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

Use teacher tools for all warm up activities! Multiply fractions

Write Fractions as Decimals

Multiply Whole Numbers by Decimals

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?

Problem 1a 0.1 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

Concept Development- Students will need a Place Value Chart! Problem 1a 0.1 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?

Problem 1a 0.1 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.

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

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

Problem 1c 0.01 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

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

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

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.

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

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

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

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

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

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!

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

Problem 4c 0.07 x 0.2 Solve this problem independently. Compare your answer with your partner when you’re done.

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

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

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