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.

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

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

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

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 =

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

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

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

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

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

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

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.

Concept Development – Problem 1 39.1 ÷ 17 3.91 ÷ 17

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.

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

Concept Development – Problem 2 63.6 ÷ 73 6.36 ÷ 73

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

Concept Development – Problem 3

End of Lesson Activities Debrief Problem Set Homework Exit Ticket

Exit Ticket

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

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 ≈

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.

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

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 ≈

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?