Lesson Plan

Adding Mixed Numbers Using the Decomposition Strategy

Make the number work for you! Use this lesson to teach your students to add mixed numbers with like denominators using the strategy of decomposition.
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Need extra help for EL students? Try the Number Talks with Mixed Numbers Addition pre-lesson.
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Need extra help for EL students? Try the Number Talks with Mixed Numbers Addition pre-lesson.

Learning Objectives

Students will be able to solve addition problems with mixed numbers that have like denominators using the decomposition strategy.

The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
EL adjustments

Introduction

(5 minutes)
  • Create two piles of markers. Both piles will have boxes of markers and some loose markers. (Example: pile one has 3 boxes of markers and 2 loose markers. Pile two has 2 boxes of markers and 5 loose markers.)
  • Ask your students to describe what they see and to think about how they would add them together.
  • Explain to students that one strategy for adding up these markers would be to group like items (whole boxes or loose markers) together. For example, 3 boxes of markers + 2 boxes of markers equals 5 boxes of markers and 2 loose markers plus 5 loose markers equals 7 loose markers. The total is 5 boxes of markers and 7 loose markers.
  • Explain that today they will add mixed numbers (a number that has a part that is a whole and a part that is a fraction) and this is one of the strategies they are going to use. They are going to add the whole number parts together and the fractional parts together before finding the total.
  • Show your students a group of markers and then ask them how they could decompose or break the 8 markers into 2 groups. (Examples: 1 + 7 = 8, 5 + 3 = 8, 4 + 4 = 8)
  • Write 8/8 on the board. Ask students how they could decompose 8/8 into 2 groups. (Examples: 5/8 + 3/8 = 8/8 or 2/8 + 6/8 = 8/8)
  • Write 13/8 on the board. Ask students how they could decompose 13/8 into 2 groups. (Examples: 10/8 + 3/8 = 13/8 or 8/8 + 5/8 = 13/8)
  • Point out to students that by decomposing 13/8 into 8/8 + 5/8 they have made it into 1 + 5/8. Explain that this will be the second strategy they use today when adding mixed numbers.

Beginning

  • Provide student-friendly definitions of the terms "mixed number," "decompose," "strategy," "fraction," and "whole number" in students' home language (L1), if possible, and English (L2).

Intermediate

  • Allow students to discuss in pairs before contributing suggestions for decomposing to the whole class.