Multiplication of Decimals Using Models

Multiplying Decimals by Whole Numbers

This means 4 groups of two tenths. Multiply 4 × 0.2 This means 4 groups of two tenths. 4 × 0.2 = 0.8 Introduce the concept of multiplying a whole number times a tenth. What does the model represent? (hundredths) What would 0.2 look like on this model? (2 columns) Discuss how the model represents the problem. Have students determine the answer before showing the answer. 0.2 + 0.2 + 0.2 + 0.2 = 0.8

This means 3 groups of three tenths. Multiply 3 × 0.3 This means 3 groups of three tenths. 3 × 0.3 = 0.9 Continue the same discussion with the models on this slide and the next one. 0.3 + 0.3 + 0.3 = 0.9

This means 3 groups of six tenths. Multiply 3 × 0.6 This means 3 groups of six tenths. 0.6 + 0.6 + 0.6 = 1.8 3 × 0.6 = 1.8

Now, you try one…….. Use your activity page to model this problem. 5 × 0.4 = 2.0 Students will color their own model on the activity page before showing the product. Discuss writing 2.0 to represent two wholes. 0.4 + 0.4 + 0.4 + 0.4 + 0.4 = 2.0

This means 8 groups of six hundredths. Multiply 8 × 0.06 This means 8 groups of six hundredths. Continue similar discussions with these samples multiplying a whole number times hundredths. What equations have you seen that look like this? When would you see a problem like this in real life? (when dealing with money) 8 × 0.06 = 0.48

Multiply 5 × 0.25 This means 5 groups of twenty-five hundredths. What do you think the answer will be? Can you use what you know about money to solve this? 5 × 0.25 = 1.25

It’s easier to see the answer if we complete the whole. Let’s try another one…….. Use your activity page to model this problem: 2 × 0.73 = 1.46 Allow students to color their two groups of 0.73 as they wish. If students showed this in different ways, allow them to share with the class. After they are done, discuss how they could break apart 0.73 to complete a whole. It’s easier to see the answer if we complete the whole.

1.28 Here’s one more for you to try…….. Use your activity page to model this problem: 4 × 0.32 = 1.28 Encourage students to complete the whole as they color in the model.

What if the model is different? Work with a partner to choose the correct model to represent each problem. Use a dry erase board and a marker to identify your answer choice. Be ready to justify your answer!

Paul used this model to represent 1 whole. Which model represents 1.2 x 3? A. B.

Lisa used the model below to represent one whole. Which model represents 2(1.9)? A. B.

STAAR Question 2016

Let’s Review What do you notice about these problems? 0.06 × 8 0.48 × 8 0.48 0.32 × 2 0.64 0.25 × 5 1.25 0.73 × 2 1.46 0.32 × 4 1.28 Allow time for students to share their observations. Discuss the decimal placement in the problem and in the product. What do you notice about these problems?

Let’s Review What do you notice about these problems? 0.2 × 4 0.8 0.3 × 4 0.8 0.3 × 3 0.9 0.6 × 3 1.8 0.4 × 5 2.0 Allow time for students to share their observations. Discuss the decimal placement in the problem and in the product. What do you notice about these problems?