaching this module. These will give you background knowledge and visual examples of how the standards should be taught in your grade level. Graham Fletcher Progression of Multiplication Video and Progression of Division Video https://gfletchy.com/progression-videos/ 3.OA.A Student understanding of multiplication and division is new to 3rd grade and should be developed through activities and problems involving equal-sized groups, arrays, and area models. Reaching fluency with these operations requires students to use variations of the standard algorithms without visual models and this could take much of the year for many students. Students should be given opportunities to explain their thinking verbally and in written expression including comparisons of strategies (arrays, equal groups).

The following resources are a menu of ideas you can choose from to meet the needs of your students. The standards taught in this unit are connected within this domain and to concepts in other domains. Many of the resources listed here will connect more than one standard. Ready Math from Curriculum Associates Unit 1 Howard County Math Resources Quarter 1 (See table on pg. 2) scroll down the page and click on the standard you are working on for lesson resources and tasks. Georgia Math Units (see table on pg. 2) Unit 2 Engage NY: https://www.engageny.org Module 1 (Topics A, B, C, D & E) Module 3 (Topics A, B, C & F) Illustrative Mathematics Tasks 3.OA.A.2 Fish Tanks Markers in Boxes

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3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers within 100. For example, determine the unknown number that makes the equation true in each of the equations: 8 x ? = 48, 5 = ? ÷ 3, 6 x 6 =? Understand properties of multiplication and the relationship between multiplication and division. 3.OA.B.5 Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication). 3 x 5 x 2 can be solved by (3 x 5) x 2 or 3 x (5 x 2) (Associative property of multiplication). One way to find 8 x 7 is by using 8 x (5 + 2) = (8 x 5) + (8 x 2). By knowing that 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 = 40 + 16 = 56 (Distributive property of multiplication over addition)

3.OA.A.4 How does division relate to multiplication? How can you use multiplication to help you divide? 7 times what makes 35? ___ divided by 5 equals 5? 44 divided by what number has a product of 11? 3.OA.B.5 5x4 is the same as? Why would you want to group factors in different ways when multiplying? How might knowing about breaking apart a factor into smaller products be helpful? Are these equations true? 4 x 5 = 20 34 = 7 x 5 3 x 6 = 9 x 2 2 x (3 x 4) = 8 x 3 8 x 6 = 7 x 6 + 6 4 x (10 ÷ 2) = 40 ÷ 2

When interpreting division, teachers should use the terms “number of shares” or “number of groups”. Students use numbers, words, pictures, physical objects, or equations to represent problems, explain their thinking and show their work. Sets of counters, number lines to skip count and relate to multiplication and arrays will aid students in solving problems involving multiplication and division. Allow students to model problems using these tools. Students should model a problem using a drawing and/or equation to find the solution.

3.OA.B.5 In 3rd grade, students apply properties of operations as strategies to multiply and divide. Students do not need to use the formal terms for these properties. Third grade students are introduced to the distributive property of multiplication as a strategy for using products they know to solve problems they do not know.

Illustrative Mathematics Tasks 3.OA.A.4 Finding the Unknown in a Division Equation

Illustrative Mathematics Tasks https://www.illustrativemathematics.org/

3.OA.B.5 Valid Equalities?(Part 2)

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3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Multiply and divide within 100. 3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of 3rd grade, know from memory all products of two one-digit numbers and related division facts.

3.OA.B.6 What is the unknown-factor in the question 45 divided by 9? What number do you multiply by 9 to get 45? If 7x8 is 56, what is 56 divided by 8 ? Find the unknown-factor. 3.OA.C.7 What is 7 x 8? 8 x 7? What is 56 divided by 8? 56 divided by 7?

For example: 7 x 8 = (5 + 2) x 8. I know 5 times 8 is 40 and 2 times 8 is 16. I can add the two products, 40 plus 16 and get 56. The distributive property is the basis for the standard multiplication algorithm that students can use to fluently multiply multi-digit numbers, which appears in 5th grade. 3.OA.B.6 The connection between multiplication and division should be introduced early in the year.. Students understand division as an unknown factor problem. For example, find 15 ÷ 3 by finding the number that makes 15 when multiplied by 3. 3.OA.C.7 Organizing fluency practice to focus most heavily on products and unknown factors that are understood but not yet fluent can speed learning and support fact fluency. Speed and efficiency are relative to each individual student’s needs. Timed tests should be used with caution. Practice and support should continue all year.


3.OA.C.7 Kiri’s Multiplication Matching Game

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Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.D.9 Identify arithmetic patterns (including patterns in the addition and multiplication tables) and explain them using properties of operations. For example, analyze patterns in the multiplication table and observe that 4 times a number is always even (because 4 x 6 = (2 x 2) x 6 = 2 x (2 x 6), which uses the associative property of multiplication).

3.OA.D.9 What do you notice about the numbers highlighted in the multiplication table? What patterns do you notice in this addition table? What patterns do you notice in this multiplication table? Explain why the pattern works this way? How can using a chart help you to recognize patterns in addition or multiplication?

3.OA.D.9 Students can investigate addition and multiplication tables in search of patterns and explain or discuss why these patterns make sense mathematically and how they are related to the properties of operations.


3.OA.D.9 Addition Patterns Making a Ten Patterns in the Multiplication Table Symmetry of the Addition Table

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Mathematics – Grade 4

Table of Contents Module 1: Number and Operations in Base Ten, Part 1 (Approx. 5 weeks) Module 2: Operations and Algebraic Thinking (Approx. 6 weeks) Module 3: Number and Operations in Base Ten, Part 2 (Approx. 2 weeks) Module 4: Number and Operations- Fractions (Approx. 10 weeks) Module 5: Measurement and Data (Approx. 8 weeks) Module 6: Geometry (Approx. 3 weeks) Mathematical Practices: Literacy Skills for Mathematical Proficiency: MP.1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies. MP.2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary. MP.3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas. MP.4. Model with mathematics. 4. Write mathematical arguments. MP.5. Use appropriate tools strategically. MP.6 Attend to precision. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning.


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Module 1: Number and Operations in Base Ten, Part 1 Suggested Time: Approx. 5 weeks

TEACHER CONTENT KNOWLEDGE Module Overview: Place Value and Rounding Students generalize place value understanding to read and write numbers to 1,000,000 using standard form, word form, and expanded form. Students will understand that a multi-digit whole number with one digit in one place has 10 times the value it would have in the place to its right. They compare the relative size of the numbers and round numbers to the nearest hundred thousand, which builds on 3rd grade rounding concepts. Computation By the end of 4th grade, students should fluently add and subtract multi-digit whole numbers up to 1,000,000 using standard algorithms. The following videos are a great place to start before teaching this module. These will give you background knowledge and visual examples of how the standards should be taught in your grade level. Graham Fletcher Progression of Addition and Subtraction Video https://gfletchy.com/progression-videos/ Pre-Requisite Skills and Knowledge: Read and write whole numbers, understand place value to the thousands place, multiply by 10, understand place value, compare the values of two digits, understand the meaning of the mathematical symbols <, >, and =, recall basic addition facts, recall basic subtraction facts, recognize addition and subtraction as inverse operations, round to tens and hundreds, know if the value of a given digit is less than, greater than, or equal to 5. Vocabulary: period, word form, standard form, expanded form, place value, compare, greater than symbol (>), less than symbol (<), sum, difference, regroup, round, estimate, multiples, tens, hundreds, thousands, tenths, hundredths, whole number, more than, less than, equal, round Fluency Practice Daily

● 3.OA.C.7- Fluently multiply and divide within 100. By the end of 3rd grade know from memory all products of two one-digit numbers and related division facts. ● 3.NBT.A.2- Fluently add and subtract within 1000 ● 4.NBT.A.2- Read and write multi-digit whole numbers using base-ten numerals (standard form), number names (word form),

and expanded form. Optional Resource:

● Number Talks (see table on Pg. 2)

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Standards Question Stems and Prompts Teacher Friendly Notes Activities/ Resources Generalize place value understanding for multi-digit whole numbers. 4.NBT.A.1 Recognize that in a multi-digit whole number (less than or equal to 1,000,000), a digit in one place represents 10 times as much as it represents in the place to its right. For example, recognize that 7 in 700 is 10 times bigger than the 7 in 70 because 700 ÷ 70 = 10 and 70 x 10 = 700. 4.NBT.A.2 Read and write multi-digit whole numbers (less than or equal to 1,000,000) using standard form, word form, and expanded form (e.g. the expanded form of 4256 is written as 4 x 1000 + 2 x 100 + 5 x 10 + 6 x 1). Compare two multi-digit numbers based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship.

4.NBT.A1 Compare 1-10-100. What happens when you multiply by 10? What happens if you divided by 10? What are some ways you could model 10 times as many? What is the relationship between the digits in this number? How can you use multiplication and division to describe the relationship between digits on a place value chart? How is the 2 in the number 582 similar to and different from the 2 in the number 528? 4.NBT.A.2 Place these numbers on a number line. Which number is larger? Which number is smaller? What is the order? How would adding a 0 to this number impact its place value?

4.NBT.A.1 & 2 Students need multiple opportunities to use contextual problems to read and to write multi-digit whole numbers. Students reason about the magnitude of digits in a number and analyze the relationship of numbers. Students can develop their understanding of millions by using a place value chart to understand the pattern of times ten in the base-ten system; for example, 20 hundreds can be bundled into 2 thousands.

The following resources are a menu of ideas you can choose from to meet the needs of your students. Ready Math from Curriculum Associates Unit 1 Georgia Math Units (see table on pg. 2) Unit 1 Howard County Math Resources (See table on pg. 2) scroll down the page and click on the standard you are working on for lesson resources and tasks. Engage NY: https://www.engageny.org Module 1 (Topics A-E) Illustrative Mathematics Tasks https://www.illustrativemathematics.org/

4.NBT.A.1 Threatened and Endangered Thousands and Millions of Fourth Graders

4.NBT.A.2 Ordering 4-digit Numbers

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4.NBT.A.3 Round multi-digit whole numbers to any place (up to and including the hundred-thousand place) using understanding of place value.

Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.B.4 Fluently add and subtract within 1,000,000 using appropriate strategies and algorithms.

4.NBT.A.3 What is the next closest… ____ is closer to ___ than ___ I rounded up/down because… Estimate… What makes 5 special in rounding? How does your understanding of place value help you to compare and order numbers? 4.NBT.A.4 When we have more than 9 units we have to convert. What place value is____ in? ______ represents _______place value. Write _____ in expanded form. Why is it important that we line up our number according to place value? How can place value be used to determine the sum or difference of two numbers? What could the two numbers be when regrouping is required? not required? Why is there an extra digit above the tens column?

4.NBT.A.3 This standard refers to place value understanding, which extends beyond an algorithm or procedure for rounding. Students should have multiple experiences using a number line and a hundreds chart as tools to support their work with rounding. Fourth grade students build on their work in third grade of rounding to the nearest 10 or hundred. In fifth grade, students are expected to be able to round decimals to any place. 4.NBT.A.4 Students should be able to understand and explain multi-digit arithmetic rather than merely following a sequence of directions, rules, or procedures they do not understand. In previous grades, students built a conceptual understanding of addition and subtraction including the regular one-for-ten trades between adjacent places. Speed and efficiency are relative to each individual student’s needs. Timed tests should be used with caution. Practice and support should continue all year.

4.NBT.A.3 Rounding on the Number Line Rounding to the Nearest 1,000

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Mathematics – Grade 5 Table of Contents Module 1: Number and Operations in Base Ten (Approx. 10 weeks) Module 2: Number and Operations- Fractions (Approx. 9 weeks) Module 3: Operations and Algebraic Thinking (Approx. 3 weeks) Module 4: Measurement and Data (Approx. 10 weeks) Module 5: Geometry (Approx. 4 weeks) Mathematical Practices: Literacy Skills for Mathematical Proficiency: MP.1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies. MP.2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary. MP.3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas. MP.4. Model with mathematics. 4. Write mathematical arguments. MP.5. Use appropriate tools strategically. MP.6 Attend to precision. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning.


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Module 1: Number and Operations in Base Ten Suggested Time: Approx. 10 weeks

TEACHER CONTENT KNOWLEDGE Module Overview: Students develop understanding of why division procedures work based on the meaning of base-‐ten numerals and properties of operations. They finalize fluency with multi-‐digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. In grade five, a critical area of instruction is for students to integrate decimal fractions into the place value system, develop an understanding of operations with decimals to hundredths, and work towards fluency with whole number and decimal operations. Pre-Requisite Skills and Knowledge: standard form, word form, expanded form, read and write multi-digit whole numbers using base ten numerals, perform multi digit arithmetic Vocabulary: Exponents, tenths, hundredths, thousandths, digit, powers of ten, expanded form, standard form, word form, value, place value, standard algorithm, product, quotient, dividend, divisor, factor, area model, array, less than, greater than, equal to, append a zero Fluency Practice Daily: ● 3.OA.C.7- Fluently multiply and divide within 100. By the end of 3rd grade know from memory all products of two one-digit numbers and related division facts. ● 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. ● 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Optional Resource:

● Number Talks (see table on Pg. 2)

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Standards Question Stems and Prompts Teacher Friendly Notes Activities/ Resources

Number and Operations in Base Ten (NBT) Understand the place value system. 5.NBT.A.1 Recognize that in a multi-‐digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-‐ number exponents to denote powers of 10.

5.NBT.A.1 Explain the relationship between the two 7’s in the number 657,782. What do you notice when you move to the digit to the right? What if you move to the digit on the left? What is a number that is 10 times larger than _____? What is a number that is 10 times smaller than ____? What patterns do you see within the place value system? How do two numbers compare that are the same digit, butare in different place value locations? 5.NBT.A.2 What patterns do you see when you multiply by different powers of ten? What do you notice when you multiply decimals by powers of ten? What pattern do you see when you multiply by 10? Explain how your pattern works for any given exponent.

The following videos are a great place to start before teaching this module. These will give you background knowledge and visual examples of how the standards should be taught in your grade level. Graham Fletcher Progression of Multiplication Video and Progression of Division Video https://gfletchy.com/progression-videos/ 5.NBT.A.1 Students use place value to understand that multiplying a decimal by 10 results in the decimal point appearing one place to the right (eg., 10 x 4.2 = 42) since the result is ten times larger than the original number.Students also make the connections that dividing by 10 results in the decimal point appearing one place to the left (eg., 4 ÷ 10 = 0.4) since the number is 10 times smaller (or 1/10 of the original). 5.NBT.A.2 Powers of 10 is a fundamental aspect of the base-‐ten system. Students extend their understanding of place to explain patterns in the number of zeros of the product when multiplying a number by powers of 10, including the placement of the decimal point. New at grade five is the use of whole number exponents to denote powers of 10.

The following resources are a menu of ideas you may choose from to meet the needs of your students. Ready Math from Curriculum Associates

Unit 1- Lessons 1-9 Georgia Math Units (see table on pg. 2) Unit 1 Unit 2 Unit 3 Howard County Math Resources (See table on pg. 2) scroll down the page and click on the standard you are working on for lesson resources and tasks. EngageNY

Module 1: Topics A-F Module 2: Topic A-C/E-H

Illustrative Mathematics Tasks https://www.illustrativemathematics.org/ NBT.A.1 Tenths and Hundredths Multiplying Decimals by 10 NBT.A.2 Marta’s Multiplication Error

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5.NBT.A.3 Read and write decimals to thousandths using standard form, word form, and expanded form (e.g., the expanded form of 347.392 is written as 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000)). Compare two decimals to thousandths based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship. 5.NBT.A.4 Round decimals to the nearest hundredth, tenth, or whole number using understanding of place value. Perform operations with multi-‐digit whole numbers and with decimals to hundredths.

5.NBT.A.3 Write this number in word form and expanded form. How are the two types of expanded form related to one another? What strengths does each variation have? How do you know _____ is greater/less than ____? 5.NBT.A.4 Where would this number be on the number line? Based on what you’re rounding to, what two numbers are your possible solutions? How do you know that your rounded solution is accurate? What are real life situations might make sense for your rounding?

5.NBT.A.3 5th grade students build upon prior understanding of decimal notations for fractions and addition of fractions with denominators of 10 and 100. Students use concrete models or drawings and number lines to extend this understanding to decimals to the thousandths. Models may include base-‐ten blocks, place value charts, grids, pictures, drawings, manipulatives and technology. Money is also a good medium to provide meaning for decimals. For example: If represents 1, then represents 1/10, and represents 1/00, explain why the following both represent the number 0.23.

5. NBT.A.4 Students use place value understanding to round decimals to any place. When rounding a decimal to a given place, students may identify two possible answers and use their understanding of place value to compare the given number to the possible answers. Students can use benchmark numbers (e.g., 0, 0.5, 1, and 1.5) to support their work.

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5.NBT.B.5 Fluently multiply multi-‐digit whole numbers (up to three-‐digit by four-‐digit factors) using appropriate strategies and algorithms. 5.NBT.B.6 Find whole-‐number quotients and remainders of whole numbers with up to four-‐digit dividends and two-‐digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.B.5 How do the various strategies for multiplication relate to the standard algorithm? Explain your thinking process as you use the algorithm. 5.NBT.B.6 How are the various strategies for division related? Explain your thinking process as you completed your division. How can you use the relationship between multiplication and division to help you divide? To check your answer for reasonableness?

5.NBT.B.5 In grade five students fluently multiply multi-‐ digit whole numbers using the standard algorithm. The standards call for understanding the standard algorithm in terms of place value, and this should be the most important goal for instruction. 5.NBT.B.6 In fourth grade, students’ experiences with division were limited to dividing by one-‐digit divisors. This standard extends students’ prior experiences with strategies, illustrations, and explanations. For example: 1,716 ÷ 16 There are 100 16’s in 1,716. 1,716 – 1,600 = 116 I know there are at least five 16’s in 116. 116 – 80 = 36. I can take out at least 2 more 16’s. 36 – 32 = 4. I took a total of 107 groups of 16 with 4 left over. So the quotient is 107 r 4.

Illustrative Mathematics Tasks NBT.A.5 Rounding to Tenths and Hundredths

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5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations; assess the reasonableness of answers using estimation strategies. (Limit division problems so that either the dividend or the divisor is a whole number.)

5.NBT.B.7 How are the various strategies used by your classmates related? What are the similarities/ differences in the strategies? How do the models or drawings support your understanding of operations with decimals? Explain your strategy for adding, subtracting, multiplying or dividing decimals.

9,984 ÷ 64

5.NBT.B.7 In grade five students build on work with comparing decimals in fourth grade and begin to add, subtract, multiply, and divide decimals to hundredths. Students focus on reasoning about operations with decimals using concrete models, drawings, various strategies, and explanations. They extend the models and written models they developed for whole numbers in grades one through four to decimal values. Students might estimate answers based on their understanding of operations and the value of the numbers. For example:

Illustrative Mathematics Tasks0 NBT.A.7 What is 23 ÷ 5?

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KNOX COUNTY SCHOOLS CURRICULUM & INSTRUCTION ......Multiplicative identity property of 1- a x 1 = 1...

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