Application Problem (8 minutes)

Materials: Personal white board

Martha, George, and Elizabeth sprint a combined distance of 10,000 meters. Martha sprints 3,206 meters.

George sprints 2,094 meters. How far does Elizabeth sprint? Solve using an algorithm or a simplifying strategy.

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Martha, George, and Elizabeth sprint a combined distance of 10,000 meters. Martha sprints 3,206 meters.

George sprints 2,094 meters. How far does Elizabeth sprint? Solve using an algorithm or a simplifying strategy.

10,000 m

Elizabeth sprints 4,700 meters.

Martha

George

Elizabeth

3,206

+ 2,094

5,300

10,000

- 5,300

4,700

Eureka 4th Module 2 L. 1

Objective: Express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric

length.

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Fluency Practice (10 minutes)

• Convert Units 4.MD.1 (2 minutes)
• Meter and Centimeter Number Bonds 4.MD.1 (8 minutes)

Convert Units (2 minutes)

100 centimeters is the same as how many meters?

100 cm = ____ m

100 cm = 1 m

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200 cm = ____ m

200 cm = 2 m

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300 cm = ____ m

300 cm = 3 m

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800 cm = ____ m

800 cm = 8 m

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500 cm = ____ m

500 cm = 5 m

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How many centimeters are in 1 meter?

1 m = ____ cm

1 m = 100 cm

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2 m = ____ cm

2 m = 200 cm

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7 m = ____ cm

7 m = 700 cm

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4 m = ____ cm

4 m = 400 cm

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9 m = ____ cm

9 m = 900 cm

Meter and Centimeter Number Bonds (8 min)

Materials: (S) Personal white board

150 cm

1 m

50 cm

How many centimeters are in 1 meter?

100 cm

On your personal white boards, write a number bond filling in the unknown part.

180 cm

1 m

80 cm

How many centimeters are in 1 meter?

100 cm

On your personal white boards, write a number bond filling in the unknown part.

120 cm

1 m

20 cm

How many centimeters are in 1 meter?

100 cm

On your personal white boards, write a number bond filling in the unknown part.

125 cm

1 m

25 cm

100 cm

On your personal white boards, write a number bond filling in the unknown part.

105 cm

1 m

5 cm

100 cm

On your personal white boards, write a number bond filling in the unknown part.

107 cm

1 m

7 cm

100 cm

On your personal white boards, write a number bond filling in the unknown part.

2 m

1 m

___

cm

100

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100 cm

Fill in the unknown part.

3 m

100 cm

2 m

Show a number bond with a whole of 3 meters and pull

out 100 centimeters. Name the other part in meters.

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5 m

100 cm

4 m

Show a number bond with a whole of 5 meters and pull

out 100 centimeters. Name the other part in meters.

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8 m

100 cm

7 m

Show a number bond with a whole of 8 meters and pull

out 100 centimeters. Name the other part in meters.

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9 m

100 cm

8 m

Show a number bond with a whole of 9 meters and pull

out 100 centimeters. Name the other part in meters.

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10 m

100 cm

9 m

Show a number bond with a whole of 10 meters and pull

out 100 centimeters. Name the other part in meters.

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Concept Development (32 minutes)

Materials: Personal white board

Problem 1: Understand 1 centimeter, 1 meter, and 1 kilometer in terms of concrete objects.

Metric Units of Length

length of a staple

height of a countertop

distance to Tuolumne Market

Problem 2: Compare the sizes and note relationships between meters and kilometers as conversion equivalencies.

1 km = 1,000 m.

How many meters are in 2 km? 3 km? 7 km? 70 km?

2000

7000

70,000

3000

Problem 2: Compare the sizes and note relationships between meters and kilometers as conversion equivalencies.

Write 2,000 m = ____ km on your board.

If 1,000 m equals 1 km, 2,000 m equals how many kilometers?

2,000 m = 2 kilometers.

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8,000 m = ____ km

8,000 m = 8 km

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10,000 m = ____ km

10,000 m = 10 km

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9,000 m = ____ km

9,000 m = 9 km

Problem 2: Compare the sizes and note relationships between meters and kilometers as conversion equivalencies.

Compare kilometers and meters.

A kilometer is a longer distance because we need 1,000 meters to equal 1 kilometer.

1 kilometer is 1,000 times as much as 1 meter.

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Let’s convert, or rename, 1 km 500 m to meters.

1 km 500 m = ______ m

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1 kilometer is equal to how many meters?

1,000 meters.

1,000 meters plus 500 meters is 1,500 meters.

Problem 2: Compare the sizes and note relationships between meters and kilometers as conversion equivalencies.

1 kilometer 300 meters is equal to how many meters?

1 km 300 m = ___ m

1,300 meters

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5 km 30 m = ___ m

Careful!! It’s not 530 meters.

5 kilometers equals how many meters?

5,000 meters

So, 5 km 30 m =

5,030 meters!

Problem 2: Compare the sizes and note relationships between meters and kilometers as conversion equivalencies.

2,500 meters is equal to how many kilometers? How do you know?

2 km 500 m. We made two groups of 1,000 meters, so we have 2 kilometers and 500 meters.

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5,005 meters is equal to how many kilometers? How do you know?

5 km 5 m. We made five groups of 1,000 meters, so we have 5 kilometers and 5 meters.

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Problem 3: Add mixed units of length using the algorithm or simplifying strategies.

5 km + 2,500 m =

Talk for one minute with your partner about how to solve this problem.

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We can’t add different units together.

We can convert the kilometers to meters before adding.

5 kilometers equals 5,000 meters, so ...

5,000 m + 2,500 m = 7,500 m.

We could then rename 7,500 m to 7 km 500 m.

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Problem 3: Add mixed units of length using the algorithm or simplifying strategies.

Renaming 7,500 m to 7 km 500 m creates a mixed unit.

Mixed units can be helpful when using a simplifying strategy.

A simplifying strategy makes the problem simpler or easier.

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Are you going to use the algorithm or a simplifying strategy to solve?

Simplifying strategy.

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Why?

There is no regrouping.

The units are easy to combine.

It’s just like adding place value units.

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Problem 3: Add mixed units of length using the algorithm or simplifying strategies.

5 km + 2,500 m =

5 km + 2 km 500 m OR

5,000 m + 2,500 m =

7,500 m = 7 km 500 m

When we added meters, the answer was 7,500 m.

When we added mixed units, the answer was 7 km 500 m.

Are these answers equal? Why or why not?

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It is the same amount because

7 km = 7,000 m and 7,000 m + 500 m = 7,500 m.

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Problem 3: Add mixed units of length using the algorithm or simplifying strategies.

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1 km 734 m + 4 km 396 m =

Simplifying strategy or the algorithm?

Discuss with a partner.

Choose the way you want to do it. You will have two minutes.

If you finish before the two minutes are up, try solving it a different way.

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Let’s have two pairs of students work at the board, one pair using the algorithm and one pair recording a simplifying strategy.

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Problem 4: Subtract mixed units of length using the algorithm or simplifying strategies.

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10 km – 3 km 140 m =

Simplifying strategy or the algorithm?

Discuss with a partner.

Choose the way you want to do it. You will have two minutes.

If you finish before the two minutes are up, try solving it a different way.

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Let’s have two pairs of students work at the board, one pair using the algorithm and one pair recording a simplifying strategy.

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Problem 5: Solve a word problem involving mixed units of length using the algorithm or simplifying strategies.

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Sam practiced his long jump in P.E. On his first attempt, he jumped 1 meter 47 centimeters. On his second attempt, he jumped 98 centimeters. How much farther did Sam jump on his first attempt than his second?

Take two minutes with your partner to draw a tape diagram to model this problem.

Problem 5: Solve a word problem involving mixed units of length using the algorithm or simplifying strategies.

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Sam practiced his long jump in P.E. On his first attempt, he jumped 1 meter 47 centimeters. On his second attempt, he jumped 98 centimeters. How much farther did Sam jump on his first attempt than his second?

Your diagrams show a comparison between two values.

How can you solve for the unknown?

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Problem 5: Solve a word problem involving mixed units of length using the algorithm or simplifying strategies.

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Sam practiced his long jump in P.E. On his first attempt, he jumped 1 meter 47 centimeters. On his second attempt, he jumped 98 centimeters. How much farther did Sam jump on his first attempt than his second?

Your diagrams show a comparison between two values.

How can you solve for the unknown?

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Subtract 98 cm from 1 m 47 cm.

Problem 5: Solve a word problem involving mixed units of length using the algorithm or simplifying strategies.

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Sam practiced his long jump in P.E. On his first attempt, he jumped 1 meter 47 centimeters. On his second attempt, he jumped 98 centimeters. How much farther did Sam jump on his first attempt than his second?

Will you use the algorithm or a simplifying strategy?

Let’s have two pairs of students work at the board, one pair using the algorithm and one pair recording a simplifying strategy.

Time for the Problem Set.

Do your personal best!