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**Lesson 17: Objective: Relate decimal and fraction multiplication**

By the end of this lesson, you will be able to… Lesson 17: Objective: Relate decimal and fraction multiplication 5th Grade Module 4– Lesson 17 K. Clauson

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**Use teacher tools for all warm up activities!**

Multiply fractions

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**Write Fractions as Decimals**

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**Multiply Whole Numbers by Decimals**

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Application Problem Ms. Casey grades 4 tests during her lunch. She grades 1/3 of the remainder after school. If she still has 16 tests to grade after school, how many tests are there?

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Problem 1a x 4 Concept Development Read this multiplication expression using unit form and the word of Write this expression as a multiplication sentence using a fraction and solve- Do NOT simplify your product Write this as a decimal on your board 1 tenth of 4 1/10 x 4 = 4/10 0.4

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**Concept Development- Students will need a**

Place Value Chart! Problem 1a x 4 = 0.4 Let’s compare the 4 ones that we started with to the product that we found, 4 tenths. Place 4 and 0.4 on a place value chart and talk to your partner about what happened to the digit 4 when we multiplied by 1 tenth. Why did our answer get smaller?

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Problem 1a x 4 = 0.4 Concept Development Why did our answer get smaller? Answer: This is like 4 copies of 1 tenth. There are 40 tenths in 4 wholes. 1 tenth of 40 is 4. The unit is tenths, so the answer is 4 tenths. The digit 4 stays the same because we are multiplying by 1 of something, but the unit is smaller, so the digit 4 shifted one space to the right. The answer is 4 tenths.

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Higher level thinking! What about 1/100 of 4? Multiply and show your thinking on a place value chart. What about 1/1000 of 4? 0.04 0.004

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Problem 1b 0.1 x 2 Concept Development Read this multiplication expression using unit form and the word of Write this expression as a multiplication sentence using a fraction and solve- Do NOT simplify your product Write this as a decimal on your board 1 tenth of 2 1/10 x 2 = 2/10 0.2

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Problem 1c x 6 Concept Development Read this multiplication expression using unit form and the word of Write this expression as a multiplication sentence using a fraction and solve- Do NOT simplify your product Write this as a decimal on your board 1 hundredth of 6 1/100 x 6 = 6/100 0.06

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Problem 2a 0.1 x 0.1 Write this as a fraction multiplication sentence and solve it with a partner. Let’s draw this as an area model to see if this makes sense. What should I draw first? 1/10 x 1/10 = 1/100

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Problem 2a 0.1 x 0.1 1/10 x 1/10 = 1/100 Let’s draw this as an area model to see if this makes sense. Look at the double-shaded parts, what is 1/10 of 1/10? Write the answer as a decimal. 1/100 0.01 1 10 1 10

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Problem 2a 0.1 x 0.1 Let’s show this multiplication on the place value chart. When writing 1 tenth, where do we put the digit 1? Turn and talk to your partner about what happened to the digit 1 that started in the tenths place, when we took 1 tenth of it. Answer! The digit shifted 1 place to the right. We were taking a part of 1 tenth, so the answer is smaller than 1 tenth. It makes sense that the digit shifted to the right one place again because the answer got smaller.

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Problem 2b 0.2 x 0.1 Write this as a fraction multiplication sentence and solve it with a partner. Show me 2 tenths on your place value chart. Explain to your partner what happened when you multiply it by 1 tenth! 2/10 x 1/10 = 2/100

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Problem 2c 1.2 x 0.1 Show me 1.2 on your place value chart. Explain to your partner what happened when you multiply it by 1 tenth. Write this as a fraction multiplication sentence. How can we express 1.2 as a fraction greater than 1? 12/10 x 1/10 = 12/100

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Problem 3a 0.1 x 0.01 Work with a partner to show this as fraction multiplication.

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Problem 3b 0.5 x 0.01 Visualize a place value chart. When writing 0.5, where will the digit 5 be? What will happen as we multiply by 1 hundredth? Show the solution to this problem using fraction multiplication. Show the answer as a decimal. In the tenths place The 5 will shift two places to the right to the thousandths place. 5/10 x 1/100 = 5/1000 0.005

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Problem 3c 1.5 x 0.01 Express 1.5 as a fraction greater than 1 Show the solution to this problem using fraction multiplication. Write the answer as a decimal. 15/10 15/10 x 1/100 = 15/1000 0.015

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Problem 4a 7 x 0.2 I am going to rewrite this problem expressing the decimal as a fraction. 7 x 2/10 0.2 = 2/10 * They show the same thing! This is like multiplying fractions like we’ve been doing!

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Problem 4b 0.7 x 0.2 Work with a partner to show the solution using fraction multiplication.

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Problem 4c x 0.2 Solve this problem independently. Compare your answer with your partner when you’re done.

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**Get Ready to Finish the Problem Set on Your Own!**

Complete Problem Set for Lesson 17 Fast finishers: Math Center Activities- choice boards, extra Sprint challenge CML packets/ worksheets Problem Solving pages 5th Grade Module 4– Lesson 17 K. Clauson

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**5th Grade Module 4- Lesson 17**

LET’S Debrief Take 2 minutes to check your answers with your partner. Let’s share any insights you had while solving these problems. 5th Grade Module 4- Lesson 17 K. Clauson

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**5th Grade Module 4– Lesson 17**

EXIT TICKET LESSON 17 5th Grade Module 4– Lesson 17 K. Clauson

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