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What is One Thousandth?

Grade 5: Unit 5: Lesson 1

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Lesson Purpose

The purpose of this lesson is for students to recognize the unit of thousandths in relationship to tenths and hundredths.

Lesson Narrative

In grade 4, students studied decimal fractions with denominators 10 and 100. They represented tenths and hundredths with hundredths grids, number lines, and decimal notation.

In this lesson students make sense of representations of tenths, hundredths, and thousandths with hundredths grid diagrams, fractions, and decimals. They also see relationships between these values, namely that a tenth of a tenth is a hundredth and a tenth of a hundredth is a thousandth. Students may use informal language to describe the relationship between decimals (for example, to get from 0.01 to .001 you add a zero in front of the one.) This language supports students in sharing their developing understanding. Teachers should ask questions to help students develop more precise language to describe base-ten representations (for example, what does the extra 0 you wrote in .001 represent?). They will have many opportunities to develop this understanding in upcoming lessons.

Learning Goals

•Understand the relationship between one tenth, one hundredth and one thousandth.

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Let’s make sense of thousandths.

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Estimation Exploration:

One Tiny Piece

Warm-Up

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What Do You Know About Thousandths?

Activity 1

The purpose of this activity is for students to share what they know about one tenth and one hundredth, and consider what they might know about one thousandth. Students make a poster showing what they know about these numbers and then discuss different representations they made. If students show tenths, hundredths or thousandths on a number line or with base ten diagrams, highlight these representations in the synthesis, as they are familiar from grade 4.

This activity is meant to be an invitational opportunity for students to bring their lived experience into the math classroom. Consider taking a walk through the community where your students live and noticing places that decimals are seen and used. Take pictures or notes that capture the details of your observations. Be prepared to share these artifacts with students during the synthesis.

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What do you know about 1 tenth?

What do you know about 1 hundredth?

What do you know about 1 thousandth?

Launch

•Groups of 2

•Give students access to hundredths grids on the blackline master.

•Give students access to chart paper and colored pencils, crayons, or markers.

•“Work with your partner to make a poster showing what you know about the numbers 1 tenth, 1 hundredth, and 1 thousandth.”

Student Work Time

•

6-8 minutes: partner work time

•Monitor for students who:

◦represent the numbers with fractions

◦represent the numbers with decimals

◦represent the numbers with diagrams

Student Responses

There are ten 1/10s in 1. It’s less than 1. I can also write it as 0.1.
1/100 is small. It’s smaller than 1/10. There are one hundred 1/100s in 1. There are ten 1/100s in 1/10. I can also write it as 0.01. I can put it on the number line.
1/1,000 is really small. It’s smaller than 1/100. There are one thousand 1/1,000s in 1. It would take a long time to count to 1 by 1/1,000s. I wonder how to make a drawing of 1/1,000 because there are so many of them in 1. I wonder if there’s a coin that worth a thousandth of a dollar.

Activity Synthesis

Invite students to share their posters.

“What are some ways to represent 1 tenth?”

I can write it as a fraction or a decimal. I can divide a rectangle into 10 equal pieces. I can put it on the number line.

“What was challenging about representing 1 hundredth with a drawing or diagram?”

Answers vary. It was hard to divide something into 100 equal pieces because that’s a lot.

“What was challenging about representing 1 thousandth with a drawing or diagram?”

Dividing a rectangle into 1,000 pieces would take forever.

“In the next activity we will make and compare drawings of these numbers.”

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What are some ways to represent 1 tenth?

Launch

•Groups of 2

•Give students access to hundredths grids on the blackline master.

•Give students access to chart paper and colored pencils, crayons, or markers.

•“Work with your partner to make a poster showing what you know about the numbers 1 tenth, 1 hundredth, and 1 thousandth.”

Student Work Time

•

6-8 minutes: partner work time

•Monitor for students who:

◦represent the numbers with fractions

◦represent the numbers with decimals

◦represent the numbers with diagrams

Student Responses

There are ten 1/10s in 1. It’s less than 1. I can also write it as 0.1.
1/100 is small. It’s smaller than 1/10. There are one hundred 1/100s in 1. There are ten 1/100s in 1/10. I can also write it as 0.01. I can put it on the number line.
1/1,000 is really small. It’s smaller than 1/100. There are one thousand 1/1,000s in 1. It would take a long time to count to 1 by 1/1,000s. I wonder how to make a drawing of 1/1,000 because there are so many of them in 1. I wonder if there’s a coin that worth a thousandth of a dollar.

Activity Synthesis

Invite students to share their posters.

“What are some ways to represent 1 tenth?”

I can write it as a fraction or a decimal. I can divide a rectangle into 10 equal pieces. I can put it on the number line.

“What was challenging about representing 1 hundredth with a drawing or diagram?”

Answers vary. It was hard to divide something into 100 equal pieces because that’s a lot.

“What was challenging about representing 1 thousandth with a drawing or diagram?”

Dividing a rectangle into 1,000 pieces would take forever.

“In the next activity we will make and compare drawings of these numbers.”

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What was challenging about representing 1 hundredth with a drawing or diagram?

Launch

•Groups of 2

•Give students access to hundredths grids on the blackline master.

•Give students access to chart paper and colored pencils, crayons, or markers.

•“Work with your partner to make a poster showing what you know about the numbers 1 tenth, 1 hundredth, and 1 thousandth.”

Student Work Time

•

6-8 minutes: partner work time

•Monitor for students who:

◦represent the numbers with fractions

◦represent the numbers with decimals

◦represent the numbers with diagrams

Student Responses

There are ten 1/10s in 1. It’s less than 1. I can also write it as 0.1.
1/100 is small. It’s smaller than 1/10. There are one hundred 1/100s in 1. There are ten 1/100s in 1/10. I can also write it as 0.01. I can put it on the number line.
1/1,000 is really small. It’s smaller than 1/100. There are one thousand 1/1,000s in 1. It would take a long time to count to 1 by 1/1,000s. I wonder how to make a drawing of 1/1,000 because there are so many of them in 1. I wonder if there’s a coin that worth a thousandth of a dollar.

Activity Synthesis

Invite students to share their posters.

“What are some ways to represent 1 tenth?”

I can write it as a fraction or a decimal. I can divide a rectangle into 10 equal pieces. I can put it on the number line.

“What was challenging about representing 1 hundredth with a drawing or diagram?”

Answers vary. It was hard to divide something into 100 equal pieces because that’s a lot.

“What was challenging about representing 1 thousandth with a drawing or diagram?”

Dividing a rectangle into 1,000 pieces would take forever.

“In the next activity we will make and compare drawings of these numbers.”

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What was challenging about represent 1 thousandth with a drawing or diagram?

Launch

•Groups of 2

•Give students access to hundredths grids on the blackline master.

•Give students access to chart paper and colored pencils, crayons, or markers.

•“Work with your partner to make a poster showing what you know about the numbers 1 tenth, 1 hundredth, and 1 thousandth.”

Student Work Time

•

6-8 minutes: partner work time

•Monitor for students who:

◦represent the numbers with fractions

◦represent the numbers with decimals

◦represent the numbers with diagrams

Student Responses

There are ten 1/10s in 1. It’s less than 1. I can also write it as 0.1.
1/100 is small. It’s smaller than 1/10. There are one hundred 1/100s in 1. There are ten 1/100s in 1/10. I can also write it as 0.01. I can put it on the number line.
1/1,000 is really small. It’s smaller than 1/100. There are one thousand 1/1,000s in 1. It would take a long time to count to 1 by 1/1,000s. I wonder how to make a drawing of 1/1,000 because there are so many of them in 1. I wonder if there’s a coin that worth a thousandth of a dollar.

Activity Synthesis

Invite students to share their posters.

“What are some ways to represent 1 tenth?”

I can write it as a fraction or a decimal. I can divide a rectangle into 10 equal pieces. I can put it on the number line.

“What was challenging about representing 1 hundredth with a drawing or diagram?”

Answers vary. It was hard to divide something into 100 equal pieces because that’s a lot.

“What was challenging about representing 1 thousandth with a drawing or diagram?”

Dividing a rectangle into 1,000 pieces would take forever.

“In the next activity we will make and compare drawings of these numbers.”

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Represent Numbers on a Hundredths Grid

Activity 2

MLR7: Compare and Contrast

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The grid represents 1. What does the shaded region represent? Be prepared to explain your reasoning.

Launch

•Groups of 2

•“Today we are going to investigate some really small numbers.”

Student Work Time

•2 minutes: independent work time

•8 minutes: partner work time

Student Responses

1/10 0.1 because there are 10 columns so the shaded part is one tenth.
1/100 or 0.01 because there are 100 small squares in the whole so each one is 1/100.
1,000 because there are 10 of the tiny rectangles in each square and 100 squares in the whole so that’s tiny 100 x 10 =1,000 rectangles in the whole.
Sample response: Maybe as 0.001 if the pattern for 1/10 and 1/100 of writing another 0 continues.

Activity Synthesis

•Display the last image.

•“How many of the tiny shaded rectangles are there in the whole unit square? How do you know?”

1,000 because there are 10 in the small square and 100 of those squares in the whole.

•“How much of the whole square is shaded?”

There is one tiny rectangle shaded and there are 1,000 of those in the whole so 1/1,000 is shaded. There is 1/10 of 1/100 shaded. That’s 1/10 x 1/100. There is 1/100 divided by 10 because the hundredth is divided into 10 equal pieces.

“The number 1/1,000 can also be written in decimal form as 0.001. Like the fraction, we call it ‘thousandth.’”

“How do you think you would write 4/1,000 as a decimal?”

0.004

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The grid represents 1. What does the shaded region represent? Be prepared to explain your reasoning.

Launch

•Groups of 2

•“Today we are going to investigate some really small numbers.”

Student Work Time

•2 minutes: independent work time

•8 minutes: partner work time

Student Responses

1/10 0.1 because there are 10 columns so the shaded part is one tenth.
1/100 or 0.01 because there are 100 small squares in the whole so each one is 1/100.
1,000 because there are 10 of the tiny rectangles in each square and 100 squares in the whole so that’s tiny 100 x 10 =1,000 rectangles in the whole.
Sample response: Maybe as 0.001 if the pattern for 1/10 and 1/100 of writing another 0 continues.

Activity Synthesis

•Display the last image.

•“How many of the tiny shaded rectangles are there in the whole unit square? How do you know?”

1,000 because there are 10 in the small square and 100 of those squares in the whole.

•“How much of the whole square is shaded?”

There is one tiny rectangle shaded and there are 1,000 of those in the whole so 1/1,000 is shaded. There is 1/10 of 1/100 shaded. That’s 1/10 x 1/100. There is 1/100 divided by 10 because the hundredth is divided into 10 equal pieces.

“The number 1/1,000 can also be written in decimal form as 0.001. Like the fraction, we call it ‘thousandth.’”

“How do you think you would write 4/1,000 as a decimal?”

0.004

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How many of the small rectangular pieces (one of them is shaded) are there in the unit square? Explain or show your thinking.

Launch

•Groups of 2

•“Today we are going to investigate some really small numbers.”

Student Work Time

•2 minutes: independent work time

•8 minutes: partner work time

Student Responses

1/10 0.1 because there are 10 columns so the shaded part is one tenth.
1/100 or 0.01 because there are 100 small squares in the whole so each one is 1/100.
1,000 because there are 10 of the tiny rectangles in each square and 100 squares in the whole so that’s tiny 100 x 10 =1,000 rectangles in the whole.
Sample response: Maybe as 0.001 if the pattern for 1/10 and 1/100 of writing another 0 continues.

Activity Synthesis

•Display the last image.

•“How many of the tiny shaded rectangles are there in the whole unit square? How do you know?”

1,000 because there are 10 in the small square and 100 of those squares in the whole.

•“How much of the whole square is shaded?”

There is one tiny rectangle shaded and there are 1,000 of those in the whole so 1/1,000 is shaded. There is 1/10 of 1/100 shaded. That’s 1/10 x 1/100. There is 1/100 divided by 10 because the hundredth is divided into 10 equal pieces.

“The number 1/1,000 can also be written in decimal form as 0.001. Like the fraction, we call it ‘thousandth.’”

“How do you think you would write 4/1,000 as a decimal?”

0.004

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How do you think we write the number one thousandths as a decimal? Explain your reasoning.

Launch

•Groups of 2

•“Today we are going to investigate some really small numbers.”

Student Work Time

•2 minutes: independent work time

•8 minutes: partner work time

Student Responses

1/10 0.1 because there are 10 columns so the shaded part is one tenth.
1/100 or 0.01 because there are 100 small squares in the whole so each one is 1/100.
1,000 because there are 10 of the tiny rectangles in each square and 100 squares in the whole so that’s tiny 100 x 10 =1,000 rectangles in the whole.
Sample response: Maybe as 0.001 if the pattern for 1/10 and 1/100 of writing another 0 continues.

Activity Synthesis

•Display the last image.

•“How many of the tiny shaded rectangles are there in the whole unit square? How do you know?”

1,000 because there are 10 in the small square and 100 of those squares in the whole.

•“How much of the whole square is shaded?”

There is one tiny rectangle shaded and there are 1,000 of those in the whole so 1/1,000 is shaded. There is 1/10 of 1/100 shaded. That’s 1/10 x 1/100. There is 1/100 divided by 10 because the hundredth is divided into 10 equal pieces.

“The number 1/1,000 can also be written in decimal form as 0.001. Like the fraction, we call it ‘thousandth.’”

“How do you think you would write 4/1,000 as a decimal?”

0.004

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Lesson Synthesis

Today we represented 1 tenth, 1 hundredth, and 1 thousandth in different ways.

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Lesson Synthesis

What are some different ways that you can represent 1 hundredth?

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Lesson Synthesis

What are some different ways that you can represent 1 thousandth?

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Journal Prompt:

One Thousandths

Cool-Down

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Cool-Down

What did you learn about 1 thousandth? What do you still wonder about 1 thousandth?

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Image Citations

https://pixabay.com/photos/daisy-meadow-in-measure-love-5060056/

Creative Commons BY-NC-SA

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