2. Lesson 10: I can multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products. 5th Grade Module 2 – Lesson 10

3. Get Your White Boards Ready! 5th Grade Module 2 – Lesson 10 3 X 2 is? 3 x 2 x 10 ÷ 10 is? 6 6 6 6 5 x 0.3 is? 5 x 0.3 x 10 ÷ 10 is? 1.5 3 x 2.5 is? 7.5 3 x 2.5 x 10 ÷ 10 is? 7.5 2 x 3.4 is? 6.8 2 x 3.4 x 10 ÷ 10 is? 6.8 Why are the products the same when we multiply by 10 and then divide by 10?

4. Get Your White Board Ready! 5th Grade Module 2 – Lesson 10 7.463 Say the Number Represent this number in a two-part number bond with ones as one part and thousandths as the other part. Draw on your whiteboard. 7.463 __ ones ______ thousandths Now represent this number in a two-part number bond with tenths and thousandths. 7.463 74 tenths 63 thousandths 7463 Now represent this number in a two-part number bond with hundredths & thousandths. 7.463 746 hundredths 3 thousandths

5. Draw three different two-part number bonds for the number. 5th Grade Module 2 – Lesson 10 8.972 1.Using ones & thousandths. 2.Using tenths & thousandths. 3.Using hundredths & thousandths. 1.Using ones & thousandths. 2.Using tenths & thousandths. 3.Using hundredths & thousandths. Volunteer to share their solutions below…

6. Draw three different two-part number bonds for the number. 5th Grade Module 2 – Lesson 10 6.849 1.Using ones & thousandths. 2.Using tenths & thousandths. 3.Using hundredths & thousandths. 1.Using ones & thousandths. 2.Using tenths & thousandths. 3.Using hundredths & thousandths. Volunteer to share their solutions below…

7. Application Problem 5th Grade Module 2 – Lesson 10 The fifth-grade craft club is making aprons to sell. Each apron takes 1.25 yards of fabric that costs $3 per yard and 4.5 yards of trim that costs $2 per yard. What does it cost the club to make one apron? If the club wants to make $1.75 profit on each apron, how much should they charge per apron? Solution on next slide…

8. Solution to Application Problem 5th Grade Module 2 – Lesson 10

9. Concept Development Round the factors to estimate the product 40 x 2 = 80 43 x 2.4 Predict whether our estimate is greater than or less than the actual product? Turn & Talk Predict whether our estimate is greater than or less than the actual product? Turn & Talk

10. 5th Grade Module 2 – Lesson 10 43 x 2.4 Let’s solve the product by decomposing the factors and building an area model. Record in your journal with me. How can we rename 2.4 using only tenths? 24 tenths Let’s decompose 24 tenths in expanded form along the length of our rectangle. 20 + 4 tenths The width is 43 whole units. Decompose 43 into expanded form. 3 + 40 Find the partial products for each section. Then add each row. 60 12 800 160 = 72 = 960 2 4 tenths x 4 3 7 2 9 6 0 10 3 2 Lets Build the Algorithm Don’t forget the unit!! tenths 43 x 24 tenths = 1,032 tenths (unit form) 43 x 2.4 = 103.2 (standard form)

11. 5th Grade Module 2 – Lesson 10 We just used unit form to multiply a decimal by a double digit. Now let’s learn another strategy to make it a little quicker. We can multiply one of the factors by 10 and then divide the product by 10. This is a simplifying short cut for multiplying by tenths. We can multiply one of the factors by 10 and then divide the product by 10. This is a simplifying short cut for multiplying by tenths. 2.4 x 4 3 X 10 24 x 43 7 2 9 6 0 1 0 3 2 ÷ 10 = 103.2 Why does that work? Turn & Talk Why does that work? Turn & Talk

12. 5th Grade Module 2 – Lesson 10 We estimated that 43 x 2.4 is about 40 x 2 = 80 The actual product is 103.2 Is the actual a reasonable answer compared to our estimate? Turn & Talk We estimated that 43 x 2.4 is about 40 x 2 = 80 The actual product is 103.2 Is the actual a reasonable answer compared to our estimate? Turn & Talk

13. Let’s Solve 3.5 x 42 5th Grade Module 2 – Lesson 10 First, round the factors and estimate the product. Record your work in your journal. First, round the factors and estimate the product. Record your work in your journal. 4 x 40 = 160 Naming 3.5 using tenths, draw an area model to show 3.5 x 42. Check your work with your partner. Remember to compare your answer with our estimate to make sure it is reasonable. Naming 3.5 using tenths, draw an area model to show 3.5 x 42. Check your work with your partner. Remember to compare your answer with our estimate to make sure it is reasonable.

14. Volunteers to share their solutions… 5th Grade Module 2 – Lesson 10 Or click to view solution Is 147 reasonable with our estimate of 160?

15. 5th Grade Module 2 – Lesson 10 Let’s confirm this product using the standard algorithm!! Partner A: Find the product naming 3.5 in tenths. Partner B: Find the product multiplying 3.5 by 10 and then dividing the product by 10. 3.5 x 4 2 3 5 x 4 2 x 10 3 5 tenths x 4 2 ÷ 10 Volunteers to show their answers using ink tool. How are these two ways of thinking the same? Turn & Talk How are these two ways of thinking the same? Turn & Talk

16. Let’s Try 15.6 x 73 5th Grade Module 2 – Lesson 10 First, round the factors and estimate the product. Record your work in your journal. First, round the factors and estimate the product. Record your work in your journal. 20 x 70 = 1400 Naming 15.6 using tenths, draw an area model to show 15.6 x 73. Check your work with your partner. Remember to compare your answer with our estimate to make sure it is reasonable. Naming 15.6 using tenths, draw an area model to show 15.6 x 73. Check your work with your partner. Remember to compare your answer with our estimate to make sure it is reasonable.

17. Volunteers to share their solutions… 5th Grade Module 2 – Lesson 10 Or click to view solution Is 1,138.8 reasonable with our estimate of 1,400? 100506tenths 3 30015018= 468 70 70003500420= 10,920 11,388 tenths = 1,138.8

18. 5th Grade Module 2 – Lesson 10 Let’s confirm 15.6 x 73 using the standard algorithm!! Let’s confirm 15.6 x 73 using the standard algorithm!! Partner B: Find the product naming 15.6 in tenths. Partner A: Find the product multiplying 3.5 by 10 and then dividing the product by 10. 15.6 x 7 3 1 5 6 x 7 3 x 10 1 5 6 tenths x 7 3 ÷ 10 Volunteers to show their answers using ink tool. How are these two ways of thinking the same? Turn & Talk How are these two ways of thinking the same? Turn & Talk

19. Get Ready to Complete the Rest of the Problem Set on Your Own! Complete Page 2.C.8 & 2.C.9 You will have 10-15 minutes to work. Try your Best! 5th Grade Module 2 – Lesson 10

20. Let’s discuss Michelle’s error in Problem 3. How does being fluent in whole number multi-digit multiplication help you multiply decimals?

21. 5th Grade Module 2 – Lesson 2 EXIT TICKET Page 2.C.10