1. NYS Math Module 1 Lesson 12 Objective: Multiply a decimal fraction by single-digit whole numbers, including using estimation to confirm the placement of the decimal point. I can: Add decimals 5NBT.7 Find the product 5.NBT.7

2. Sprint – Adding Decimals **** 8 minutes **** On your mark, get set, GO!

3. Find the Product 4 x 2 ones = _____ Let’s keep going. Say the multiplication in unit form. 8 ones Yes, 4 times 2 ones equals 8 ones. Say the multiplication in unit form. 4 x 0.2 = _______ 8 tenths 4 x 0.02 = _________ 8hundredths

4. Let’s continue to say the entire multiplication sentence. 5 x 3 = _______ 15 ones 5 x 0.3 = _______ 15 tenths 5 x 0.03 = ___________ 15 hundredths

5. Look carefully. Write the answer on your white board. 3 x 0.2 = _______ 0.6 3 x 0.03 = ______ 0.09 3 x 0.23 =_______ 0.69 2 x 0.14 =_______ 0.28

6. Word Problem Patty buys 7 juice boxes a month for lunch. If one juice box costs $2.79, how much money does Patty spend on juice each month? If necessary, use an area model to solve. 2.79 7 X 19.53

7. Extension Patty would spend $19.53 a month on juice. How much would she spend in 10 months? In 12 months? Work with a partner. 19.53 10 X 195.30 19.53 12 X 3906 19530 + 234.36

8. Concept Development ** Write on your white boards.** 31 x 4 = __________ 3.1 x 4 = __________ 0.31 x 4 = __________ How are these 3 problems the same ? Yes, they are the same numbers. Use area models to solve, if necessary. 12.4 124 1.24

9. How are all three problems alike? So, if all three problems have the same digits in the problem and in the product, do they have the same value? Turn and talk with your partner. Okay, so the digits are all have a different value to begin with, but they are in the same order for the product. Therefore, I can multiply first and then worry about where to place the decimal. 31 x 4 = __________ 3.1 x 4 = __________ 0.31 x 4 = __________ 12.4 124 1.24

10. 5.1 x 6 = _______ How many tenths are there in 5.1? Right, there are 51, so multiply 51 x 6 first. 51 6 X 306 306 What?Tenths. Tenths So, 306 tenths = 30.6 Here we see that we can multiply first and then worry about where to place the decimal. Let’s try it. 306 Tenths.

11. 11.4 x 4 = ____ What is the smallest unit in 11.4?Tenths 114 tenths X 456 tenths Now, let’s think about where to place the decimal. If we multiply 11 x 4 it’s 44. So our answer has to be close to 44. It would make sense to put the decimal between the 5 and 6. Okay, so lets convert 11.4 into tenths. How many tenths are there in 11.4? 4 456 tenths

12. 3.12 x 4 = ____ 312 tenths X 1248 tenths 0r 12.48 4 What’s the product?

13. + 3.22 x 5 = ____ 3.22 X 16.10 5 What’s the product? 2 numbers after the decimal in the problem, so there are 2 numbers after the decimal in the product.

14. + 3.42 x 6 = ____ 3.42 X 20.52 6 What’s the product? 20.52

15. I’m going to write four possible products. Talk to your partner about which one would be reasonable. Be ready to share your thinking. 4.12 x 7 = 2.884 28.84 0.2884 288.4 4.12 X 28.84 7 You know 4 x 7 =28, so your answer has to be around 28 ones.

16. Which of the following would be the most reasonable product? 15.8 x 3 = 47.4 4.74 0.474 474 47.4, because 15 x 3= 45, my answer has to be around 45 ones 47.4

17. What is 0.733 renamed using its smallest unit? 0.733 x 4 = 2.932 29.32 293.2 2932 2.932, because 1 x4 =4, my answer has to be around 4 ones 733 thousandths Now multiply vertically by 4. What is the product? 2932 thousandths Which of these is the most reasonable product?

18. Rename 10.733 using its smallest units and multiply by 4. What is the product? 10.733 x 4 = 4.2932 42.932 429.32 4293.2 42.932, because 10 x 4 = 40, my answer has to be around 40 ones 42932 thousandths Which of these is the most reasonable product?

19. 5.733 x 4 = 5.733 X 22.932 4

20. Problem Set Review Example 1: Pick the most reasonable product. Explain your reasoning. 3.5 x 2 7 70 700 0.7 3 x 2= 6, 7 is closest to 6. or 35 x 2= 70 tenths which is the same as 7 ones. The rest of the problems are word problems. Be sure to show your reasoning by showing all of your work!

21. Thank you for your purchase. Backgrounds, clip art, and font by: www.teachingtidbit.blogspot.com www.mycutegraphics.com www.Teacherspayteachers.com/store/Colleen-Alaniz Worksheets in this file are from NYS Math Module 1 Grade 5. I have simply minimized the pages to reduce the use of paper. For the entire module visit: www.engageny.org/resource/grade-5-mathematics-module-2