Equivalent Fractions on the Number Line
10 min
Narrative
The purpose of an Estimation Exploration is to practice estimating a reasonable answer based on experience and known information. Students can identify fractions represented by the shaded portions in tape diagrams in which unit or non-unit fractions are marked. To estimate the shaded parts in an unmarked tape, students may rely on the size of benchmark fractions—21, 31, or 41—and partition those parts mentally until it approximates the size of the shaded part. They may also estimate how many copies of the shaded part could fit in the entire diagram.
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.”
- 1 minute: partner discussion
- Record responses.
Student Task
The whole diagram represents 1. What fraction of the diagram is shaded?
Make an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample response:
- Too low: 251 to 201
- About right: 121 to 101
- Too high: 51 to 41
Activity Synthesis (Teacher Notes)
Consider asking:
- “Is anyone’s estimate less than 201? Is anyone’s estimate greater than 41?”
- “Based on this discussion does anyone want to revise their estimate?”
Standards
- 3.NF.1·Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- 3.NF.A.1·Understand a fraction <span class="math">\(1/b\)</span> as the quantity formed by 1 part when a whole is partitioned into <span class="math">\(b\)</span> equal parts; understand a fraction <span class="math">\(a/b\)</span> as the quantity formed by <span class="math">\(a\)</span> parts of size <span class="math">\(1/b\)</span>.
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Equivalent Fractions on the Number Line
10 min
Narrative
The purpose of an Estimation Exploration is to practice estimating a reasonable answer based on experience and known information. Students can identify fractions represented by the shaded portions in tape diagrams in which unit or non-unit fractions are marked. To estimate the shaded parts in an unmarked tape, students may rely on the size of benchmark fractions—21, 31, or 41—and partition those parts mentally until it approximates the size of the shaded part. They may also estimate how many copies of the shaded part could fit in the entire diagram.
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.”
- 1 minute: partner discussion
- Record responses.
Student Task
The whole diagram represents 1. What fraction of the diagram is shaded?
Make an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample response:
- Too low: 251 to 201
- About right: 121 to 101
- Too high: 51 to 41
Activity Synthesis (Teacher Notes)
Consider asking:
- “Is anyone’s estimate less than 201? Is anyone’s estimate greater than 41?”
- “Based on this discussion does anyone want to revise their estimate?”
Standards
- 3.NF.1·Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- 3.NF.A.1·Understand a fraction <span class="math">\(1/b\)</span> as the quantity formed by 1 part when a whole is partitioned into <span class="math">\(b\)</span> equal parts; understand a fraction <span class="math">\(a/b\)</span> as the quantity formed by <span class="math">\(a\)</span> parts of size <span class="math">\(1/b\)</span>.