# Lesson 20

Products in the Hundredths Place

### Lesson Purpose

The purpose of this lesson is for students to find products of tenths and tenths.

### Lesson Narrative

The purpose of this lesson is for students to find products of two decimal numbers where each decimal represents a number of tenths, using the place value reasoning and diagrams that were also useful for finding the product of a whole number and a decimal. Students explain why $$0.1 \times 0.1 = 0.01$$ in the warm-up and this opens up one strategy for finding products like $$1.5 \times 0.7$$. In particular, this can be rewritten as

$$\ (15 \times 0.1) \times (7 \times 0.1) = (15 \times 7) \times (0.1 \times 0.1)$$.

So the value of $$1.5 \times 0.7$$ is 105 hundredths or 1.05. A second approach uses area diagrams which students are familiar with from earlier lessons in this unit and from when they used them to find products of fractions. Decimals are an example of fractions and these diagrams are useful in this situation as well.

• Representation
• MLR8

Activity 1: Products of Tenths

### Learning Goals

Teacher Facing

• Use diagrams and place value reasoning to interpret and evaluate products of two decimal numbers.

### Student Facing

• Let’s multiply tenths by tenths.

### Required Materials

Materials to Copy

• Small Grids

Building Towards

### Lesson Timeline

 Warm-up 10 min Activity 1 15 min Activity 2 20 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

What do you love most about math? How are you sharing that joy with your students and encouraging them to think about what they love about math?