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?"
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