SFUSD Mathematics Core Curriculum Development Project · 2014-12-13 · 1 SFUSD Mathematics Core...

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SFUSD Mathematics Core Curriculum, Grade 4, Unit 4.5: Whole Number 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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Grade 4

4.5 Whole Number Division

Number of Days

Lesson Reproducibles Number of Copies Materials

1 Entry Task How Many Ways? 1 per student

4 Lesson Series 1 HW: How Many Ways EM SRB p 240 EM Master p 470 EM Journal p 140 Array Division Method Ind Practice (2 pages) HW: Array Division Method (2 pages) EM Math Journal 138-139 (2 pages) EM Study Links 6.1 (Master p 177) Division Stories (2 pages) Exit Slips

1 per student EM SRB 1 per student EM Journal 1 per student 1 per student EM Journal EM Study Links 1 per student 1 per student

Counters Number Cards Dice (1 per pair)

1 Apprentice Task The Baker with The Class Lineup (2 pages) 1 per pair

6 Lesson Series 2 Divvy Out Independent Practice (2 pages) HW: Divvy Out (2 pages) EM Journal p 142-143 (2 pages) EM Study Links 6.2 (Master p 178) EM Journal p 144-145 (2 pages) EM Study Links 6.3 (Master p 180) Divide with Fractional Decomposition (2 pages) HW: Divide with Fractional Decomposition Short and Long Division (2 pages) HW: Short and Long Division Division Methods Worksheet HW: Division Methods Worksheet Exit Slips

1 per student 1 per student EM Journal EM Study Links EM Journal EM Study Links 1 per student 1 per student 1 per student 1 per student 1 per student 1 per student 1 per student

Counters Base Ten Blocks

1 Expert Task School Newspaper 1 per pair Chart Paper, Rulers

6 Lesson Series 3 Checking Your Work (2 pages) HW: Checking Your Work (2 pages) EM Journal p 148-149 (2 pages) EM Study Links 6.4 (Master p 182)

1 per student 1 per student EM Journal EM Study Links

Counters Base Ten Blocks

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HW: Interpreting the Remainder EM Master p 471 Trip to Railway Museum HW: Trip to Railway Museum Exit Slips

1 per student 2 per pair 1 per student 1 per student 1 per student

1 Milestone Task Field Trip Task & Constructed Responses (2 pages) Provided by AAO

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Unit Overview

Big Idea

All whole numbers can be decomposed into equal groups. This process can be represented using abstract models (numbers, symbols, and equations) as well as concrete and pictorial representations.

Unit Objectives

● Students will be able to represent division using concrete, pictorial, and abstract models. ● Students will be able to choose and utilize a variety of algorithms to solve division problems. ● Students will be able to interpret the remainder in division word problems.

Unit Description

Students begin the unit by modeling the concept of division using various visual representations. Next, students will learn several algorithms for solving larger division problems, choosing the method they think is most useful. Finally, the students will work through division word problems to understand the meaning of a remainder and what is the best way of expressing it to make sense in context.

CCSS-M Content Standards

Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1

4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Number and Operations in Base Ten2

Use place value understanding and properties of operations to perform multi-digit arithmetic.

4.NBT.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. 1See Glossary, Table 2. 2Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

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Progression of Mathematical Ideas

Prior Supporting Mathematics Current Essential Mathematics Future Mathematics

Third Grade Unit 3.3: Students will be able to place objects in equal groups of 2, 3,4, and 5 to determine a product. Previous Fourth Grade Units: Students explored multiple models to represent multiplication. They also practiced finding all the factors of a given number, as well as finding some of its infinite multiples.

Fourth Grade: (Whole Number Division) All whole numbers can be decomposed into equal groups. This process can be represented using numbers, symbols and equations as well as a variety of models. Students will recognize the inverse relationship between multiplication and division. Students will be able to visually represent their mathematical thinking in various models as well and explain what the divisor, dividend, and remainder represent.

Fifth Grade: (Whole Number Division) All whole numbers can be decomposed into equal groups. This process can be represented using numbers, symbols and equations as well as a variety of models. Students will recognize the inverse relationship between multiplication and division. Students will be able to visually represent their mathematical thinking in various models as well and explain what the divisor, dividend, and remainder represent.

Sixth Grade: Students will fluently divide multi-digit numbers using the standard algorithm.

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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 4 Days 1 Day 6 Days 1 Day 6 Days 1 Day

Total: 20 Days

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Entry Task How Many Ways?

Apprentice Task The Baker

Expert Task School Newspaper

Milestone Task Field Trip

CCSS-M Standards

4.OA.2, 4.OA.3 4.NBT.6

4.OA.2, 4.OA.3 4.NBT.6

4.OA.2, 4.OA.3 4.NBT.6

4.OA.2, 4.OA.3 4.NBT.6

Brief Description of Task

To assess students’ current understanding of division concepts. Students represent and solve problems involving multiplication and division. They demonstrate understanding of the relationship between multiplication and division. They can multiply and divide within 100. They can solve two-step word problems using the four operations.

Students apply and present their knowledge of division models to word problems.

Students work in small groups to figure out the most efficient scenarios for running the printing and funding of a school newspaper

Students apply knowledge of completed unit to answer eight constructed responses and two tasks regarding field trips.

Source SFUSD Teacher Created MARS Exam 2007, Grade 4 Georgia Department of Education

SFUSD Teacher Created

Lesson Series 1

Lesson Series 2

Lesson Series 3

CCSS-M Standards

4.OA.2 4.NBT.6

4.OA.2, 4.OA.3 4.NBT.6

4.OA.2, 4.OA.3 4.NBT.6

Brief Description of Lessons

Students will learn about different ways to visually represent their division problems through explicit teaching, group work, games, and exploration.

Students will learn and practice various division strategies with computational questions and word problems.

Students practice strategies for checking their work and interpret the remainder in division questions.

Sources Everyday Mathematics TERC Investigations

WCCUSD-West Contra Costa Unified School District Everyday Mathematics

Everyday Mathematics SFUSD Teacher Created

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Entry Task How Many Ways?

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will assess prior knowledge of division.

CCSS-M Standards Addressed: 4.OA.2

Potential Misconceptions:

● Students may confuse factors with quotient. ● Students say one thing, but represent a different thing.

Launch: Remind students of their work in third grade with division. Talk about the prior unit on factors and multiples (4.4) and how they used visual representations like tallies, pictographs, number lines, etc. for their multiplication models. Today’s task is a way to explore the upcoming unit. During: Students will work in groups to create a visual aid that contains all of the different ways they represented 24. They can solve the problem any way they see fit as long as they include/show how they came to their solution. Monitor class progress by circulating from group to group. Closure/Extension: The class will participate in a gallery walk noting the different ways their classmates answered the question. Highlight the different representations that are used by the students.

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How Many Ways?

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: equal, visually represent, divisor, dividend, quotient Sentence frames: I created ____equal groups of ____. My strategy was to_______. 24 is equal to ______ groups of _________.

Differentiation Strategies: Support:

● Demonstrate a method to remind students of what they learned last year. ● Give manipulatives to struggling students.

Extension

● Student may write word problems to fit each of the models the student has created. Assist student in getting started, if necessary. Participation Structures (group, partners, individual, other):

● Groups

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Lesson Series #1

Lesson Series Overview: Students will explore different models for representing division and then will apply these models to solve simple division word problems. CCSS-M Standards Addressed: 4.OA.2, 4.OA.3, 4.NBT.6 Time: 4 Days

Lesson Overview – Day 1 Resources

Description of Lesson: This lesson connects to the Entry Task the students completed the day before. They are focusing on concrete and pictorial representations of division. Start the lesson by referring back to the multiple models for division that the students created in the Entry Task. Chart the students’ models as you review their work from yesterday. See an example of a chart in the Resources file (Division Representations and Algorithms). But the chart should include the bar method, equations, circle sets, arrays and number lines. After creating the chart, give the students new numbers to divide into equal groups (suggested numbers: 18, 20, 30, 36). Challenge them to use all methods from the chart to represent the division problems. Ask students to discuss which methods they prefer and why. If students need an extension, have them try to create a word problem (real-world situation) that would fit with the particular division. Notes: Make sure that when you use the traditional equation representation, that you show the various ways to do it: 25/5, 25 ÷ 5, etc. There are 3 Exit Slips that can be used in this lesson series.

Division Representations and Algorithms Homework: How Many Ways Homework (Revised Apprentice Task)


Description of Lesson: In the first half of the class students will play Division Arrays from Everyday Mathematics. When introducing the game, highlight the relationship between multiplication and division.

Everyday Mathematics Student Reference Book, p. 240 Everyday Mathematics Math Masters, p. 470

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In the second half of class, give the students a division word problem (Everyday Mathematics Grade 4 Teacher’s Lesson Guide p. 402) and have them represent and solve their problem using the multiple methods they practiced the past two days. You can either assign one model to each table group or have each group try out different models.

Everyday Mathematics Teacher’s Lesson Guide, p. 402 Homework: Everyday Mathematics Math Journal, p. 140


Description of Lesson: The students will be using arrays to solve division problems of bigger numbers. Model how to take a division problem and convert it into an array in which the divisor is one dimension of the array. See Array Division Method to see how it’s done with the problem 150/6. You could start with an easier problem, such as 30/5 and use counters to model how to break a dividend into multiples of the divisor. After modeling how to do this with a bigger number, have kids practice this method with a partner, giving them a new division (such as 180/5). Have students complete the Array Division Method Independent Practice Worksheet. Choose one problem to review as an exit slip.

Array Division Method (teacher sheet) Array Division Method Independent Practice Homework: Array Division Method Homework


Description of Lesson: Students will use the division models that they practiced during the past two days to solve division word problems. Give each group a different division problem and have them make a poster showing how they solved the problem, representing their thinking with multiple models. Notes:

• Do not use any problems that require remainders.

Division Stories Everyday Mathematics Math Journal, pp. 138–139 (#1 & 3) Homework: Everyday Mathematics Study Links 6.1 (Math Masters, p. 177)

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Apprentice Task

The Baker



Math Objectives: ● Students show different mathematical models for the division

problems. ● Students explain their mathematical thinking.

CCSS-M Standards Addressed: 4.OA.2, 4.OA.3, 4.NBT.6 Potential Misconceptions:

● Students may incorrectly use the numbers given in the problem.

Launch: Divide the class up into groups of 2 or 3. Tell students that today’s task will be a chance to share what they have learned over the past few lessons. Remind students to read the task carefully and to use the models that they know best to solve the questions. You may wish to read over the task together to clarify any questions. During: Students will work in pairs or trios on the problems. Monitor class progress. Closure/Extension: Students who finish early can get a copy of the extension Class Line-Up. Students can share their work in partnerships/groups. Classroom share answers, allowing students to build on each other’s answers. Use the results to build on any misconceptions or to add extensions.

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The Baker




Vocabulary: leftover, calculations, fill in the empty spaces, baked, goods Sentence frames: I figured this problem out by ______. I used _____ because ________.

Differentiation Strategies: Support:

● Change numbers or limit which food to solve for (e.g., only find cookies and bagels). ● Reduce the number of questions that need to be completed. ● Have students work with a partner.

Extension:

● “ZhiChao is having a birthday party and needs 58 of each baked good. How many boxes of cookies, donuts, muffins, and bagels will he need?” Participation Structures (group, partners, individual, other):

● Individual work ● Whole group discussion

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Lesson Series #2

Lesson Series Overview: Students will be introduced to and practice increasingly more abstract algorithms for solving division problems. CCSS-M Standards Addressed: 4.OA.2, 4.OA.3, 4.NBT.6 Time: 6 days


Description of Lesson: Begin this series of lessons with a discussion about the purpose of practicing different abstract methods for calculating division problems. The idea is that all people think differently and in our exploration of different methods students will find the method that best suits their learning style. It’s important that they keep an open mind and persevere through each method because they’ll discover the one they like best. Start by following the lesson Divvy Out Greater Numbers. It gives you step-by-step instructions on how to teach the Divvy Out Method, which is a more visual representation of the Partial Products Method. Start a chart of Abstract Division Methods. List Divvy Out Method with an example. Notes: If your students have demonstrated an understanding of the concept of division through the use of models to represent division situations, they are ready to start this next lesson series. If not, continue to work on division models through word problems. Throughout this lesson series, conduct Math Talks that deals with division. Encourage students to use the various methods you’ve been studying. See the Math Teaching Toolkit for more information.

Divvy Out Greater Numbers Lesson pp. 1–8 **Divvy Out Greater Numbers Lesson p. 10 Divvy Out Independent Practice Worksheet Homework: Divvy Out Homework **If students are having trouble understanding the Divvy Out Method, they can try it with more basic facts. Refer to Divvy Out Greater Numbers Lesson p. 10 as a guide.

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Description of Lesson: Students prepare to use the Partial Quotients Division Method. Follow Lesson 6.2 from Everyday Mathematics Grade 4.

Everyday Mathematics Math Journal, pp. 142–143 Homework: Everyday Mathematics Study Links 6.2, (Math Masters, p. 178)


Description of Lesson: Students learn to use the Partial Quotients Division Method. Follow Lesson 6.3 from Everyday Mathematics Grade 4. Add the Partial Quotients Method (with an example) to the Abstract Division Methods chart.

Everyday Mathematics Math Journal, pp. 144–145 Homework: Everyday Mathematics Study Links 6.3, (Math Masters p. 180)


Description of Lesson: Students learn to use the Fractional Decomposition Division Method. Follow the WCCUSD lesson Divide with Fractional Decomposition.** After practicing with a partner, have kids complete the Divide with Fractional Decomposition Independent Practice Worksheet. Add the Fractional Decomposition Division Method (with an example) to the Abstract Division Methods chart. Notes: **It is recommended that students start with simpler problems such as: 627/3, 816/4, 344/8, 276/6, 2282/7. Later they can work with the larger problems. All problems should use one-digit divisors.

Divide with Fractional Decomposition WCCUSD Lesson pp. 2–5 Divide with Fractional Decomposition Independent Practice Worksheet Homework: Divide with Fractional Decomposition Homework


Description of Lesson: Students will make the connection between the Partial Quotients and two more abstract methods (Short and Long Division). Start by explaining that today they will learn two more abstract methods for dividing numbers.

Video link comparing Short and Long Division: https://www.youtube.com/watch?v=7NkVYLJ1nfw Short and Long Division Independent Practice Worksheet Homework:

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Emphasize that these are other options for dividing, but that no method is the “right” method. Introduce the Short Division Method concurrently with Partial Quotients. Show how the partial quotients listed on the right side of the division problem mirror the digits of the quotient in the Short Division Method. You are showing how place value is accounted for in the Short Division Method. Provide problems for students to practice this method with partners (examples: 625/5, 762/3, 932/4). Then introduce Long Division Method. See video link comparing Short and Long Division - you could introduce in the same way. Provide problems for kids to practice method with partners (you could use same numbers as above or problems like: 710/2, 1044/4, 2365/5). Continue on to the Short and Long Division Independent Practice Worksheet. Add the Short Division Method and Long Division Method (with examples) to the Abstract Division Methods chart.

Short and Long Division Homework


Description of Lesson: The students will solve division problems using a variety of algorithms. Refer students to the Abstract Division Methods chart. Have students talk to a partner about the method that at this point they think works best for them and why. With a partner, they are going to solve a division problem using three different methods on the Division Methods Worksheet. In the fourth square, they are going to explain which method works best for them and why. While the kids can work with a partner, each child will fill out his or her own worksheet. Finish with a conversation about which method they think works best for them. You might conduct a class tally or graph to record the information.

Division Methods Worksheet Homework: Division Methods Worksheet (Teacher adds division problem)

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Expert Task School Newspaper



Math Objectives: ● Students use a variety of models and algorithms to solve word

problems involving division. ● Students explain mathematical thinking.


● Students may use the wrong operations to solve the problems. ● Students may use the numbers incorrectly to solve the different parts

of the problem.

Supplies: Scratch paper Pencils Chart Paper Rulers Color Pencils or Markers Launch: Students are divided into groups of two to four. Each group is given the task. Students will work together to solve the tasks and present their information in poster format. During: As the groups solve the task, they create a poster to show how the task was solved and what the solutions are. All students should work together to calculate solutions. The poster should show each group’s mathematical thinking in a clear and concise way. Closure/Extension: Posters should be hung in the front of the room for everyone to see. Each group can present its poster to the class and field questions. Alternatively, students can do a walk around the classroom and leave positive comments and questions on a separate sheet of paper for each poster.

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School Newspaper




Vocabulary: newspaper, newsprint, publish, advertisement, expenses, purchase, budget Sentence frames: We created _______ equal groups of __________. Used the ____________ strategy to solve this problem. When we compared __________ to ___________, we found that ____________ was the better/worse ___________.

Differentiation Strategies:

Intervention: • Have students work in small groups or with a partner. • Adjust the number of copies needed for the newspapers. Extension: • How many extra copies of the newspaper could you make using the paper that you purchased? How do you know? • If the school decided to charge $20 for the use of the copy machine, how would this change your answers? • If each of the teachers in your school also wanted a copy of the newspaper, show how that would change your results. • What would you need to charge for the advertisements if you wanted them to use no more than 2 pages? Tell why. • If the school will not allow you to use the copy machine and you have to use a local printer, how would this affect the costs?

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

● Partner and/or Group Task

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Lesson Series #3 Lesson Series Overview: First students practice two methods for checking their division computation. Next, students learn how to interpret the remainder so that it makes sense within the context of a word problem. Then students practice solving division problems in which there is a remainder and the different ways to express that remainder. Finally, they apply the lessons they learned to a real-world problem. CCSS-M Standards Addressed: 4.OA.2, 4.OA.3, 4.NBT.6 Time: 6 Days


Description of Lesson: Students explore how to check their work by using an estimation or multiplication. Discuss how it’s important to check your work after completing a division problem. There are two methods that will be presented to the students: estimation or multiplication. Model how you can check your work by estimating. For instance, 216/6 could be rounded to 200/5 = 40 or 279/3 could be rounded to 270/3 = 90. You then know that your answer should be close to 40 in the first example and 90 in the second. Give students a few problems to divide and then have them check their work with an estimation. Possible examples: 368/8, 292/4, 4228/7. Then model how you can use multiplication (the inverse operation of division) to check their division. Based on the work they’ve completed earlier, you could ask kids to come up with the operation that they would use to check their work. Because kids can “pretend” to do the multiplication (fix the multiplication so that their answer works) have them use the Lattice Method of Multiplication (taught in Unit 4.3 Whole Number Multiplication) that cannot be fudged as easily. Give students a few problems to divide, and then have them check their work with a multiplication. Possible examples: 741/3, 1365/5, 1260/4. Have kids complete the Checking Your Work Independent Practice Worksheet. Notes: There is a page of Exit Slip problems with remainders that can be used in this lesson series.

Checking Your Work Independent Practice Worksheet Homework: Checking Your Work Homework (Teacher provides problems on template)

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Description of Lesson: Students will learn to express and interpret the remainder in division problems. Follow Lesson 6.4 in Everyday Mathematics Grade 4. Notes: Create a poster for the students that illustrates the three options of what to do with the remainder and an example of a word problem that fits into each category. In addition to Everyday Mathematics examples in the teacher’s guide, refer to this worksheet for more ideas: Interpret Remainder Resource Sheets. Starting today, you could start conducting Math Talks that deal with division and remainders. See the file Math Talks - Remainders for ideas of topics for your talks. See the Math Teaching Toolkit for more information about how to do Math Talks. There is a page of Exit Slip problems with remainders that can be used in this lesson series.

Everyday Mathematics Math Journal, pp. 148–149 Interpret Remainder Resource Sheets Math Talks: Remainders Homework: Everyday Mathematics Study Links 6.4 (Math Masters, p. 182)


Description of Lesson: Students will create word problems that match the different ways to interpret the remainder. Review the poster that you created yesterday to show different ways to interpret the remainder. The challenge for today is to have each group create three different word problems (see note below) that match each remainder situation (ignore, report as fraction or decimal, and round up). Do not have them label each remainder situation because it will be used as a gallery walk for the rest of the class later. Have the students produce a rough draft for you to review before they make the final poster to identify each remainder situation (but not to label it on poster). If you think your students will struggle with this activity, spend time as a class brainstorming examples of word problem that would match each remainder situation.

Homework: Interpreting the Remainder Homework

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When students are done with their posters, have them do a gallery walk in which they have to identify what to do with the remainder in each problem. You could have them label each situation with a post-it or have them write their thoughts in a math notebook. Notes: Have students choose simpler division problems under 100 so that they’re not also dealing with dividing large numbers while figuring out what to do with the remainder. If you have time, conduct a Math Talk that deals with division and remainders. See the file Math Talks - Remainders for ideas of topics for your talks. See the Math Teaching Toolkit for more information about how to do Math Talks. There is a page of Exit Slip problems with remainders that can be used in this lesson series.


Description of Lesson: Students return to division algorithms, but now complete larger problems that involve remainders. Return to the poster of Abstract Division Methods. Explain that so far you’ve used these methods with problems that could be easily broken into equal groups; you’ve not had to consider the remainder. Now that you have a better understanding of the meaning of the remainder and what to do with it, we’re going to practice calculating larger division problems that involve a remainder. Choose a division problem, such as 476/3, and show how to solve that problem using the different methods and how to express the remainder in each example. Show how the remainder can be written in different ways. In the Divvy Out and Partial Quotients Methods you could write the remainder as “r2.” In the Fractional Decomposition you could express it as a fraction (⅔). In the Short and Long Division, you could express it in both ways. In further examples, you can show how the fraction can be expressed as a decimal if it’s a decimal equivalent that you know (½ = 0.5 or ¼ = 0.25). Give the students more examples to try, working together with a partner (examples:

Choose one of four worksheets (Division, Graph Paper Division, Long Division, Long Division) for: independent practice homework

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498/4, 618/5, 985/6). You could choose which division method to use or let them choose. Then have students complete one of the Independent Practice Worksheets. You can choose one of the four for classwork and one for homework, depending on the needs of your students, or let them choose one to work on, starting in class and finishing at home. Notes: If you have time, conduct a Math Talk that deals with division and remainders. See the file Math Talks - Remainders for ideas of topics for your talks. See Math Teaching Toolkit for more information about how to do Math Talks. There is a page of Exit Slip problems with remainders that can be used in this lesson series.


Description of Lesson: Students Practice division of larger numbers through the Everyday Mathematics game, Division Dash. Model with another student how to play the game Division Dash. Start with two-digit dividends. After students understand the rules, have them play with three- and four-digit dividends. Notes: If you have time, conduct a Math Talk that deals with division and remainders. See the file Math Talks - Remainders for ideas of topics for your talks. See the Math Teaching Toolkit for more information about how to do Math Talks. There is a page of Exit Slip problems with remainders that can be used in this lesson series.

Everyday Mathematics Student Reference Book, p. 241 Everyday Mathematics Math Masters, p. 471

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Description of Lesson: Students will work in groups to solve a problem that involves the concepts we’ve studied in this unit. Introduce the problem, Trip to Railway Museum, to the students. It’s important that they understand the parameters of the problem. Make sure they understand that there are possible combinations of buses that the fourth grade class can take. Also emphasize the fact that there must be at least one teacher on each bus (hence, no more than nine buses). Have the students start the work in pairs. For students that need help getting started, ask them how can they use the concepts we’ve been studying in this unit to help them solve the problem. After all pairs have gotten a few combinations, have them join another pair to create a group of four. Have them share their results, noting similarities and new combinations. After they work together to find new combinations, bring the class together to again share what they’ve found. To finish up, have students articulate the strategies that they used to find the different combinations of buses. Notes: If you have time, conduct a Math Talk that deals with division and remainders. See the file Math Talks - Remainders for ideas of topics for your talks. See Math Teaching Toolkit for more information about how to conduct Math Talks.

Trip to Railway Museum Homework: Trip to Railway Museum Homework

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Milestone Task

Field Trips



Math Objectives: ● Students use a variety of models and algorithms to solve word

problems involving division. ● Students explain mathematical thinking.


● Students may use the wrong operations to solve the problems. ● Students may use the numbers incorrectly to solve the different parts

of the problem.

Launch: Students are given no time limit for the task. They each have scratch paper, pencils, and the task. Students have been told/are reminded that this is the Milestone Task (which includes performance task and constructed responses) that will end the unit on division. During: Students are working to respond to three short answer problems and one task. Students are working alone. Closure/Extension: Score the Milestone Task. Use the data to guide your Milestone Task student evaluation and to notify students and their parents of progress and potential areas of need. Go over the performance task and constructed responses. Student created posters for the task would deepen understanding for students who may have still been confused over some of the processes.

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Field Trip




Vocabulary: rent, size options, budget Sentence frames: The school must order _______ buses to carry all of the students. _________ buses will not be completely full. Hugo had ______ pennies four months ago. _________ can be divided by 5 and have a remainder of 2. Miel drove _________ miles a day.

Differentiation Strategies: Intervention:

● Eliminate the one or more of the problems from the constructed response. ● Change instructions to “Explain using models, words, OR equations”

Extension: ● Create a step-by-step poster (8.5 x 11) explaining how to solve this problem.

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

● Individual

SFUSD Mathematics Core Curriculum Development Project · 2014-12-13 · 1 SFUSD Mathematics Core...

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