1. Engage NY Math Module 2
Lesson 29: Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown.

2. Unit Conversions How many pounds are in 1 ton?
Complete the following conversions.
1 ton = ______ lb
How many pounds are in 1 ton?
2,000 lb
1 km = ______ m
How many meters are in 1 kilometer?
1,000 m
1 qt = ______ pt
How many pints are in 1 quart?
2 pt
1 cm = ______ mm
How many millimeters are in 1 centimeter?
10 mm

3. Unit Conversions What is our conversion factor?
Complete the following conversions.
2.67 tons = ______ lbs
What is our conversion factor?
1 ton = 2,000 lbs
Using your conversion factor, solve to show how many lbs are in 2.67 tons.
2.67 x 2,000 = 5,340 lbs
0.084 km = ______ m
1 km = 1,000 m
Using your conversion factor, solve to show how many m are in km.
0.084 x 1,000 = 84 m

4. Unit Conversions What is our conversion factor?
Complete the following conversions.
2.75 qt = ______ pt
What is our conversion factor?
1 qt = 2 pt
Using your conversion factor, solve to show how many pt are in 2.75 qt.
2.75 x 2 = 5.5 pt
843 cm = ______ mm
1 cm = 10 mm
Using your conversion factor, solve to show how many mm are in 843 cm.
843 x 10 = 8,430 mm

5. Divide by Two-Digit Numbers
In your notebooks, solve two of the following problems using the standard algorithm.
8.61 ÷ 21
0.41
4.9 ÷ 14
0.35
24 ÷ 16
1.5

6. Application Problem
A one-year (52 week) subscription to a weekly magazine is $ Greg calculates that he would save $ if he subscribed to the magazine instead of purchasing it each week at the store. What is the price of the individual magazine at the store?
Each magazine costs $4.99.
$219.53
$259.48
Multiples of 52
364 – 7
416 – 8
468 – 9 52
$259.48
-208
514
4.99
468
468
468

7. Concept Development – Problem 1
Lamar has kilograms of potatoes to deliver in equal amounts to 18 stores. 12 of the stores are in the Bronx. How many kilograms of potatoes will be delivered to stores in the Bronx?
Will the amount delivered to the stores in the Bronx be more or less than half of the total amount of potatoes delivered? How do you know?
More than half because more than half of the stores are in the Bronx.
Let’s solve this together.
This two step equal groups with group size unknown problem requires first dividing to find the value of one unit and then multiplying to find the value of 12 of those units.

8. Concept Development – Problem 1
How can you know that your final answer is reasonable? Was the amount delivered to the Bronx stores more than half of the total?
How did you determine if your decimal was placed reasonably in your product?
You were multiplying by 12 so your answer needed to be more than 750 but less than 7,500. The only place that makes sense to put the decimal made the answer 903 – not 90.3 or 9,030.

9. Concept Development – Problem 2
Valerie uses 12 oz of detergent each week for her laundry. If there are 75 oz of detergent in the bottle, in how many weeks will she need to buy a new bottle of detergent? Explain how you know.
In your journals, solve this problem with your tablemates.
The interpretation of the remainder in this single-step equal groups with number of groups unknown problem requires that students recognize the need to buy the detergent in 6 weeks. Although there will be a small amount of detergent left after the sixth week, there is not enough to do a seventh week of laundry.
The quotient was more than 6, why can’t Valerie wait another week before buying detergent?
The quotient is the number of weeks the detergent will last. It will last a little more than 6 weeks, but she won’t have enough for all the laundry in the seventh week.

10. Concept Development – Problem 3
The are of a rectangle is m². If the length is 16 m, what is its perimeter.
Solve this problem in your journal. Check with your tablemates after finishing.

11. Concept Development – Problem 4
A city block is 3 times as long as it is wide. If the total distance around the block is 0.48 kilometers, what is the area of the block in square meters?
Solve this problem in your journal. Check with your tablemates after finishing.
Problems 3 and 4 require students to apply their knowledge of area and perimeter to find missing sides using division, and then use that information to answer the question. In Problem 3, area information must be used to find perimeter, and in Problem 4, perimeter must be used to find area. In both cases, students must account for the existence of 2 pairs of equal sides in their calculations. In Problem 3, students may find it more helpful to draw a rectangle than a tape diagram. However, the 3 times as long relationship in Problem 4 might be better modeled using a tape diagram. An added complexity of Problem 4 is the need to convert between kilometers and meters.

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

13. Exit Ticket
Solve.
Hayley borrowed $1,854 from her parents. She agreed to repay them in equal installments over the next 18 months. How much will Hayley still owe her parents after a year?

14. Problem Set
These problems are the concept development problems from the lesson.

15. Homework Task
Solve the word problems, using a bar model.
Michelle wants to save $150 for a trip to Six Flags Amusement Park. If she saves $12 each week, how many weeks will it take her to save enough money for the trip?
Karen works for 85 hours over a two week period. She earns $1, over this period. How much does Karen earn for 8 hours of work?
The area of a rectangle is m2. If the length is 18 m, what is the perimeter of the rectangle?

16. Homework Task
Solve the word problems, using a bar model.
Tyler baked 702 cookies. He sold them in boxes of 18. After selling all the boxes of cookies, he earned $ What was the cost of one box of cookies?
A park is 4 times as long as it is wide. If the distance around the park is 12.5 kilometers, what is the area of the park?