Compare Fractions with the Same Denominator
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that the size and the number of unit fractions can help us compare fractions. Students can see that the two diagrams have the same-size parts, but they cannot see how much of one diagram is shaded, prompting them to think about the number of shaded parts. While students may notice and wonder many things about these images, what fractions could be represented by the partially hidden strip is the important discussion point.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (5)
- 1Observe two strips with same-size parts→Both strips divided into fourths (same size pieces)
- 2Identify bottom strip fraction→3 out of 4 parts shaded = 3/4
- 3Notice top strip is partially covered→Cannot see how many parts are shaded
- 4Wonder about hidden fraction→Could be 2/4 (less), 3/4 (equal), or 4/4 (more) compared to bottom
- 5Recognize comparison depends on number of parts→Same-size parts means more parts shaded = larger fraction
Sample Response
Students may notice:
- The parts on the strips are the same size.
- The bottom strip shows 43.
- Part of the top strip is covered.
- How many parts are shaded on the top strip?
- Is the top strip more shaded than the bottom strip?
- Is the top strip less shaded than the bottom strip?
Activity Synthesis (Teacher Notes)
- “How many parts could be shaded on the top strip? Could less than 43 be shaded? Could more than 43 be shaded?” (If 2 parts are shaded, that's 42, which is less than 43. If 3 parts are shaded, that's 43. If the whole strip is shaded, that's 44, which is more than 43.)
Standards
Building Toward
- 3.NF.3.d·Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
- 3.NF.A.3.d·Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols <span class="math">\(>\)</span>, =, or <span class="math">\(<\)</span>, and justify the conclusions, e.g., by using a visual fraction model.
20 min
15 min
Knowledge Components
All skills for this lesson
Role Legend
Target
Essential
Supporting
Foundational
All lesson KCs
3 skills
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Compare Fractions with the Same Denominator
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that the size and the number of unit fractions can help us compare fractions. Students can see that the two diagrams have the same-size parts, but they cannot see how much of one diagram is shaded, prompting them to think about the number of shaded parts. While students may notice and wonder many things about these images, what fractions could be represented by the partially hidden strip is the important discussion point.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (5)
- 1Observe two strips with same-size parts→Both strips divided into fourths (same size pieces)
- 2Identify bottom strip fraction→3 out of 4 parts shaded = 3/4
- 3Notice top strip is partially covered→Cannot see how many parts are shaded
- 4Wonder about hidden fraction→Could be 2/4 (less), 3/4 (equal), or 4/4 (more) compared to bottom
- 5Recognize comparison depends on number of parts→Same-size parts means more parts shaded = larger fraction
Sample Response
Students may notice:
- The parts on the strips are the same size.
- The bottom strip shows 43.
- Part of the top strip is covered.
- How many parts are shaded on the top strip?
- Is the top strip more shaded than the bottom strip?
- Is the top strip less shaded than the bottom strip?
Activity Synthesis (Teacher Notes)
- “How many parts could be shaded on the top strip? Could less than 43 be shaded? Could more than 43 be shaded?” (If 2 parts are shaded, that's 42, which is less than 43. If 3 parts are shaded, that's 43. If the whole strip is shaded, that's 44, which is more than 43.)
Standards
Building Toward
- 3.NF.3.d·Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
- 3.NF.A.3.d·Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols <span class="math">\(>\)</span>, =, or <span class="math">\(<\)</span>, and justify the conclusions, e.g., by using a visual fraction model.