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Metric Conversion and Division by Powers of Ten

Grade 5: Unit 6: Lesson 4

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Let’s convert units.

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True or False:

Divide by a Hundred and a Thousand

Warm-Up

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Long Jump, Javelin Throw, and Shot Put

Activity 1

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Launch

•Groups of 2

•Display the table shown in the student workbook.

•“What do you notice? What do you wonder?” (Who are those people? What is a javelin? What is a shot put? What is the long jump? Some of the numbers are close. Why are the long jump numbers so much smaller?)

•Record responses for all to see.

•“This table shows the results from track and field events.”

Student Work Time

•2 minutes: quiet think time

•10 minutes: partner work time

•Monitor for students who observe that when they convert the whole number distances in centimeters to meters they get decimals to the hundredth.

Student Responses

Check student work
Sample responses: Meters because there are too many centimeters to imagine, but there are fewer meters and they are longer so it is easier for me to picture how far it is.
They might need to measure to the nearest centimeter to see who comes in first place, second place, and third place. A meter is so big that measuring these distances to the nearest meter is not very accurate.

Activity Synthesis

•Display:

727 divided by 100 = 7.27

4,566 divided by 100 = 45.66

1,580 divided by 100 = 15.80

•“What patterns do you notice?”

The measurements in centimeters are whole numbers but the measurements in meters are in hundredths. All the digits in the numbers are the same but they shifted 2 places to the right. So the 7 hundreds in centimeters is 7 ones in meters.

•“Why does dividing by 100 represent how many meters are in the given centimeters?”

I know there are 100 centimeters in each meter so each centimeter is 1/100 of a meter.

•“How did you find the result of 727 divided by 100?”

I went place by place. 7 hundreds divided by 100 is 7 ones. 2 tens divided by 100 is 2 tenths. 7 ones divided by 100 is 7 hundredths.

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Launch

•Groups of 2

•Display the table shown in the student workbook.

•“What do you notice? What do you wonder?” (Who are those people? What is a javelin? What is a shot put? What is the long jump? Some of the numbers are close. Why are the long jump numbers so much smaller?)

•Record responses for all to see.

•“This table shows the results from track and field events.”

Student Work Time

•2 minutes: quiet think time

•10 minutes: partner work time

•Monitor for students who observe that when they convert the whole number distances in centimeters to meters they get decimals to the hundredth.

Student Responses

Check student work
Sample responses: Meters because there are too many centimeters to imagine, but there are fewer meters and they are longer so it is easier for me to picture how far it is.
They might need to measure to the nearest centimeter to see who comes in first place, second place, and third place. A meter is so big that measuring these distances to the nearest meter is not very accurate.

Activity Synthesis

•Display:

727 divided by 100 = 7.27

4,566 divided by 100 = 45.66

1,580 divided by 100 = 15.80

•“What patterns do you notice?”

The measurements in centimeters are whole numbers but the measurements in meters are in hundredths. All the digits in the numbers are the same but they shifted 2 places to the right. So the 7 hundreds in centimeters is 7 ones in meters.

•“Why does dividing by 100 represent how many meters are in the given centimeters?”

I know there are 100 centimeters in each meter so each centimeter is 1/100 of a meter.

•“How did you find the result of 727 divided by 100?”

I went place by place. 7 hundreds divided by 100 is 7 ones. 2 tens divided by 100 is 2 tenths. 7 ones divided by 100 is 7 hundredths.

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Hurdles

Activity 2

MLR1: Stronger and Clearer Each Time

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Launch

•Groups of 2

•“Work with your partner on the first three problems.”

Student Work Time

•5–7 minutes: partner work time

•“Now, you are going to work independently to show or explain whether you think Tyler’s strategy will always work.”

•3–5 minutes: independent work time

Student Responses

Check student work
Sample response: When I go from meters to kilometers I divide by 1,000. Each digit in the number shifts three places to the right.
Sample response: When Tyler divides by 10, he shifts all the digits 1 place to the right. When he divides by 100, he shifts the digits 2 places to the right. When he divides by 1,000, he shifts the digits 3 places to the right.
Sample responses:

I think it will always work because I tried it with some other numbers.
I think it aways works because when I move one place to the right the value of a digit is multiplied by 1/10.

Activity Synthesis

MLR1 Stronger and Clearer Each Time

•“Share with your partner your response as to whether or not Tyler’s strategy will always work. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”

•3–5 minutes: structured partner discussion

•Repeat with 1–2 different partners.

•If needed, display question starters and prompts for feedback.

◦“Can you give an example to help show …?”

◦“Can you add a diagram, table, or representation to show …?”

•“Revise your initial draft based on the feedback you got from your partners.”

•2–3 minutes: independent work time

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Launch

•Groups of 2

•“Work with your partner on the first three problems.”

Student Work Time

•5–7 minutes: partner work time

•“Now, you are going to work independently to show or explain whether you think Tyler’s strategy will always work.”

•3–5 minutes: independent work time

Student Responses

Check student work
Sample response: When I go from meters to kilometers I divide by 1,000. Each digit in the number shifts three places to the right.
Sample response: When Tyler divides by 10, he shifts all the digits 1 place to the right. When he divides by 100, he shifts the digits 2 places to the right. When he divides by 1,000, he shifts the digits 3 places to the right.
Sample responses:

I think it will always work because I tried it with some other numbers.
I think it aways works because when I move one place to the right the value of a digit is multiplied by 1/10.

Activity Synthesis

MLR1 Stronger and Clearer Each Time

•“Share with your partner your response as to whether or not Tyler’s strategy will always work. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”

•3–5 minutes: structured partner discussion

•Repeat with 1–2 different partners.

•If needed, display question starters and prompts for feedback.

◦“Can you give an example to help show …?”

◦“Can you add a diagram, table, or representation to show …?”

•“Revise your initial draft based on the feedback you got from your partners.”

•2–3 minutes: independent work time

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Launch

•Groups of 2

•“Work with your partner on the first three problems.”

Student Work Time

•5–7 minutes: partner work time

•“Now, you are going to work independently to show or explain whether you think Tyler’s strategy will always work.”

•3–5 minutes: independent work time

Student Responses

Check student work
Sample response: When I go from meters to kilometers I divide by 1,000. Each digit in the number shifts three places to the right.
Sample response: When Tyler divides by 10, he shifts all the digits 1 place to the right. When he divides by 100, he shifts the digits 2 places to the right. When he divides by 1,000, he shifts the digits 3 places to the right.
Sample responses:

I think it will always work because I tried it with some other numbers.
I think it aways works because when I move one place to the right the value of a digit is multiplied by 1/10.

Activity Synthesis

MLR1 Stronger and Clearer Each Time

•“Share with your partner your response as to whether or not Tyler’s strategy will always work. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”

•3–5 minutes: structured partner discussion

•Repeat with 1–2 different partners.

•If needed, display question starters and prompts for feedback.

◦“Can you give an example to help show …?”

◦“Can you add a diagram, table, or representation to show …?”

•“Revise your initial draft based on the feedback you got from your partners.”

•2–3 minutes: independent work time

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Lesson Synthesis

Today we converted from smaller metric distance units to larger metric distance units. We noticed and explained patterns in numbers when they are divided by 10, 100, and 1,000.

“Today we converted from smaller metric distance units to larger metric distance units. We noticed and explained patterns in numbers when they are divided by 10, 100, and 1,000.”

“What are the missing values in the table? How do you know?” (7.864 kilometers and 2,037 meters. To get from meters to kilometers, I divide by 1,000 and to get from kilometers from meters I multiply by 1,000 because there are 1,000 meters in a kilometer.)

“How is converting from smaller meters to larger kilometers the same and how is it different from converting from larger kilometers to smaller meters?” (In both cases you keep the same digits, only their place values change and they change by 3 place values ;in both cases. When I go from meters to kilometers the digits shift 3 places to the right and when I go from kilometers to meters they shift 3 places to the left.)

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Lesson Synthesis

“What are the missing values in the table? How do you know?”

“Today we converted from smaller metric distance units to larger metric distance units. We noticed and explained patterns in numbers when they are divided by 10, 100, and 1,000.”

“What are the missing values in the table? How do you know?” (7.864 kilometers and 2,037 meters. To get from meters to kilometers, I divide by 1,000 and to get from kilometers from meters I multiply by 1,000 because there are 1,000 meters in a kilometer.)

“How is converting from smaller meters to larger kilometers the same and how is it different from converting from larger kilometers to smaller meters?” (In both cases you keep the same digits, only their place values change and they change by 3 place values ;in both cases. When I go from meters to kilometers the digits shift 3 places to the right and when I go from kilometers to meters they shift 3 places to the left.)

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Lesson Synthesis

How is converting from smaller meters to larger kilometers the same and how is it different from converting from larger kilometers to smaller meters?

“Today we converted from smaller metric distance units to larger metric distance units. We noticed and explained patterns in numbers when they are divided by 10, 100, and 1,000.”

“What are the missing values in the table? How do you know?” (7.864 kilometers and 2,037 meters. To get from meters to kilometers, I divide by 1,000 and to get from kilometers from meters I multiply by 1,000 because there are 1,000 meters in a kilometer.)

“How is converting from smaller meters to larger kilometers the same and how is it different from converting from larger kilometers to smaller meters?” (In both cases you keep the same digits, only their place values change and they change by 3 place values ;in both cases. When I go from meters to kilometers the digits shift 3 places to the right and when I go from kilometers to meters they shift 3 places to the left.)

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Han’s run

Cool-Down

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Cool Down: Han’s Run

Han ran 12,500 meters last week. How many kilometers is that? Explain or show your reasoning.

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Image Citations

https://pixabay.com/photos/running-hurdles-athletics-4338238/

https://pixabay.com/photos/sports-athletics-hurdle-sprint-men-659224/

https://pixabay.com/photos/athletics-sports-javelin-throw-649650/

https://pixabay.com/photos/athletics-shot-put-sports-649636/

https://pixabay.com/photos/athletics-shot-put-sports-1526988/

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