Engage NY Math Module 2

1. Engage NY Math Module 2 Lesson 27: Divide decimal dividends by two digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method.

2. Divide by Multiples of 10 • 1.2 ÷ 6 • Solve this equation expressing the whole in tenths. • 12 tenths ÷ 6 = 2 tenths • 1.2 ÷ 6 = 0.2 • 1.2 ÷ 60 = ? • Write 12 tenths ÷ 60 as a three-step division sentence taking out the ten. • (1.2 ÷ 10) ÷ 6 = 0.12 ÷ 6 = 0.02

3. Divide by Multiples of 10 • 8.4 ÷ 4 • Solve this equation expressing the whole in tenths. • 84 tenths ÷ 4= 21 tenths • 8.4 ÷ 4= 2.1 • 8.4 ÷ 40 = ? • Write 84 tenths ÷ 40 as a three-step division sentence taking out the ten. • (8.4 ÷ 10) ÷ 4= 0.84 ÷ 6 = 0.21

4. Divide by Multiples of 10 • 6÷ 3 • Solve this equation expressing the whole in ones. • 6 ones ÷ 3 = 2 ones • 6 ÷ 3 = 2 • 6 ÷ 60 = ? • Write 6 ones ÷ 60 as a three-step division sentence taking out the ten. • (6 ÷ 10) ÷ 6 = 0.6 ÷ 6 = 0.1

5. Divide by Multiples of 10 • 0.32÷ 4 • Solve this equation expressing the whole in hundredths. • 32 hundredths ÷ 4 = 8 hundredths • 0.32 ÷ 4 = 0.08 • 0.32 ÷ 40 = ? • Write 32 hundredths ÷ 40 as a three-step division sentence taking out the ten. • (0.32 ÷ 10) ÷ 4 = 0.032 ÷ 4 = 0.008

6. Unit Conversions • Complete the following conversions. • 1 L = ______ mL • How many milliliters are in 1 L? • 1,000 mL • 1 ft= ______ in • How many inches are in 1 ft? • 12 in • 1 kg = ______ g • How many grams are in 1 kilogram? • 1,000 g • 1 lb= ______ oz • How many ounces are in 1 lb? • 16 oz

7. Unit Conversions • Complete the following conversions. • 0.732 L = ______ mL • What is our conversion factor? • 1 L = 1,000 mL • Using your conversion factor, solve to show how many mL are in 0.732 L. • 0.732 x 1,000 = 732 mL • 0.037 L = ______ mL • What is our conversion factor? • 1 L = 1,000 mL • Using your conversion factor, solve to show how many mL are in 0.037 L. • 0.037 x 1,000 = 37 mL

8. Unit Conversions • Complete the following conversions. • 0.537 kg = ______ g • What is our conversion factor? • 1 kg = 1,000 g • Using your conversion factor, solve to show how many g are in 0.537 kg. • 0.537 x 1,000 = 537 g • 0.04 kg = ______ g • What is our conversion factor? • 1 kg = 1,000 g • Using your conversion factor, solve to show how many g are in 0.04 kg. • 0.04 x 1,000 = 40 g

9. Divide by Two-Digit Numbers • In your notebooks, solve two of the following problems using the standard algorithm. • 83.03 ÷ 23 • 3.61 • 6.76 ÷ 13 • 0.52 • 12.43 ÷ 11 • 1.13 • 65.94 ÷ 21 • 3.14

10. Application Problem Michael has 567 pennies, Jorge has 464, and Jamie has 661. If the pennies are shared equally by the 3 boys and 33 of their classmates, how much money will each classmate receive? Express your final answer in dollars. 567 464 + 661 1,692 4 7 Multiples of 36 36 -- 1 72 -- 2 108 -- 3 144 -- 4 180 -- 5 216 -- 6 252 – 7 288 – 8 36 1, 6 9 2 47 pennies = 0.47 of a dollar = $0.47 Each classmate will receive $0.47 dollars. -14 4 2 5 2 2 5 2 0

11. Concept Development – Problem 1 • In a 77 kilometer relay race, each of 22 team members run an equal distance. How many kilometers does each team member run? • Write a division equation to solve for the number of kilometers run by each team member. • 77 ÷ 22 • Let’s solve this together using our multiples. Multiples of 22 22 – 1 44 – 2 66 – 3 88 – 4 110 – 5 . 5 3 22 7 7 . 0 -6 6 1 1 Each team member will run 3.5 km during the race. 0 - 1 1 0 0

12. Concept Development – Problem 1 • This problem could also be solved using estimation to give us a number to start the standard algorithm.

13. Concept Development – Problem 2 • A vial contains 14.7 mL of serum that is then split equally into 21 tiny containers. How much serum is in each new container? • In your journals, write a division equation that matches this story problem. • 14.7 ÷ 21 • Before solving this problem, let’s reason about what our quotient might be. Will there be more than 1 mL in each container or less than 1 mL? Justify your thinking. • It will have to be less than 1 mL because there are more containers than mL of serum. To have 1 mL in each container, there would have to be 21 mL of serum and we only have about 15 mL of serum. . 7 0 21 1 4 . 7 Now solve this problem in your journal. -1 4 7 0 0.7 ml of serum is in each small container.

14. Concept Development – Problem 2 • What is the quotient? • 0.7 • Is our actual quotient reasonable? Does the placement of the decimal make sense? • We said we should have less then 1 mL in each vial, and we did.

15. Concept Development – Problem 3 • The surface area of a rectangular piece of construction paper is 140.25 square inches. If the paper’s length is 17 inches, what is the width? • In your journals, write a division equation you would use to solve this problem. • 140.25 ÷ 17 • Before solving this problem, let’s reason about what our quotient might be. Tell me how to estimate 140.25 ÷ 17. • 140.25 ÷ 17 ≈ 140 ÷ 20 = 7 Now solve this problem in your math journal. Multiples of 17 17 – 1 34 – 2 51 – 3 68 – 4 85 – 5 102 – 6 119 – 7 136 – 8 8 . 2 5 17 1 4 0 . 2 5 The other side of the paper was 8.25 inches long. -1 3 6 4 2 - 34 8 5 -8 5

16. Concept Development – Problem 3

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

18. Exit Ticket

19. Problem Set 1. Divide, then check using multiplication. • 5.6 ÷ 16 • 21 ÷ 14 • 24 ÷ 48 • 36 ÷ 24 • 81 ÷ 54 • 15.6 ÷ 15 • 5.4 ÷ 15 • 16.12 ÷ 52 • 2.8 ÷ 16

20. Problem Set • 30.48 kg of beef was placed into 24 packages of equal weight. What is the weight of one package of beef? • What is the length of a rectangle whose width is 17 inches and whose area is 582.25 in2? • A soccer coach spent $162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost? • A craft club makes 95 identical paperweights to sell. They collect $230.85 from selling all the paperweights. If the profit the club collects on each paperweight is two times as much as the cost to make each one, what does it cost the club to make each paperweight?

21. Homework Task 1. Divide and check. • 7 ÷ 28 • 51 ÷ 25 • 6.5 ÷ 13 • 132.16 ÷ 16 • 561.68 ÷ 28 • 604.8 ÷ 36

22. Homework Task • In a science class, students water a plant with the same amount of water each day for 28 consecutive days. If the students use a total of 23.8 liters of water over the 28 days, how many liters of water did they use each day? How many milliliters did they use each day? • A seamstress has a piece of cloth that is 3 yards long. She cuts it into shorter lengths of 16 inches each. How many of the shorter pieces can she cut? • Jenny filled 12 pitchers with an equal amount of lemonade in each. The total amount of lemonade in the 12 pitchers was 41.4 liters. How much lemonade would be in 7 pitchers?