Add and Subtract Fractions - Firstline Schools

MISSION OVERVIEW

Grade 5, Mission 3

Add and Subtract Fractions

In this Mission, students will develop flexibility with addition and subtraction of fractions so they can mentally or numerically solve, reason, and estimate their calculations. The Mission begins with concrete and pictorial work (using area models and number lines) and moves to numeric work with word problems by the end.

CURRICULUM MAP

Curriculum Map

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Curriculum Map

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WEEK

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1

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IDL (23) | SGL (23)

IDL (10) | SGL (10)

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IDL (29) | SGL (29)

IDL (23) | SGL (23)

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IDL (20) | SGL (20)

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IDL (21) | SGL (21)

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IDL (16) | SGL (16)

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M6

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?2018 Zearn, Inc. Portions of this work, Zearn Math, are derivative of Eureka Math and licensed by Great Minds. ?2018 Great Minds. All rights reserved.

? 2018 Zearn Portions of this work, Zearn Math, are derivative of Eureka Math and licensed by Great Minds. ? 2018 Great Minds. All rights reserved. Eureka Math was created by Great Minds in partnership with the New York State Education Department and also released as EngageNY.

ZEARN Mission Overview

G5M3

Overview of Topics and Lesson Objectives

Each mission is broken down into topics. A topic is a group of lessons that teach the same concept. For each topic, Zearn offers Whole Group Fluencies, Whole Group Word Problems, Small Group Lessons, and Independent Digital Lessons. There is a balance of Independent Digital Lessons and Small Group Lessons in each topic of a mission to ensure every student learns with a mix of modalities, feedback, and support while engaging in grade-level content. Throughout each mission, students work on grade-level content with embedded remediation to fill gaps in prior knowledge.

Lesson Objective

Topic A

Lesson 1 Lesson 2

Topic B

Lesson 3 Lesson 4 Lesson 5 Lesson 6

Equivalent Fractions

4.NF.1, 4.NF.3c, 4.NF.3d

Make equivalent fractions with the number line, the area model, and numbers.

Make equivalent fractions with sums of fractions with like denominators.

Making Like Units Pictorially

5.NF.1, 5.NF.2

Add fractions with unlike units using the strategy of creating equivalent fractions.

Add fractions with sums between 1 and 2.

Subtract fractions with unlike units using the strategy of creating equivalent fractions.

Subtract fractions from numbers between 1 and 2.

Lesson 7 Solve two-step word problems.

Topic C

Lesson 8 Lesson 9

Mid-Mission Assessment: Topics A-B

Making Like Units Numerically

5.NF.1, 5.NF.2 Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.

Add fractions making like units numerically.

Lesson 10 Add fractions with sums greater than 2.

INDEPENDENT DIGITAL LESSON

SMALL GROUP LESSON

2

ZEARN Mission Overview

G5M3

Lesson Objective

Lesson 11 Subtract fractions making like units numerically.

INDEPENDENT DIGITAL LESSON

Lesson 12 Subtract fractions greater than or equal to 1.

Topic D

Further Applications

5.NF.1, 5.NF.2

Lesson 13

Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.

Lesson 14 Strategize to solve multi-term problems.

Lesson 15

Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.

Lesson 16 Explore part-to-whole relationships.

End-of-Mission Assessment: Topics C-D

SMALL GROUP LESSON

Foundational Missions

For each mission, Zearn Math highlights the foundational missions, the earlier content where concepts are introduced and developed. Teachers can access foundational missions directly from the mission page of their Teacher Account to address any gaps in prior knowledge. Zearn recommends that teachers assign foundational missions during Flex Day or during additional non-core instruction time. It is important to use a foundational mission to support a struggling student, rather than an unaligned mission, because the content students learn in each foundational mission supports their Core Day learning.

Foundational Missions for G5M3: G3M5 Fractions as Numbers, G4M5 Equivalent Fractions

3

ZEARN Mission Overview

G5M3

Mission Overview

In Mission 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This mission marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

In Topic A, students revisit the foundational Grade 4 standards addressing equivalence. When equivalent, fractions represent the same amount of area of a rectangle and the same point on the number line. These equivalencies can also be represented symbolically.

Furthermore, equivalence is evidenced when adding fractions with the same denominator. The sum may be decomposed into parts (or recomposed into an equal sum). An example is shown as follows:

This also carries forward work with decimal place value from Missions 1 and 2, confirming that like units can be composed and decomposed.

5 tenths + 7 tenths = 12 tenths = 1 and 2 tenths 5 eighths + 7 eighths = 12 eighths = 1 and 4 eighths In Topic B, students move forward to see that fraction addition and subtraction are analogous to whole number addition and subtraction. Students add and subtract fractions with unlike denominators (5.NF.1) by replacing different fractional units with an equivalent fraction or like unit. 1 fourth + 2 thirds = 3 twelfths + 8 twelfths = 11 twelfths

This is not a new concept, but certainly a new level of complexity. Students have added equivalent or like units since kindergarten, adding frogs to frogs, ones to ones, tens to tens, etc.

4

ZEARN Mission Overview

G5M3

1 boy + 2 girls = 1 child + 2 children = 3 children

1 liter ? 375 mL = 1,000 mL ? 375 mL = 625 mL

Throughout the mission, a concrete to pictorial to abstract approach is used to convey this simple concept. Topic A uses paper strips and number line diagrams to clearly show equivalence. After a brief concrete experience with folding paper, Topic B primarily uses the rectangular fractional model because it is useful for creating smaller like units by means of partitioning (e.g., thirds and fourths are changed to twelfths to create equivalent fractions as in the diagram below). In Topic C, students move away from the pictorial altogether as they are empowered to write equations clarified by the model.

Topic C also uses the number line when adding and subtracting fractions greater than or equal to 1 so that students begin to see and manipulate fractions in relation to larger whole numbers and to each other. The number line allows students to pictorially represent larger whole numbers. For example, "Between which two whole numbers does the sum of 1 3/4 and 5 3/5 lie?"

This leads to an understanding of and skill with solving more complex problems, which are often embedded within multi-step word problems: Cristina and Matt's goal is to collect a total of 3 1/2 gallons of sap from the maple trees. Cristina collected 1 3/4 gallons. Matt collected 5 3/5 gallons. By how much did they beat their goal?

Word problems are a part of every lesson. Students are encouraged to draw tape diagrams, which encourage them to recognize part-whole relationships with fractions that they have seen with whole numbers since Grade 1.

5

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