1. Engage NY Math Module 2
Lesson 13: Use whole number multiplication to express equivalent measurements.

2. Divide by 10, 100, and 1000
30 ÷ 10 =
40 ÷ 10 =
300 ÷ 100 =
400 ÷ 10 =
3,000 ÷ 1,000 =
4,000 ÷ 10 =
5,000 ÷ 1,000 =
40,000 ÷ 10 =
50 ÷ 10 =
700 ÷ 100 =
500 ÷ 100 =
7,000 ÷ 100 =
5,000 ÷ 100 =
70,000 ÷ 100 =
3,000 ÷ 100 =
700,000 ÷ 100 =
30,000 ÷ 1,000 =
7,000,000 ÷ 1,000 =
50,000 ÷ 1,000 =

3. Multiply Using the Area Model
Use the area model to solve the following in your math notebook. Check your answer with the standard algorithm.
5.21 x 34
177.14
8.35 x 73
609.55

4. Unit Conversions 1 ft = _____ in
I foot is the same as how many inches? 12
2 ft = _____ in 24
3 ft = _____ in 36
4 ft = _____ in 48

5. Unit Conversions 10 ft = _____ in 120 5 ft = _____ in 6084
12 ft = _____ in
144

6. Unit Conversions 100 cm = _____ m
I00 centimeters is the same as how many meters? 1
200 cm = _____ m 2
300 cm = _____ m 3
600 cm = _____ m 6

7. Unit Conversions 800 cm = _____ m 8 400 cm = _____ m 412
500 cm = _____ m 5

8. Application Problem Hands-on conversion reading activity
Every string has an exact match.
Measure your string using the following directions.
Blue strings = measure your string to the nearest FOOT
Orange strings = measure your string to the nearest INCH
Tan strings = measure your string to the nearest METER
Green strings = measure your string to the nearest CENTIMETER
After you measure your string, you will find your string’s match which will be a different color.
Record your equivalent measures in your math journal.
In a few sentences, explain how the same sized piece of string can have two different measurements.

9. Concept Development
Distribute a copy of the Grade 5 Mathematics Reference Sheet to each student.
Turn and talk with your tablemates. How might this document help us solve problems?
Today we’ll be using this Reference Sheet to help us convert between various units of measure. Discuss with your table the types of measurement units you see on this sheet.
Turn to a new page in your journal. Divide your page into three sections labeled Length, Weight, and Volume/Capacity. Talk with your table about which units are used for each type of measurement and record those units in the appropriate column in your journal.

10. Concept Development LENGTH WEIGHT VOLUME/CAPACITY Centimeter Gram Cup
Millimeter
Milligram
Fluid ounces
Meter
Kilogram
Pint
Kilometer
Pound
Quart
Feet
Ounce
Gallon
Yards
Ton
Liter
Mile
Milliliter
Kiloliter

11. Concept Development – Problem 1(a):
15 feet = _____ inches
How can we use the patterns we just saw in our Application Problem to help us convert from feet to inches?
Visualize the tape measure we just used to measure in feet and inches. How many inches did we see in each foot? 12
Let’s draw a number line to show what we saw. You draw your own number line in your journal.

12. Concept Development – Problem 1(a):
15 feet = _____ inches
If one foot, or one unit, is equal to 12 inches, how can I find what 15 feet is equal to?
We can add 12 inches 15 times.
We can skip count by twelves 15 times.
We can multiply 12 times 15.
If one unit is 12 inches, then 10 units is 120 inches, and 5 more units would be 60 inches, so that’s 180 inches.
Therefore, we could use repeated addition, skip counting, or multiplication. If I wanted to express this conversion as a multiplication equation, what would it look like? Would this method work for any situation in which I wanted to name feet as inches?
15 ft x 12 = 180 inches

13. Concept Development – Problem 1(a):
15 feet = _____ inches
We just converted from feet to inches. Which unit is larger, feet or inches?
Feet
Think back to our Application Problem. Remind me why we need so many inches to make just 15 feet. Discuss this with your tablemates.
Inches are a smaller unit; we need more of them to make the larger units, feet.

14. Concept Development – Problems 1(b/c):
Use the same procedure to solve the following problems in your math journal.
150 feet = _____ inches
1800 inches
152 feet = _____ inches
1824 inches
21 feet = ______ inches
252 inches
210 feet = _____ inches
2520 inches

15. Concept Development – Problem 2(a):
3 tons 140 pounds = _____ pounds
Let’s use our thinking about multiplication to solve this one. At your table, discuss which part of the Reference Sheet will help us solve this one.
1 ton = 2,000 pounds
How is this problem slightly different from the first one we solved?
We are converting tons and pounds to just pounds.
Let’s start with the 3 tons. In your journal draw a double number line showing tons and pounds.
Look at your drawing. How many pounds are equal to 3 ton?
1 ton ton ton
2,000 pounds
4,000 pounds ,000 pounds

16. Concept Development – Problem 2(a):
3 tons 140 pounds = _____ pounds
Are we finished? Have we found a weight equal to what we started with?
No.
Why not?
We have 140 more pounds.
What do we need to do with those 140 pounds?
3 tons 140 pounds equals how many pounds altogether?
6,140 pounds
1 ton ton ton
2,000 pounds ,000 pounds ,000 pounds

17. Concept Development – Problem 2(b):
42 feet 9 inches = _____ inches
Let’s use our thinking about multiplication to solve this one. At your table, discuss the conversion factor we will use to solve this problem. Add this to your Reference Sheet.
1 foot = 12 inches
Let’s start with the 42 feet. In your journal draw a double number line showing feet and inches.
Look at your drawing. How many inches are equal to 42 feet?
504 inches
1 foot feet feet
12 inches
24 inches inches

18. Concept Development – Problem 2(b):
42 feet 9 inches = _____ inches
Are we finished? Have we found a weight equal to what we started with?
No.
Why not?
We have 9 more inches.
What do we need to do with those 9 inches?
42 feet 9 inches equals how many inches altogether?
513 inches
1 foot feet feet
12 inches
24 inches inches

19. Concept Development – Problem 3:
_____ ounces = 9 pounds 11 ounces
Look at your Reference Sheet. Tell your neighbor the conversion factor that you’ll use to solve this problem.
1 pound = 16 ounces
In your journal draw a double number line showing pounds and ounces. Use multiplication and addition to solve. Compare your answer with your neighbor’s work as you go.
How many ounces are equal to 9 pounds 11 ounces?
155 ounces
1 pound pounds pounds
16 ounces
32 ounces ounces

20. Concept Development – Problem 4:
155 gallons = _____ quarts = _____ pints
Use your Reference Sheet to help you solve this problem independently. If you’d like you may draw a double number line.
1 gallon = 4 quarts
1 quart = 2 pints
155 gallons equals how many quarts? Find the number of quarts mentally.
100 gallons is 400 quarts, 50 gallons is 200 quarts and 5 gallons is 20 quarts. So, 155 gallons is 620 quarts.
155 gallons x 4 = 620 quarts
Find the number of pints in 620 quarts mentally.
There are 2 pints in every quart so just double every place value.
620 x 2 = 1,240 pints

21. Concept Development – Problem 4:
Use your Reference Sheet to help you solve these problems independently in your journal.
57 gallons 1 quart = _____ quarts
57 x 4 = = 229 quarts
63 quarts 3 pints = ______ pints
63 x 2 = = 129 pints

22. Exit Ticket

23. Problem Set
Display Problem Set on the board. Allow time for the students to complete the problems with tablemates.