### Lesson plan

# Multiplication of Mixed Numbers with Area Models

#### Learning Objectives

Students will be able to use an area model to solve multiplication problems with mixed numbers.

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

#### Introduction

*(10 minutes)*

- Review area models with whole numbers by showing students an example (see related media).
- Explain, "Today we are going to use area models to multiply a mixed number times a whole number."
- Remind students that a
**mixed number**is a number that has a whole number and a fraction, like 5½.

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- Write a mixed number multiplication problem on board (i.e.,
**3¼ x 2**). - Decompose the mixed number (
**3 + ¼**). - Draw a rectangle on the board. Label the short side with a 2.
- Draw a line to divide the long side of the rectangle into two parts. Write 3 and ¼ over the two divided parts so that you have a rectangle that has an area of
**2 x 3**and one with an area of**2 x ¼**. - Multiply to find the area of each portion of the divided rectangle and write the product inside the corresponding piece of rectangle (i.e., 6 and 2/4).
- Add the two
**partial products**(parts of the total answer) to get the answer. - Simplify the fraction and rewrite the multiplication sentence with the answer (i.e.,
**3¼ x 2 = 6½**).

#### Guided Practice

*(15 minutes)*

- Guide students through another example (i.e.,
**15 x 4½**) Remember to decompose two-digit whole numbers and draw additional sections in the area model as needed. - Give students a problem to try with a partner (i.e.,
**13 x 5⅙**). - Give students a "try it" problem to solve independently (i.e.,
**1⅔ x 6**). Circulate and offer support as needed. Then go over the problem as a class.

#### Independent working time

*(15 minutes)*

- Hand out scratch paper or have students work in math notebooks.
- Write three problems that have a mixed number times a whole number on the board and instruct students to solve them independently using area models (i.e.,
**7 x 2⅘**,**6¾ x 19**,**25 x 3⅛**). - Circulate and offer support as needed.

#### Differentiation

**Support:**

- Provide additional examples before assigning independent work.
- For independent work, assign problems with unit fractions or single-digit whole numbers.

**Enrichment:**

- Assign challenge problems with a fraction times a mixed number and have students try the same strategy to solve (i.e.,
**5¾ x ½**).

#### Assessment

*(5 minutes)*

- Hand out a piece of scratch paper to each student.
- Write a multiplication problem on the board (i.e.,
**3⅛ x 9**). - Have students solve using an area model.
- Collect student work as an exit ticket and check for understanding.

#### Review and closing

*(5 minutes)*

- Ask and discuss, "How can this strategy help us understand fractions and multiplication?"