Multiplying and Dividing Decimals

1. Multiplying and Dividing Decimals Marta Garcia, Buncombe County Schools Amy LeHew, Charlotte-Mecklenburg Schools Drew Polly, UNC Charlotte Thursday, October 31 8:30-9:15 Cedar A

2. Goals of the Session Today we will: Explore multiplication of decimals and connect the multiplication work of whole numbers to decimals Explore division of decimals and connect the division work of whole numbers to decimals

3. Let’s Get to Work! Use base ten blocks to justify why 3 x 50 is ten times larger than 3 x 5.

4. Grade 3 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. Use base ten blocks to justify why 3 x 50 is ten times larger than 3 x 5

5. Use the thinking on the left to solve 6 x 50 Associative Property: Why is the Product Ten Times Larger? 6 x 5 = 30 3 groups of 10

6. CCSS.Math.Content.4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. • CCSS.Math.Content.4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1

7. What does it mean to be Ten Times Bigger? Student responses to how many times greater is 4 x 100 than 4 x 10? —4 x 100 is 360 times bigger than 4 x 10 4 x 100 is 90 times bigger than 4 x 10 — —4 x 100 is 100 times bigger than 4 x 10

8. 5th Grade —5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used

9. Proving Equivalence with Decimals Remember 2 x 30 = 3 x 20 .2 x 30 = 20 x .3

10. Comparing Two Generalizations What’s the “rule” 20 x 30 2 x 3 “Count the zeros” What’s the “rule” .2 x .3 2 x 3 “Count the decimal places”

11. Understanding the Standards —4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. —5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

12. True or False? 200 divided by 40 = 20 divided by 4

13. Dividing Decimals Explore… —32 divided by 8 3.2 divided by 8 .32 divided by 8

14. Sally … Making Sandwiches —We have 99.99 grams of peanut butter to use to make sandwiches. If we put 0.3 grams on each sandwich, how many sandwiches can we make? —“I know that I can move the decimal in both numbers one spot to the right to make 99.9 divided by 3. I then just divided and got my answer 33.3. We can make 33.3 sandwiches. ——What did Sally do mathematically when she moved the decimal? —What does Sally “understand” about place value? —What question could we ask Sally to assess her understanding?

15. Comparing Two Generalizations What’s the “rule” 80,000 divided by 400 “Just cross out the zeros” What’s the “rule” 8.88 divided by 0.4 “Just move the decimal.”

16. Making Connections —How does the multiplication and division of decimals connect the base ten work from prior grades?

17. Questions? Reflections?

18. Contact Information Marta- marta.garcia@bcsemail.org Amy- amy.lehew@cms.k12.nc.us Drew- drew.polly@uncc.edu