What Is a Thousandth?
10 min
Narrative
The purpose of this Estimation Exploration is to invite students to think about small fractions of a quantity in context. The mosaic pictured here is made up of many small square tiles. Square tiles are arranged in a complex pattern and are not identical in size but students can relate the denominator of a fraction giving the size of each tile, relative to the whole mosaic, to the total number of tiles making the mosaic. This helps them think of a fraction with a large denominator which prepares them to think about the fraction 1,0001 in this lesson.
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
What fraction of the whole image is 1 single square tile?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample responses:
- too low: 10,0001 or less
- about right: 3,0001 to 5001
- too high: 1001 or more
Activity Synthesis (Teacher Notes)
- “How did you make your estimate?” (I tried to estimate how many tiles made the whole picture and then used that as my denominator.)
- “We will be investigating very small numbers and how to represent them in the next several lessons.”
Standards
- 5.NBT.A·Understand the place value system.
- 5.NBT.A·Understand the place value system.
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
What Is a Thousandth?
10 min
Narrative
The purpose of this Estimation Exploration is to invite students to think about small fractions of a quantity in context. The mosaic pictured here is made up of many small square tiles. Square tiles are arranged in a complex pattern and are not identical in size but students can relate the denominator of a fraction giving the size of each tile, relative to the whole mosaic, to the total number of tiles making the mosaic. This helps them think of a fraction with a large denominator which prepares them to think about the fraction 1,0001 in this lesson.
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
What fraction of the whole image is 1 single square tile?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample responses:
- too low: 10,0001 or less
- about right: 3,0001 to 5001
- too high: 1001 or more
Activity Synthesis (Teacher Notes)
- “How did you make your estimate?” (I tried to estimate how many tiles made the whole picture and then used that as my denominator.)
- “We will be investigating very small numbers and how to represent them in the next several lessons.”
Standards
- 5.NBT.A·Understand the place value system.
- 5.NBT.A·Understand the place value system.