Ways to Compare Fractions
10 min
Narrative
The purpose of this Warm-up is for students to practice estimating a reasonable fractional value on a number line. The reasoning here prepares students to use benchmarks as a way to compare fractions later in the lesson.
The Warm-up gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3).
Launch
- Groups of 2
- Display the number line.
- “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
What number is represented by the point on the number line?
Make an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample response:
- Too low: 51 to 41
- About right: 52 to 21
- Too high: 53 to 43
Activity Synthesis (Teacher Notes)
- “How did you decide what fraction would be ‘about right’?” (The point is a little to the left of the middle point, so the fraction must be a little less than 21.)
- “Would writing the label ‘1’ as ‘1010’ or as ‘100100’ help us make better estimates? Why or why not?” (Sample response: It could, because it would help us mentally partition the number line into 10 or 100 parts, which makes it possible to estimate more accurately.)
Standards
Building On
- 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>.
Building Toward
- 4.NF.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
- 4.NF.A.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <span class="math">\(>\)</span>, =, or <span class="math">\(<\)</span>, and justify the conclusions, e.g., by using a visual fraction model.
15 min
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Ways to Compare Fractions
10 min
Narrative
The purpose of this Warm-up is for students to practice estimating a reasonable fractional value on a number line. The reasoning here prepares students to use benchmarks as a way to compare fractions later in the lesson.
The Warm-up gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3).
Launch
- Groups of 2
- Display the number line.
- “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
What number is represented by the point on the number line?
Make an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample response:
- Too low: 51 to 41
- About right: 52 to 21
- Too high: 53 to 43
Activity Synthesis (Teacher Notes)
- “How did you decide what fraction would be ‘about right’?” (The point is a little to the left of the middle point, so the fraction must be a little less than 21.)
- “Would writing the label ‘1’ as ‘1010’ or as ‘100100’ help us make better estimates? Why or why not?” (Sample response: It could, because it would help us mentally partition the number line into 10 or 100 parts, which makes it possible to estimate more accurately.)
Standards
Building On
- 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>.
Building Toward
- 4.NF.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
- 4.NF.A.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <span class="math">\(>\)</span>, =, or <span class="math">\(<\)</span>, and justify the conclusions, e.g., by using a visual fraction model.