Engage NY Math Module 2

Lesson 13: Use whole number multiplication to express equivalent measurements.

30 ÷ 10 = 300 ÷ 100 = 3,000 ÷ 1,000 = 5,000 ÷ 1,000 = 50 ÷ 10 = 500 ÷ 100 = 5,000 ÷ 100 = 3,000 ÷ 100 = 30,000 ÷ 1,000 =

50,000 ÷ 1,000

= 40 ÷ 10 = 400 ÷ 10 = 4,000 ÷ 10 = 40,000 ÷ 10 = 700 ÷ 100 = 7,000 ÷ 100 = 70,000 ÷ 100 = 700,000 ÷ 100 = 7,000,000 ÷ 1,000 =

Divide by 10, 100, and 1000

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

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

Unit Conversions

• 10 ft = _____ in• 120

• 5 ft = _____ in• 60

• 7 ft = _____ in• 84

• 12 ft = _____ in• 144

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

Unit Conversions

• 800 cm = _____ m• 8

• 400 cm = _____ m• 4

• 1,200 cm = _____ m• 12

• 500 cm = _____ m• 5

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.

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.

Concept Development

• LENGTH• Centimeter• Millimeter• Meter• Kilometer• Feet• Yards• Mile

• WEIGHT

• Gram• Milligram• Kilogram• Pound• Ounce• Ton

• VOLUME/CAPACITY

• Cup• Fluid ounces• Pint• Quart• Gallon• Liter• Milliliter• Kiloliter

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.

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

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.

Concept Development – Problems 1(b/c):

• 150 feet = _____ inches• 1800 inches

• 152 feet = _____ inches• 1824 inches

• 21 feet = ______ inches• 252 inches

• 210 feet = _____ inches• 2520 inches

• Use the same procedure to solve the following problems in your math journal.

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 2 ton 3 ton

4,000 pounds 6,000 pounds

2,000 pounds

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 2 ton 3 ton

2,000 pounds 4,000 pounds 6,000 pounds

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 2 feet . . . 42 feet

24 inches 504 inches

12 inches

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 2 feet . . . 42 feet

24 inches 504 inches

12 inches

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 2 pounds . . . 9 pounds

32 ounces 144 ounces

16 ounces

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

Concept Development – Problem 4:

• 57 gallons 1 quart = _____ quarts• 57 x 4 = 228 + 1 = 229

quarts

• 63 quarts 3 pints = ______ pints• 63 x 2 = 126 + 3 = 129 pints

• Use your Reference Sheet to help you solve these problems independently in your journal.

Exit Ticket

Problem Set

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