Engage NY Math Module 2

1. Engage NY Math Module 2 Lesson 25: Use basic facts to approximate decimal quotients with two-digit divisors, reasoning about the placement of the decimal point.

2. Rename Tenths and Hundredths • State the following numbers as decimals. • 10 tenths • 1 • 90 tenths • 9 • 94 tenths • 9.4 • 100 tenths • 10 • 700 tenths • 70 • 783tenths • 78.3 • 372 tenths • 37.2 • 9 hundredths • .09 • 10 hundredths • .10 • 90 hundredths • .90 • 98hundredths • .98 • 100 hundredths • 1 • 900 hundredths • 9 • 980 hundredths • 9.8 • 1,000 hundredths • 10 • 7,000 hundredths • 70 • 7,400 hundredths • 74 • 7,418 hundredths • 74.18 • 4,835 hundredths • 48.35

3. Divide Decimals by 10 • 3,800 ÷ 10 = ? • 380 • When dividing by 10, digits shift how many places to the right? 3 8 0 0 3 8 0 0

4. Divide Decimals by 10 • 380 ÷ 10 = ? • 38 • 38 ÷ 10 = ? • 3.8 3 8 0 3 8 0 3 8 3 8

5. Divide Decimals by 10 • In your journals, draw a large place value mat and show the “shifts” in order to solve the following problems. • 3.8 ÷ 10 = • 270 ÷ 10 = • 2.7 ÷ 10 = • 4,900 ÷ 10 = • 49 ÷ 10 = • 0.49 ÷ 10 =

6. Divide Decimals by Multiples of 10 • 1.2 ÷ 4 • Solve this equation expressing the whole in tenths. • 12 tenths ÷ 4 = 3 tenths • 1.2 ÷ 4 = 0.3 • 1.2 ÷ 40 = ? • Write 12 tenths ÷ 40 as a three-step division sentence taking out the ten. • (1.2 ÷ 10) ÷ 4 = 0.12 ÷ 4 = 0.03

7. Divide Decimals by Multiples of 10 • 2.4÷ 2 • Solve this equation expressing the whole in tenths. • 24 tenths ÷ 2 = 12 tenths • 2.4 ÷ 2 = 1.2 • 2.4 ÷ 20 = ? • Write 24 tenths ÷ 20 as a three-step division sentence taking out the ten. • (2.4 ÷ 10) ÷ 2 = 0.24 ÷ 2 = 0.12

8. Divide Decimals by Multiples of 10 • 8÷ 2 • Solve this equation expressing the whole in ones. • 8 ones ÷ 2 = 4 ones • 8 ÷ 2 = 4 • 8 ÷ 20 = ? • Write 8 ones ÷ 20 as a three-step division sentence taking out the ten. • (8 ÷ 10) ÷ 2 = 0.8 ÷ 2 = 0.4

9. Divide Decimals by Multiples of 10 • 0.35÷ 5 • Solve this equation expressing the whole in hundredths. • 35 hundredths ÷ 5= 7 hundredths • 0.35 ÷ 5 = 0.07 • 0.35 ÷ 50 = ? • Write 35 hundredths ÷ 50 as a three-step division sentence taking out the ten. • (0.35 ÷ 10) ÷ 5 = 0.035 ÷ 5 = 0.007

10. Application Problem • Ms. Heinz spent 12 dollars on 30 bus tokens for the field trip. What was the cost of 12 tokens? $12.00 ÷ 30 = 12.00 ÷ (3 x 10) = (12.00 ÷ 3) ÷ 10 = 4.00 ÷ 10= $0.40 per token $0.40 x 12 = 0.40 x (10 x2)= (0.40 x 10) x 2 = 4.00 x 2 = $8.00 for 12 bus tokens

11. Concept Development – Problem 1 • In module 1, we rounded our decimal factors to estimate the product. We will estimate quotients now by rounding the whole and divisor. • 39.1 ÷ 17 • Just as we did before, round the divisor first. What is 17 rounded to the nearest ten? • 20 • Let’s record our estimation. We need to round our whole, 39.1, to a number that can easily be divided by 20. Turn and share your ideas with your table. • 39.1 ÷ 17 ≈ ______ ÷ 20 • What could we round 39.1 to? • 40 • 39.1 ÷ 17 ≈ 40 ÷ 20 = 4 ÷ 2 = 2 • 39.1 ÷ 17 ≈ 2

12. Concept Development – Problem 1 • 3.91 ÷ 17 • Think about the size of this related quotient based on the estimation we just made. • The whole has the same digits, but it is 1 tenth the size of the first one. The quotient will probably be around 2 tenths because that is 1 tenth as large as 2. • Let’s estimate the quotient. Since our divisor is the same, let’s use the same estimate of 20. Can you think of a multiple of 2 that would be close to 3.91? • 4 • 4 ÷ 20 ≈ ? • Show how to find the estimated quotient writing it as a 3 step division sentence taking out the ten. • 4 ÷ 20 = 4 ÷ 10 ÷ 2 = 0.4 ÷ 2 = 0.2 • Show the equation to find the estimated quotient. • 4 ÷ 20 = 0.2 • Why is estimating useful? • It helps give us a starting place when we need to find the actual quotient, just like with whole numbers.

13. Concept Development – Problem 1 • 39.1 ÷ 17 • 3.91 ÷ 17

14. Concept Development – Problem 2 • 63.6 pounds of rice were put into 73 bags. About how many pounds of rice were in each bag? • 63.6÷ 73 = _______ • Thinking about this story problem, will the number of pounds in each bag be more than 1 pound or less than 1 pound? Discuss this with your table and how you know. • It should be less than 1 pounds because there are 73 bags and only 63 pounds of rice. There’s not enough to put 1 pound in each bag. • Let’s estimate the quotient. • What can we round our divisor to? • 70 • What can we estimate our whole to be? • 63 is in the whole and that is a multiple of 7.

15. Concept Development – Problem 2 • 63.6÷ 73 = _______ • What is the estimation expression in standard form? • 63 ÷ 70 • Show how to solve this problem using a 3 step division sentence. • 63 ÷ 10 ÷ 7 = 6.3 ÷ 7 = 0.9 • There are about 0.9 pounds of rice in each bag. • What if there were only 6.36 pounds of rice to put into 73 bags? How does this problem relate to the previous problem? • Our dividend is one tenth less than the first problem so this quotient should be one tenth less than the first problem. • Solve this problem in your journal. • 6.36 ÷ 73 ≈ 6.3 ÷ 70 = 6.3 ÷ 10 ÷ 7 = 0.63 ÷ 7 = 0.09

16. Concept Development – Problem 2 • 63.6 ÷ 73 • 6.36 ÷ 73

17. Concept Development – Problem 3 • 11.72 ÷ 42 = ___ Read this division sentence in word form. • 11 and 72 hundredths divided by 42. • In your journals, round the divisor and whole then estimate the quotient. • 12 ÷ 40 = 12 ÷ 10 ÷ 4 = 1.2 ÷ 4 = 0.3

18. Concept Development – Problem 3

19. End of Lesson Activities Debrief Problem Set Homework Exit Ticket

20. Exit Ticket

21. Problem Set 1. Estimate the quotients. • 3.24 ÷ 82 • 361.2 ÷ 61 • 7.15 ÷ 31 • 85.2 ÷ 31 • 27.97 ÷ 28

22. Problem Set • 2. Estimate the quotient in (a). Use your estimated quotient to estimate (b) and (c). • 7.16 ÷ 36 • 716 ÷ 36 • 71.6 36

23. Problem Set 3. Edward bikes the same route to and from school each day. After 28 school days, he bikes a total distance of 389.2 miles. • Estimate how many miles he bikes in one day. • If Edward continues his routine of biking to school, about how many days altogether will it take him to reach a total distance of 500 miles? 4. Xavier goes to the store with $40. He spends $38.60 on 13 bags of popcorn. • About how much does a bag of popcorn cost? • Does he have enough money for another bag? Use your estimate to explain your answer.

24. Homework Task 1. Estimate the quotients. • 3.53 ÷ 51 • 24.2 ÷ 42 • 9.13 ÷ 23 • 79.2 ÷ 39 • 7.19 ÷ 58

25. Homework Task • 2. Estimate the quotient in (a). Use your estimated quotient to estimate (b) and (c). • 9.13 ÷ 42 • 913 ÷ 42 • 91.3 42

26. Homework Task 3. Mrs. Huynh bought a bag of 3 dozen toy animals as party favors for her son’s birthday party for $28.97. Estimate the price of each toy animal. 4. Carter drank 15.75 gallons of water in 4 weeks. He drank the same amount of water each day. • Estimate how many gallons he drank in one day. • Estimate how many gallons he drank in one week. • About how many days altogether will it take him to drink 20 gallons?