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Unit 5, Lesson 6: Methods for Multiplying
Decimals
Let’s look at some ways we can represent multiplication of decimals.
6.1: Which One Doesn’t Belong: Products
Which expression doesn’t belong? Explain your reasoning.
6.2: Using Properties of Numbers to Reason about Multiplication
- Elena and Noah used different methods to compute. Both computations were correct.
Analyze the two methods, then discuss these questions with your partner.
Which method makes more sense to you? Why?
What might Elena do to compute? What might Noah do to compute? Will the two methods result in the same value?
- Compute each product using the equation and what you know about fractions, decimals, and place value. Explain or show your reasoning.
A. B. C. D.
a. b. c.
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6.3: Using Area Diagrams to Reason about Multiplication
- In the diagram, the side length of each square is 0.1 unit.
b. How can you use the area of each square to find the area of the rectangle? Explain or show your reasoning.
c. Explain how the diagram shows that the equation is true.
a. Explain why the area of each square is not 0. square unit.
- Label the squares with their side lengths so the area of this rectangle represents.
a. What is the area of each square?
b. Use the squares to help you find. Explain or show your reasoning.
- Label the squares with their side lengths so the area of this rectangle represents. Next, use the diagram to help you find. Explain or show your reasoning.
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Unit 5, Lesson 6: Methods for Multiplying Decimals
- Find each product. Show your reasoning.
a.
b.
c.
- You can use a rectangle to represent.
- One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon.
- Calculate each sum or difference.
a. What must the side length of each square represent for the rectangle to correctly represent?
b. What area is represented by each square?
c. What is? Show your reasoning.
a. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
b. Is the cost of gas greater in Buffalo or in Toronto? How much greater?
a. b. c. d.
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(from Unit 5, Lesson 2)
- Find the value of using any method.
(from Unit 4, Lesson 11)
- Find the area of the shaded region. All angles are right angles. Show your reasoning.
(from Unit 1, Lesson 1)
- a. Priya finds by calculating , then moving the decimal point three places to the left. Why does Priya’s method make sense?
b. Use Priya’s method to calculate. You can use the fact that.
c. Use Priya’s method to calculate.
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