# SFUSD Mathematics Core Curriculum Development Project€¦ · 5.NBT.6 Find whole-number quotients...

### Transcript of SFUSD Mathematics Core Curriculum Development Project€¦ · 5.NBT.6 Find whole-number quotients...

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SFUSD Mathematics Core Curriculum, Grade 5, Unit 1: Whole Number Multiplication and Division, 2014–2015

SFUSD Mathematics Core Curriculum Development Project

2014–2015

Creating meaningful transformation in mathematics education

Developing learners who are independent, assertive constructors of their own understanding

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SFUSD Mathematics Core Curriculum, Grade 5, Unit 1: Whole Number Multiplication and Division, 2014–2015

Grade 5

5.1 Whole Number Multiplication and Division

Number of Days

Lesson Reproducibles Number of

Copies Materials

1 Entry Task Math Academy (3 pages) 1 per student extra paper for workspace

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Lesson Series 1 HW: Multiplication Chart 0-12 EngageNY 5.2.A.1 Student Pages (6 pages) EngageNY 5.2.A.2 Student Pages (7 pages) EngageNY 5.2.B.3 Student Pages (7 pages) EngageNY 5.2.B.4 Student Pages (7 pages) EngageNY 5.2.B.6 Student Pages (6 pages) EM Lesson 2.7 pp. 47-49 (3 pages) EM Lesson 2.7 Study Link

1 per student 1 per student 1 per student 1 per student 1 per student 1 per student EM Journal EM Study Link

personal white boards place value charts

1 Apprentice Task Is Lebron Correct? Student Pages (2 pages) 1 per student

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Lesson Series 2 EM Lesson 1.5 pp. 13-15 EM Student Reference Book p. 306 - Factor Captor EM Math Masters pp. 453-454 - Factor Captor Grids (2 pages) HW: EM Study Link 1.5 EM Lesson 4.2 pp. 101-102 HW: EM Study Link 4.2 EM Student Reference Book p. 303 - Division Dash EM Lesson 4.4 pp. 106-108 EM Student Reference Book p. 302 - Divisibility Dash HW: EM Study Link 4.4 EM Lesson 4.6 pp. 111-114 HW: EM Study Link 4.6 EM Project 12 CA9-CA12

EM Journal EM SRB 1 per pair EM Study Link EM Journal EM Study Link EM SRB EM Journal EM SRB EM Study Link EM Journal EM Study Link EM Journal

EM Math Deck grid paper calculators coin-size counters

1 Expert Task Math Card Shuffle Task Cards

Math Card Shuffle Student Pages Math Card Shuffle Exit Slip

1 set per pair 1 set per pair 1 per student

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SFUSD Mathematics Core Curriculum, Grade 5, Unit 1: Whole Number Multiplication and Division, 2014–2015

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Lesson Series 3 Is This 364 ÷ 15? (2 pages) HW: And Is This 364 ÷ 15 too? Is This 252 ÷ 12? Student Pages (2 pages) HW: Is This 562 ÷ 16? Gallery Walk Response Sheet EM Student Reference Book p. 334 - Multiplication and Division Top-It EM Student Reference Book p. 325 - Name That Number!

1 per student 1 per student 1 per pair 1 per student 1 per student EM SRB EM SRB

EM Math Deck

2 Milestone Task Middle School Prep

Middle School Prep 2 1 per student 1 per pair

chart paper and markers

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Unit Overview

Big Idea The operations of multiplication and division can be used in real-world situations involving joining equal groups, separating equal groups, comparison, or combinations, and can be represented by visual models, numerical expressions, and written explanations. Unit Objectives

● Students will be able to fluently multiply and divide multi-digit whole numbers using a variety of algorithms (standard, partial products, partial quotients, area model, and rectangular arrays).

● Students will be able to connect a chosen algorithm for multiplication or division with a visual representation. ● Students will be able to explain patterns in the number of zeroes in the product when multiplying or dividing a whole number by powers of 10. ● Students will be able to demonstrate their knowledge of place value and multiplication/division as they create and solve problems in context.

Unit Description This unit develops students’ fluency manipulating multiplication and division, expressing their understanding of the concepts through a variety of algorithms, models, and situational problems. Students are given practice with writing and interpreting numerical expressions, multiplying and dividing using powers of 10, using 3- and 4-digit factors and 2-digit divisors. Students continue to build knowledge of and fluency with place value as it relates to whole number multiplication and division algorithms and their visual representations.

CCSS-M Content Standards Operations and Algebraic Thinking Write and interpret numerical expressions. 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Number and Operations in Base Ten Understand the place value system. 5.NBT.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. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6 Find whole-number quotients 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.

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Progression of Mathematical Ideas Prior Supporting Mathematics Current Essential Mathematics Future Mathematics

In fourth grade, students learned how to multiply a one-digit whole number by another number of up to four-digits and multiply two two-digit numbers. Students also found whole number quotients and remainders with a one-digit divisor and up to four-digit dividends. Students solved problems using multiplication and division, modeling the problems and interpreting solutions using numbers, visual representations (such as area models), and words.

In fifth grade, students will use the properties of multiplication and division to solve computation problems. Students will also provide reasoning for choices they make in problem solving. Students will compute using a variety of methods including algorithms (standard algorithm, partial products, partial quotient) and rectangular models to multiply and divide whole numbers. Students will show their understanding of place value of multi-digit numbers in division problems that include two-digit divisors.

Later in fifth grade units, students will multiply and divide and decimals up to the hundredths. They will also multiply fractions by a variety of numbers and divide unit fractions by whole numbers and whole numbers by unit fractions. In sixth grade, students will need to fluently divide multi-digit numbers using a standard algorithm. Sixth graders are also expected to apply previous understanding of multiplication and division to divide fractions by fractions. Students will write and interpret numerical expressions, which now include exponents and variables, and rely on fluency with vocabulary such as quotient, factor, and product.

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Unit Design All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both formative and summative assessments of student learning. The tasks are designed to address four central questions: Entry Task: What do you already know? Apprentice Task: What sense are you making of what you are learning? Expert Task: How can you apply what you have learned so far to a new situation? Milestone Task: Did you learn what was expected of you from this unit?

1 day 8 days 1 day 7 days 1 day 4 days 2 days

Total: 24 days

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Multi. & Divis. Entry Task Math Academy Multiplication and

Division Tournament

Apprentice Task Is LeBron Correct?

Expert Task Math Card Shuffle

Milestone Task Middle School Prep

CCSS-M Standards

5.OA.2 5.NBT.2, 5.NBT.5, 5.NBT.6

5.OA.2 5.NBT.2, 5.NBT.5

5.OA.2 5.NBT.5, 5.NBT.6

5.OA.2 5.NBT.2, 5.NBT.5, 5.NBT.6

Brief Description of Task

Students evaluate a variety of multiplication and division expressions in the context of a math competition at an imaginary school.

Students look for the error in sample student multiplication work. Students also compare the magnitude of multiplication expressions using what they know about multiplying by powers of ten, how the value of the factors affects the products, and area models.

Students work in pairs to perform a variety of tasks involving multiplication and division. These include evaluating a variety of multiplication and division expressions, filling in missing digits, and using computation to find the answer to questions about contexts. An exit slip is included to assess individual students.

Students will evaluate a variety of multiplication and division expressions, including some problems in context. Students will name algorithms used in solving these expressions.

Source SFUSD Teacher Created SFUSD Teacher Created SFUSD Teacher Created SFUSD Teacher Created

Lesson Series 1

Lesson Series 2

Lesson Series 3

CCSS-M Standards

5.OA.2 5.NBT.2, 5.NBT.5

5.OA.2 5.NBT.5, 5.NBT.6

5.OA.2 5.NBT.2, 5.NBT.5, 5.NBT.6

Brief Description of Lessons

This series will focus on mental math strategies for decomposing numbers, the relationship of place value to multiplication, and multiplying multi-digit numbers using a variety of algorithms and a variety of visual representations. This series will also introduce the practice of number talks and establish solid routines.

This series will focus on the two main division algorithms (long division and partial quotients). Students will link division and multiplication and practice explaining and showing mathematical thinking in a variety of ways.

This series will focus on using multiplication and division strategies in real-world situations.

Sources www.insidemathematics.org www.mathworksheets4kids.com EngageNY SFUSD Teacher Created

Everyday Mathematics SFUSD Teacher Created

Georgia Department of Education http://www.math-drills.com SFUSD Teacher Created

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Entry Task

Math Academy Multiplication and Division Tournament

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will multiply and divide whole numbers. ● Students will use a variety of multiplication algorithms fluently. ● Students will use a variety of division algorithms. ● Students will connect an algorithm to a visual representation.

CCSS-M Standards Addressed: 5.OA.2, 5.NBT.2, 5.NBT.5, 5.NBT.6 Potential Misconceptions:

● Students may confuse the order of dividend and divisor when switching between the various division notations.

● Students may not understand the meaning of “algorithm.” ● Students may not know the difference between “expression” and

“equation.” An expression is a combination of numbers and operations, for example, . An equation includes numbers, operations, and an equals sign, for example, .

Materials: Math Academy Worksheet, 1 per student blank paper (lined, grid, white) for working Launch: This task will give you a chance to show what you already know about multiplication and division of whole numbers. You will have choices of what algorithms to use. What are some of the methods/algorithms you already know? (Facilitate a discussion of a variety of methods, chart and display an example of each. Add in examples that are not mentioned by students but that are mentioned on the Entry Task.) During: Students work independently to complete the Entry Task. Closure/Extension: Provide opportunities for students to demonstrate their favorite method for peers (whole class or small group). Facilitate a discussion of the relationship between multiplication and division. Chart big ideas.

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Math Academy Multiplication and Division Tournament

How will students do this?

Focus Standards for Mathematical Practice: 6. Attend to precision. 2. Reason abstractly and quantitatively.

Structures for Student Learning: Academic Language Support:

Vocabulary: algorithm, standard algorithm, quotient, product, factor

Sentence frames: My favorite algorithm for ________ is ____________. I like it because ____________. I found ______________ to be easy/challenging.

Differentiation Strategies: • Provide multiplication facts chart. • Provide lattice grids or structured workspace.

Participation Structures (group, partners, individual, other):

• Group, partners, and individual

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Lesson Series #1 Lesson Series Overview: Students will be able to write simple expressions without evaluating them and be able to explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Additionally, they will use whole-number exponents to denote the powers of 10. Students will practice a variety of algorithms for multiplication. By the end of this series, students should have a solid ability to compute precise products and use estimation strategies to assess the reasonableness of their answers. Students will demonstrate understanding of the connections between algorithms for multiplication and the area model. CCSS-M Standards Addressed: 5.OA.2, 5.NBT.2, 5.NBT.5 Time: 8 Days

Lesson Overview – Day 1 Resources

Description of Lesson: This day is dedicated to developing the classroom Math Talk routine. Students should get experience in how to discuss their thinking and strategies using math vocabulary. Refer to the Math Teaching Toolkit for more information on how to lead a Math Talk and how to record student thinking. Math Talks are teacher-led, student-centered techniques for building math thinking and academic discourse. They are intended to last for 10–15 minutes. Because this is an introduction, take more time to discuss the routines and make them explicit; Step out of the talk to say, “Notice how Sally explained her first step, then her second step, and why she chose those steps,” or “Notice how I am writing down just what Timmy said, exactly as he said it.” Math Talks can be centered on any math topic. However, they are not used to introduce math content. Rather, Math Talks are best when the content is generally familiar to students up to their Zone of Proximal Development. Teachers deliberately set up a safe environment where each child’s thinking is valued. Students practice making their thinking explicit. Everyone practices understanding each other’s thinking. 1. Prsent the problem.

A problem is presented to the whole class or a small group. Computation problems are always presented horizontally (e.g., 43 + 35 =?) to encourage mental strategies rather than reliance on algorithms. The subject of the talk should be:

2. Students think about the problem. Students are given time (1–2 minutes) to silently, mentally think about the problem and try to find an answer. They signal quietly to the teacher (e.g., with a thumb up

Math Teaching Toolkit pp. 23–25 on Math Talks Video of teachers leading Math Talks (for reference) http://www.insidemathematics.org/index.php/classroom-video-visits/number-talks Homework: Multiplication Chart 0–12 http://www.mathworksheets4kids.com/multiplication/tables/0to12-blank.pdf

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against their chest) when they have an answer. 3. Students share their answers.

A few students volunteer to share their answers and you record them on the board. Without judgment, record answers where all students can see. Continue to take answers until all students’ answers have been shared. You can also ask the students to “turn and talk” with a partner before sharing answers.

4. Students share their thinking. Students share how they got their answers with a partner or with the larger group. Any student can provide an explanation to any answer on the board. Equity sticks can be used to ensure every student has an equal opportunity to share. Record the students’ name and thinking. Ask questions that help students express themselves, understand each other, and clarify their thinking to make sense of the problem and its solution(s). Multiple ways of solving problems are emphasized. The student’s name is attached to the solution.

Notes: Some strategies to mention if students do not volunteer them:

● Area model visualization ● Decomposition of the first factor (192 = 100 + 90 + 2 or 192 = 150 + 40 + 2) and

then multiplication of each by the second factor (partial products) ● When multiplying by 5, you can multiply by 10 and divide by 2.

If you know that some students are not fluent with their basic multiplication facts, this would be a good time to incorporate daily practice for 5–10 minutes each day so students will be better able to access and participate in the lessons that follow.

Lesson Overview – Day 2 Resources

Description of Lesson: This is a 2-day lesson. Day 1 of 2: Multiply multi-digit whole numbers and multiples of 10 using place value patterns. This lesson includes number talks and extensive practice of mental math strategies for decomposing numbers (distributive property). Students will also practice rounding whole numbers to various place values. Notes: Change the application problem at the beginning of the lesson to be “A desk has a length of 6 feet. The length is 3 times the width. What is the width?” Suggestion: Give 1 out of 3 pages for classwork to work on as a class. Students can finish at home for homework.

The next five lessons use EngageNY materials from their Module 2. These lessons include number talks, a detailed lesson sequence, practice sets, exit slips, and homework. EngageNY 5th Grade Module 2: Lesson 1 (pp. 2.A.2–2.A.14) Homework: Classwork pages in Lesson 1 EngageNY Full Module: http://www.engageny.org/sites/default/files/resource/attachments/math-g5-m2-full-module.pdf

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Lesson Overview – Day 3 Resources

Description of Lesson: Day 2 of 2: Multiply multi-digit whole numbers and multiples of 10 using place value patterns. Continue to work on number talks and extensive practice of mental math strategies for decomposing numbers (distributive property). Students will also continue to practice rounding whole numbers to various place values. Notes: On this day, the first page of student work can be checked to ensure all students understand the process of multiplying multi-digit whole numbers. Continue working on the rest of the classwork pages.

EngageNY 5th Grade Module 2: Lesson 1 (pp. 2.A.2–2.A.14)

Homework: Homework pages in Lesson 1

Lesson Overview – Day 4 Resources

Description of Lesson: Estimate multi-digit products by rounding factors to basic facts and using place value patterns. Students will discuss and practice rounding factors when estimating products of multi-digit numbers.

EngageNY 5th Grade Module 2: Lesson 2 (pp. 2.A.15–2.A.27)

Lesson Overview – Day 5 Resources

Description of Lesson: Use a tape model to model and compare numerical expressions. This lesson includes lots of practice with the meaning of multiplication and modeling expressions using a tape model.

EngageNY 5th Grade Module 2: Lesson 3 (pp. 2.B.3–2.B.16)

Lesson Overview – Day 6 Resources

Description of Lesson: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication. The unit form designates one of the factors as the “unit,” the number that is added repeatedly. For example, can be read as 31 groups of 8 (8 is the unit) or 8 groups of 31 (31 is the unit). When 8 is the unit, can be seen as 30 + 1 units. When 31 is the unit, can be seen as 10-2 units. This lesson develops this manipulation of expressions for ease of calculation.

EngageNY 5th Grade Module 2: Lesson 4 (pp. 2.B.17–2.B.29)

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Notes: Vocabulary: commutative property, distributive property Prerequisite skill: multiplication facts

Lesson Overview – Day 7 Resources

Description of Lesson: In this lesson, students work with a rectangular area model to make sense of the distributive property and the partial products and standard algorithm methods of multiplication. Notes: In the Application Problem, change the dimension of hydrogel to 3 cm from 3.2 cm. Students are not asked to multiply decimals in this unit. EngageNY uses a notation system for the standard algorithm for multiplication that may be unfamiliar. There are extensive notes in the lesson plan. Decide ahead of time whether you will teach your students this method of notation or use another more familiar method. Whatever notation you use, make sure that students are using 0s as placeholders (not x’s or blank spaces).

EngaNY 5th Grade Module 2: Lesson 6 (pp. 2.B.43–2.B.54) Partial Products Tutorial: for reference http://www.teachertube.com/viewVideo.php?video_id=142033

Lesson Overview – Day 8 Resources

Description of Lesson: Estimating products by using magnitude estimates. Notes: Use the Mental Math & Reflexes and Math Message to guide the Math Talk of the day. Do not include decimal problems; this unit only addresses whole numbers.

Everyday Mathematics Grade 5 Lesson 2.7: ● Teacher Edition Volume 1 pp. 115–119 ● Student Math Journal Volume 1 pp. 47–49 ● HW: Study Link 2.7 (Math Masters p. 53)

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Apprentice Task

Is LeBron Correct?

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will demonstrate the ability to multiply whole numbers. ● Students will demonstrate the ability to perform error analysis and

correct the error. ● Students will demonstrate fluency with a variety of algorithms and

area models. CCSS-M Standards Addressed: 5.NBT.2, 5.NBT.5 Potential Misconceptions

● Students may not be proficient on how to align digits when using the traditional method of multiplication.

● Students may not be proficient with the power of 10 rules. ● Students may struggle with breaking a number into its factors to show

that 60 x 345 and 6 x 3450 have the same product.

Materials: Is LeBron Correct? Worksheet, 1 per student Launch: Explain to students that today they will be able to use different multiplication methods to show what they have been learning thus far in this unit. In several sections, the expectation is that they will be able to explain their responses in one to two complete sentences. Please refer to the sentence frames document provided to scaffold the language for students who need additional support. In the first part of this task, students identify and correct a multiplication procedural error in the work shown using estimation to explain their reasoning. Next, they solve an alternative expression using a different method (area model or partial products). Remind students to label the methods they use and respond with complete sentences. In the second part of this task, students apply their knowledge of multiplying numbers by powers of 10. They must explain how two numbers related by powers of 10 have the same product and prove this without multiplying. In the third part of this task, students compare two given expressions, determine if these expressions have greater, less, or equal value to each other and explain their reasoning without actual calculation. During: Monitor while students will work independently during the task. Closure/Extension: Provide an opportunity at the end of the class period for students to share out their responses in each of the sections. In the first part, allow students to share what they identify as LeBron’s error and

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their corrections to his work. Ask volunteers or select students to come to the board/ELMO to show their work or have students discuss their findings in small groups, then share out with the whole class. In the second part, facilitate a discussion that re-enforces the big idea that expressions that have the same factors or the same related factors will always have the same product. In the third part, allow students to share and explain in small groups/whole class how they compared the values of each expression. Facilitate a conversation around which method of multiplication (area model, traditional algorithm or partial products) students used to prove their answers.

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Is LeBron Correct?

How will students do this?

Focus Standards for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

Structures for Student Learning: Academic Language Support:

Vocabulary: factors, product, estimation, area model, partial products, traditional algorithm, expression, reasonable Sentence frames: #1A. After using estimation, I’ve determined that LeBron’s answer is not reasonable because ________. #1B. I decided LeBron was incorrect when he ____________. I would correct LeBron’s error by ______________. #2. When comparing the products of 60 x 345 and 6 x 3450, Maribel might ________. One way Maribel might compare the products is by ________________.

Differentiation Strategies: For early finishers or high potential students, students may (on a separate piece of paper) use the context of the LeBron situation and create a math story of their own to try with fellow students. They may also create math stories for situation two and three. Tell them to write their answers for each of the situations on a different page (either on the back or separate paper) so that if they were to exchange with a peer, the answers aren’t provided. Participation Structures (group, partners, individual, other):

• This task is structured for students to complete independently, allowing you to identify students still struggling with multiplication and to identify any misconceptions that still exist. This may inform how you conduct small group work and address skills that still need to be solidified.

• The small group/whole class share out at the end of the class period is meant to give you an opportunity to reinforce big ideas and do a quick informal assessment of where most students are before grading the task individually.

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Lesson Series #2

Lesson Series Overview: Students will review/learn two algorithms for division: long division and partial quotients. Students will practice these algorithms in and out of context. Divisibility rules, factoring numbers, and writing expressions are included in this series. CCSS-M Standards Addressed: 5.OA.2, 5.NBT.5, 5.NBT.6 Time: 7 days

Lesson Overview – Day 1 Resources

Description of Lesson: Students will learn and practice divisibility rules and will review and practice finding factors of a number. Students play Factor Captor to reinforce divisibility rules. Notes: Use the Mental Math & Reflexes and Math Message to guide the Math Talk of the day. If you run out of time to play Factor Captor during this lesson, consider finding other times later to play this game several times.

Everyday Mathematics Grade 5, Lesson 1.5: ● Teacher Edition Volume 1 pp. 37–41 ● Student Math Journal Volume 1 pp. 13–15 ● HW: Study Link 1.5 (Math Masters p. 15)

Everyday Mathematics Student Reference Book p. 306, Factor Captor (save for Lesson Series 3) Everyday Mathematics Math Masters pp. 453–454, Factor Captor Grids

Lesson Overview – Day 2 Resources

Description of Lesson: Students will learn and practice the partial quotients algorithm for division. The divisibility rules learned in Day 1 will help them identify factors as they use the algorithm. This lesson extends to Day 3, so all work does not need to be completed today. Save Division Dash for Day 3. Notes: Use the Mental Math & Reflexes and Math Message to guide the Math Talk of the day. Focus on the partial quotients algorithm. Use Easy Multiples strategy/support for any student who is not fluent with basic division facts.

Everyday Mathematics Grade 5, Lesson 4.2: ● Teacher Edition Volume 1 pp. 236–241 ● Student Math Journal Volume 1 pp. 101–102 ● HW: Study Link 4.2 (Math Masters p. 104)

Everyday Mathematics Math Masters p. 109, Easy Multiples http://em-ccss.everydaymathonline.com/g_login.html (go to Free Resources videos of the algorithms being used)

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Lesson Overview – Day 3 Resources

Description of Lesson: In an extension of the lesson from Day 2, students play Division Dash to practice using division algorithms. If students did not complete work on Day 2 or if they are struggling with the content, they can also use this time to review or finish. Notes: Use the Mental Math & Reflexes and Math Message to guide the Math Talk of the day. You can give small group instruction with students who are struggling with the partial quotients algorithm.

Everyday Mathematics Student Reference Book p. 303, Division Dash (save for Lesson Series 3) Everyday Mathematics Math Masters p. 111, Division Practice (as needed to support struggling students)

Lesson Overview – Day 4 Resources

Description of Lesson: Students continue practicing the partial quotients algorithm. Play Divisibility Dash to review divisibility rules. Notes: Use the Mental Math & Reflexes and Math Message to guide the Math Talk of the day. Use Math Masters p. 109 (Day 2) and p. 111 (Day 3) for scaffolding as needed.

Everyday Mathematics Grade 5, Lesson 4.4 ● Teacher Edition Volume 1 pp. 248–253 ● Student Math Journal Volume 1 pp. 106–108 ● HW: Study Link 4.4 (Math Masters p. 110)

Everyday Mathematics Student Reference Book p. 302, Divisibility Dash (save for Lesson Series 3)

Lesson Overview – Day 5 Resources

Description of Lesson: Students practice interpreting the remainder in division problems. Students use magnitude estimates with division. Notes: Use the Mental Math & Reflexes and Math Message to guide the Math Talk of the day.

Everyday Mathematics Grade 5, Lesson 4.6: ● Teacher Edition Volume 1 pp. 259–264 ● Student Math Journal Volume 1 pp. 111–114 ● HW: Study Link 4.6 (Math Masters p. 116)

Grid paper Homework resource: http://www.math-drills.com/division.shtml

Lesson Overview – Day 6 Resources

Description of Lesson: Students learn and practice the long division algorithm with 1- and 2-digit divisors.

Everyday Mathematics Grade 5, Project 12 ● Teacher Edition Volume 1 pp. 446O–446V ● Student Math Journal Volume 1 pp. CA9–CA12

Grid Paper

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Notes: Use the Mental Math & Reflexes and Math Message to guide the Math Talk of the day.

Lesson Overview – Day 7 Resources

Description of Lesson: Students work in partners as they continue to practice the long division algorithm with 2-digit divisors. In addition, students check their division using multiplication. Provide five to ten expressions on the board or chart paper. Direct students to work in pairs write contexts for each problem and solve some with partial quotients and some with long division. They then determine what the answer of their question will be, taking into account the remainder (if any). They should check all their quotients by multiplying the quotient by the divisor (and adding any remainder). Students should also write an equation that corresponds with their multiplication procedure. Do one or two examples of this procedure with the whole class before independent or partner work begins. The focus of this work is student practice of previously taught algorithms and demonstration of ability to write an equation that corresponds to the mathematics being done. Early finishers play Division Dash or Divisibility Dash. Notes: This would be a good day for the teacher to work with students who are still struggling with dividing by a 2-digit divisor. Example problems and student work on next page.

Homework resource: http://www.math-drills.com/division.shtml

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(246 x 12) + 1 = 2,953

(343 x 23) + 6 = 7,895

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Expert Task Math Card Shuffle

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will demonstrate the ability to multiply and divide whole

numbers. CCSS-M Standards Addressed: 5.OA.2, 5.NBT.5, 5.NBT.6 Potential Misconceptions:

● Students may attempt to continue to work in partnerships during the Exit Slip portion of the activity, however, this should be done individually as it will be used as an assessment

Launch: The Expert Task is a partner learning exercise that incorporates mathematical computation using learned multiplication and division strategies with math writing and deep discussion. There are opportunities for students to work individually and then collaborate with a partner to solidify their understanding of the content. It is suggested that you laminate the task cards to allow for continued use in future years with minimal damage. Heterogeneous partnering of the students is recommended. In the first activity, introduce students to math task cards, which ask students to work with partners to solve and discuss a variety of multiplication and division problems in math story contexts. Solve math task card #1 together with the whole-class using the following guidelines:

● Step 1: (2 minutes) Students turn over the first card and complete the calculations in their workspace.

● Step 2: (2 minutes, 1 minute for each partner) Students ro-sham-bo to decide who shares first. (You may substitute any classroom norm procedure for deciding sharing order.) The first partner shares her/his solution and strategy used as well as any additional information. After one minute, the second partner shares her/his solution and points out any similarities or differences to the partner’s work.

● Step 3: (2 minutes) Students write down their own math thinking as well as their partner’s math thinking using the provided worksheet. The sentence frames on the back of the worksheet may be used if a student needs it. Students may also use this time to amend their calculations or finish any uncompleted steps.

This process is repeated for each of the first six math cards. You may choose to provide a timer or let the partnerships self-regulate time spent on task.

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Reminders such as “Two card tasks should be finished now,” may be helpful. After partners complete all of the task cards, they work on the Exit Slip individually. Collect and score the completed Exit Slips. During: Circulate and give encouragement to students as they work through the cards. Remind students to use the sentence frames if they are having difficulty with the math writing. Ensure that all partners are sharing verbally and recording both their own and their partner’s thinking. Closure/Extension: The final step involves a whole-group debriefing of each of the card tasks numbered 1–6. You may choose to omit this step if time is not available. The use of equity sticks is suggested in choosing students (or partners) to share. Encourage students to discuss their process as well as their solution.

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Math Card Shuffle

How will students do this?

Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others.

Structures for Student Learning: Academic Language Support:

Sentence frames: My answer to task ____ is __________. I found my solution by… I agree with you; however, I found my solution in another way. I… I disagree with your solution. My answer is…

Differentiation Strategies: • Homogeneous groupings could be made if desired, giving higher level groups extension tasks such as creating their own cards or giving a poster

presentation on one of their solutions. For lower level groups, partners might share the writing tasks or calculating tasks or be given a math writing worksheet with sentence frames printed on them.

Participation Structures (group, partners, individual, other):

• Task card #1 is completed together as a whole class. Students work in partnerships to complete task cards #2–6. Tasks A and B are completed individually as an exit slip. The closing section is completed as a whole group.

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Lesson Series #3 Lesson Series Overview: In this lesson series, students will have an opportunity to practice and review the relationships between multiplication and division. CCSS-M Standards Addressed: 5.OA.2, 5.NBT.2, 5.NBT.5, 5.NBT.6 Time: 4 days

Lesson Overview – Day 1 Resources

Description of Lesson: Students will practice how to interpret a division math story, the remainder, as well as check the solution by multiplying. This lesson is designed for you to instruct the problem solving process. Notes: Modifications have been made to scaffold the problem solving process.

Georgia Fifth Grade Unit 1 Are These All ? Teacher Notes Is This ? (student pages) HW: And Is This , Too? (adapted from Georgia Department of Education)

Lesson Overview – Day 2 Resources

Description of Lesson: Refer back to the lesson from Lesson Series 3 Day 1. As a whole class, create a math story together to solve with a different expression, . Students will begin to learn how to write a math story, understand it, and solve it with a partner. Students will be able to understand the relationship between multiplying and dividing numbers when showing proof of their work. Notes: The homework is necessary for Day 3. If students are struggling with division with a 2-digit divisor, modify the expression for them.

Is This ? Teacher Notes Is This ? Student Pages HW: Is This ? (adapted from Georgia Department of Education)

Lesson Overview – Day 3 Resources

Description of Lesson: After Day 2, students bring in their individual math story (Is This 562 ÷ 16?). Have each student check that their work is ready to be viewed by the class in a Gallery Walk.

Gallery Walk Response Sheet Homework/extra practice resources:

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Explain the process of a Gallery Walk to the class (see Math Teacher Toolkit). Each student will look at all the problems, and then choose two to write about on their Response Sheet. The first problem is one that fits the expression 562 ÷ 16. Students answer specific questions about why it fits. The second problem is one that does not fit the expression as well. Discuss with the class that mistakes are learning opportunities and that they keep life interesting. Also discuss how we can comment on each other’s work in a way that is directed toward the work (“This does not fit because…”) rather than the person (“You’re so dumb for doing this because…”). Connect back to the Math Talks and safe, productive math discourse. Give students time to look at the problems and respond on their sheets. Include a problem of your own or the one provided, hand-written out, as an example of a problem that does not fit. Gather as a whole class to discuss the problems that fit and did not fit. Focus on the mathematical characteristics of both sets of problems. When discussing the problems that do not fit, discuss how they can be changed to match the expression and how the expression could be changed to fit the problem. Notes: Students who are still struggling may need modifications of a simpler division expression.

http://www.math-drills.com/multiplication2.shtml http://www.math-drills.com/division.shtml

Lesson Overview – Day 4 Resources

Description of Lesson: Game Day/Review Day: This is a day dedicated to review of all concepts. Students have an opportunity to replay games previously learned. Notes: Modify games to fit the needs for students’ understanding. Use the advanced version if available, or modify the game to include larger dividends and divisors. Consider using time today to preview the Milestone Task with ELs, RSP, or other special needs students.

Student Reference Book p. 302, Divisibility Dash Student Reference Book p. 325, Name That Number! Student Reference Book p. 334, Multiplication and Division Top-It Student Reference Book p. 303, Division Dash

Homework/extra practice resources: http://www.math-drills.com/multiplication2.shtml http://www.math-drills.com/division.shtml

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Milestone Task

Middle School Prep

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will demonstrate the ability to multiply and divide whole

numbers. ● Students will demonstrate the ability to connect an algorithm with a

visual representation. ● Students will demonstrate the ability to explain patterns in the number

of zeros of the product when multiplying a number by powers of 10. CCSS-M Standards Addressed: 5.OA.2, 5.NBT.2, 5.NBT.5, 5.NBT.6 Potential Misconceptions:

● On Day 2, students may use the number of packs to divide instead of the number of pencils when deciding if there is a remainder or not.

Materials: Middle School Prep, 1 per student (Day 1) Middle School Prep 2, 1 per group (Day 2) Chart paper Markers Launch: The Milestone Task is a two-part activity that will take two days to complete. Day 1: Middle School Prep is an individual activity that gives the student a chance to show her/his understanding of the multiplication and division strategies reviewed and built upon in Unit One. Students should be given one class period to complete the first task sheet and extra paper(s) to use as needed for their workspace. Begin with a brief group or self-review session of multiplication and division work students have done during the unit. Examples of exemplary student work may be shown and discussed or students may review their math notebooks for work they think is exceptional. Key vocabulary from the unit including: representation and model or story vocabulary such as pack might be reviewed. Tell students to be as neat and complete as possible because some of the assessment points are based on the quality of their explanations. Day 2: Middle School Prep 2 will be a group activity that builds upon the previous day’s activity. Students work in groups to complete a group poster that properly addresses all of the tasks. A rubric is provided for scoring, however the activity is meant to be more of a collaborative working/learning activity that takes the previous day’s work to a higher level. Groups will then use their poster to give a presentation in any fashion the teacher chooses based on time and comfort level. Some suggestions are for groups to present to the whole class, to other groups, to the teacher during an independent activity time or to a partnering class split into groups.

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Not much preparation or explanation is needed to start the day other than possibly reviewing the classroom norms for group work. During: Day 1: Circulate around the room and provide any non-critical clarification needed. Provide students with any extra paper they may need as workspace. You may suggest that students create a small table or T-chart with important information from the story such as “23 pencils per pack.” Day 2: Circulate around the room and provide assistance as needed. This activity is more learning than assessing, so you may be more flexible in giving hints as to how to proceed. You may provide each group with a blank copy of the previous day’s activity to use as a scaffold to the new problems since they are all similar calculations. You may suggest that groups create a small table or T-chart with important information from the story. Closure/Extension: Day 1: Thank the students for their hard work and perseverance on the day’s task. Give them a heads-up that the next day they will be working in groups on a similar task. Day 2: Student presentations/gallery walk of posters. Students utilize question/comment sheet as needed then discuss whole class using “I noticed…” or “I wonder” and give compliments to their classmates about the presentations and math work.

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Middle School Prep

How will students do this?

Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 4. Model with mathematics.

Structures for Student Learning: Academic Language Support:

Vocabulary: representation, model, pack (of pencils) Sentence frames: Provide sentence frames as needed for ELs and other students who need them to be able to demonstrate their mathematical thinking. (e.g., Mrs. K will have/not have a remainder. Mrs. K will need to ______ the leftover pencils.)

Differentiation Strategies: • For Day 2, make a chart with students as needed to clarify vocabulary and problem solving procedure. • Form strategic groupings.

Participation Structures (group, partners, individual, other):

• Day 1: individual • Day 2: groups of three or four