Unit 5, Lesson 8: Calculating Products of Decimals

Transcription

1 Unit 5, Lesson 8: Calculating Products of Decimals Lesson Goals Required Materials Use an algorithm to calculate products of decimals. Understand how a multiplication algorithm works. 8.1: Number Talk: Twenty Times a Number (5 minutes) Setup: Display one problem at a time. 30 seconds of quiet think time per problem, followed by a brief whole-class discussion. Evaluate mentally Unit 5: Arithmetic in Base Ten, Lesson 8: Calculating Products of Decimals 1

2 8.2: Calculating Products of Decimals (25 minutes) Setup: Students in groups of minutes of partner work on the first 3 questions then brief whole-class discussion. 2 3 of quiet work time on the last question, followed by whole-class discussion. Unit 5: Arithmetic in Base Ten, Lesson 8: Calculating Products of Decimals 2

3 1. A common way to find a product of decimals is to calculate a product of whole numbers, then place the decimal point in the product. Here is an example for. Use what you know about decimals and place value to explain why the decimal point of the product is placed where it is. 1. Answers vary. 2. a b a. Length: 4 and 0.6 Width: 0.9 A: B:, so 2. Use the method shown in the first question to calculate each product. a. b. b. Length: 10, 6, and 0.5 Width: Use area diagrams to check your earlier calculations. For each problem: Decompose each number into its base-ten units and write them in the boxes on each side of the rectangle. Write the area of each lettered region in the diagram. Then find the area of the entire rectangle. Show your reasoning. A: B: C:, so a. 4. About centimeters. Unit 5: Arithmetic in Base Ten, Lesson 8: Calculating Products of Decimals 3

4 . Anticipated misconceptions b. Students may not recall how to use the algorithm to multiply whole numbers. Consider reviewing the process prior to the activity. 4. About how many centimeters are in 6.25 inches if 1 inch is about 2.5 centimeters? Show your reasoning. Students may think that when calculating products, the decimal points need to line up. They may even write extra zeros at the end of a factor so there are the same amount of decimal places in each factor. Although this will not affect the answer, it is more efficient to align both factors to the right. If extra zeros are written at the end of a factor, there will be extra zeros accumulated in the calculation, and this can lead to careless errors. Unit 5: Arithmetic in Base Ten, Lesson 8: Calculating Products of Decimals 4

5 8.3: Practicing Multiplication of Decimals (Optional, 15 minutes) Setup: Quiet think time to complete the activity, followed by a partner and whole-class discussion. 1. Calculate each product. Show your reasoning. If you get stuck, draw an area diagram to help. 1. a a. b. b A rectangular playground is 18.2 meters by meters. 2. a square meters a. Find its area in square meters. Show your reasoning. b. If 1 meter is approximately 3.28 feet, what are the approximate side lengths of the playground in feet? Show your reasoning. b feet and feet Unit 5: Arithmetic in Base Ten, Lesson 8: Calculating Products of Decimals 5

6 Are you ready for more? 1. Write the following expressions as decimals. a. b. c. 2. Describe the decimal that results as this process continues. 3. What would happen to the decimal if all of the positive and negative signs became multiplication symbols? Explain your reasoning. Possible Responses 1. a. 0.9 b c The decimal would consist of 0.8 sandwiched between 1 s on the left and 8 s on the right, ending with a 9 in the smallest decimal place. 3. As the process continues, the decimal alternates between being 1 and being equal to the last number that's multiplied by the previous product. Lesson Synthesis (5 minutes) How can we efficiently calculate products of decimals? 8.4: Calculate This! (Cool-down, 5 minutes) Setup: None. Unit 5: Arithmetic in Base Ten, Lesson 8: Calculating Products of Decimals 6

7 Calculate. Show your reasoning Unit 5: Arithmetic in Base Ten, Lesson 8: Calculating Products of Decimals 7