### Lesson plan

# Adding Mixed Numbers Using the Decomposition Strategy

#### 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.

#### 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.

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- Show students the problem:
**2 2/6 + 4 3/6 =** - Ask them to find the sum of the whole numbers (6) and then fractional pieces (5/6). Remind them that the denominator tells the size of the piece and the numerator the number of pieces. These fractions can be added together because they are the same size pieces.
- Have students turn to a partner and share the total value (6 5/6).
- Show students the problem:
**3 2/6 + 2 5/6 =** - Ask them to find the sum of the whole numbers (5) and then fractional pieces (7/6).
- Guide students to decompose the improper fraction 7/6 into a mixed number by following these steps:
**3 2/6 + 2 5/6****= 5 + 7/6****= 5 + 6/6 + 1/6****= 5 + 1 + 1/6****= 6 1/6**

#### Guided Practice

*(8 minutes)*

- Assign students into an effective partnership.
- Distribute math journals or binder paper.
- Give each partner pair one of the mixed number addition problems to solve:
- Problem 1:
**5 3/4 + 2 3/4** - Problem 2:
**2 5/8 + 4 6/8** - Problem 3:
**4 4/6 + 1 3/6** - Problem 4:
**2 2/5 + 3 4/5**

- Problem 1:
- Circulate the room to monitor your students' understanding.
- Come together as a class and call on students to share their work and answers on the board.
- Discuss with students what went well while solving the problem with their partner and if they have any questions.

#### Independent working time

*(15 minutes)*

- Distribute math journals or binder paper.
- Write the following problems on the board:
**4 2/3 + 5 2/3****2 4/8 + 1 7/8****2 3/6 + 4 5/6****1 3/5 + 2 3/5****2 2/4 + 5 3/4****9 3/8 + 1 7/8****4 5/6 + 3 1/6****2 5/8 + 3 6/8**

- Tell students to solve these problems using the decomposition strategy.
- Circulate and offer support.

#### Differentiation

**Support:**

- Provide students with models (fraction bars or circles) that they can color to check their computations.
- Gather students in a teacher-led group during Independent Work Time to provide extra guidance and support.

**Enrichment:**

- Challenge students to write and solve their own mixed number addition problems or give them mixed number addition problems with three addends.

#### Assessment

*(2 minutes)*

- Distribute whiteboards to each student.
- Write this equation on the board:
**6 6/7 + 3 3/7 =** - Instruct students to solve this equation on their whiteboards and to show all of their work.
- Tell students to hold up their whiteboards when they are finished so you can check their work.

#### Review and closing

*(5 minutes)*

- Show students the following solved problems and ask for their help to identify the mistakes. Have a discussion about things they can do to help avoid making similar errors.
**4 3/6 + 2 4/6**- = 6 + 1/6
- = 6 1/6

**4 3/6 + 2 4/6**- = 6 + 7/6
- = 6/6 + 1/6
- = 1 1/6

**4 3/6 + 2 4/6**- = 6 + 7/12
- = 6 7/12