# SFUSD Mathematics Core Curriculum Development ?· 1 SFUSD Mathematics Core Curriculum, Grade 6, Unit…

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SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.2: Fractions and Decimals, 20142015

SFUSD Mathematics Core Curriculum Development Project 20142015

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 6, Unit 6.2: Fractions and Decimals, 20142015

Grade 6 Unit 6.2: Fractions and Decimals

Number of Days

Lesson Reproducibles Number of Copies

Materials

2 Entry Task CPM CCC1 Lesson 6.1.1 (2 pages) HW: CPM CCC1 Lesson 6.1.1 (2 pages)

1 per pair CPM eBook

Licorice, 2 per student (optional) Straws, more than 2 per student Scissors Poster paper and markers Glue sticks or tape

3 Lesson Series 1 CPM CCC1 Lesson 6.1.2 (3 pages) HW: CPM CCC1 Lesson 6.1.2 CPM CCC1 Lesson 6.1.3 (3 pages) HW: CPM CCC1 Lesson 6.1.3

1 per pair CPM eBook 1 per pair CPM eBook

Counters, 10 per team (optional)

1 Apprentice Task Rabbit Costumes Interpreting a Division Computation

1 per student 1 per student

3 Lesson Series 2 CPM CCC1 Lesson 6.1.4 (4 pages) Resource Page 6.1.4 HW: CPM CCC1 6.1.4 (3 pages) Setting Goals

1 per pair 1 per student CPM eBook 1 per pair

1 Expert Task How much Money Reasoning about Multiplication and Division and

Place Value

1 per student 1 per student

4 Lesson Series 3 CPM CCC1 Lesson 7.2.1 (3 pages) Resource Page 7.2.1 HW: CPM CCC1 Lesson 7.2.1 CPM CCC1 Lesson 7.2.2 (2 pages) Resource Page 7.2.2 (half-page) HW: CPM CCC1 Lesson 7.2.2 CPM CCC1 Lesson 7.2.3 (2 pages) HW: CPM CCC1 Lesson 7.2.3

1 per pair 1 per student CPM eBook 1 per pair 1 per pair CPM eBook 1 per pair CPM eBook

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SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.2: Fractions and Decimals, 20142015

CPM CCC1 Lesson 7.2.4 (2 pages) HW: CPM CCC1 Lesson 7.2.4

1 per pair CPM eBook

1 Milestone Task Ribbons and Bows (2 pages) Constructed Response

Provided by AAO

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SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.2: Fractions and Decimals, 20142015

Unit Overview Big Idea

The inverse relationship between multiplication and division can be used to explain why the procedures for dividing fractions make sense.

Unit Objectives

Students will be able to use operations with decimals and long division to apply to division of fractions by fractions. Students will be able to use visual models to represent and solve problems involving division of fractions. Students will develop fluency with long division of multi-digit numbers and decimal numbers.

Unit Description

This unit begins by capitalizing on students prior knowledge and experiences with division of whole numbers, decimal numbers, and fractions with common denominators. Lessons move through tasks that emphasize long division skills, operations with decimal numbers that include addition, subtraction, multiplication and division, and culminate in activities focused on dividing fractions by fractions with unlike denominators. Students explore many different visual models for representing the division of fractions, and also investigate several methods for dividing, including a common denominator method and using a Super Giant One to simplify complex fractions.

CCSS-M Content Standards

The Number System

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

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

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

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

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

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SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.2: Fractions and Decimals, 20142015

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

In previous grades, students add and subtract fractions with unlike denominators, understand that a fraction is a division problem, and multiply and divide fractions by whole numbers. Students understand the place value system and perform operations with multi-digit whole numbers and with decimals to hundredths.

Students will learn about the relationship between multiplication and division, as well as between fractions and decimals. Students will apply this knowledge through real-world problem-solving tasks. They will be able to demonstrate these skills using equal groups, arrays, area models, number lines, multiplication tables and word problems.

In seventh grade, students will apply and extend previous understanding of operations with fractions to add, subtract, multiply and divide rational numbers. They also represent and solve problems involving proportions.

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SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.2: Fractions and Decimals, 20142015

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?

2 days 3 days 1 day 3 days 1 day 4 days 1 day Total Days: 15

Lesson Series 1

Lesson Series 2

Lesson Series 3

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SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.2: Fractions and Decimals, 20142015

(Interpreting a Division Computation)

Multiplication, Division, and Place Value)

Milestone Task Ribbon and Bows; Constructed

Response Questions

CCSS-M Standards

6.NS.1

6.NS.1, (6.NS.2, 6.NS.3) 6.NS.1, 6.NS.2 6.NS.1, 6.NS.2

Students work together to devise ways to share whole numbers of licorice equally among different numbers of people.

Make sense of and solve a real-world problem involving multiplication and division of fractions. If time permits, a second short task involves reasoning about the algorithm for long division.

The first part of the task challenges students to use their understanding of multiplication, division, and place value to solve problems without calculating by hand. The second part of the task asks students to use and explain a visual model that represents dividing fractions.

Students solve real-world and mathematical problems involving the division of fractions or decimals.

Source CPM Core Connections Course 1 Section 6.1.1, Problems 6-1 to 6-4

Part 1: MARS Task 2003 Part 2: Illustrative Mathematics

Part 1: MARS Task 2005 Part 2: Illustrative Mathematics

SVMI 2013; CPM Core Connections 1 Assessment Bank

Lesson Series 1

Lesson Series 2

Lesson Series 3

CCSS-M Standards

6.NS.1, 6.NS.2

6.NS.1

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

Brief Description of Lessons

This series builds on the context of dividing pieces of licorice evenly among several people to help students make sense of division. Students construct visual models and make connections among models to build their understanding of division and fractions. They also explore and make sense of the algorithm for long division. As they solve problems involving division, they must consider the meaning of the whole in different contexts and models. They reinforce their understanding by using multiplication to check their results.

Students extend their understanding to include division of fractions by fractions and continue to represent division using visual diagrams, including a new area model, number sentences, and verbally. The third day of this lesson series gives time for you to review. Have students do presentations, or give additional practice as needed.

Students deepen their understanding of division and move from visual models to more efficient methods for dividing fractions. Then students look at how division is like a ratio.

Sources

CPM Core Connections Course 1, Chapter 6 CPM Core Connections Course 1, Chapter 6 Illustrative Mathematics

CPM Core Connections Course 1, Chapter 7

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SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.2: Fractions and Decimals, 20142015