Repeated Fraction Groups
Interpret a whole number times a fraction as repeated groups.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Calculate 3 × 2/5. Show a model or your reasoning.
c2. Calculate 4 × 3/4. Show a model or your reasoning.
c3. Calculate 2 × 5/6. Show a model or your reasoning.
c4. Calculate 5 × 1/3. Show a model or your reasoning.
c5. Calculate 6 × 2/8. Show a model or your reasoning.
c6. Calculate 3 × 3/7. Show a model or your reasoning.
c7. Calculate 4 × 2/9. Show a model or your reasoning.
c8. Calculate 2 × 7/10. Show a model or your reasoning.
e1. Calculate 3 × 2/5. Show a model or your reasoning.
e2. What does the whole-number factor count?
Before the lesson
Recognize a whole and count equal parts.
Materials
- Pencil: 1 per student
- Plain paper sheets: 2 per student
- Projector: 1 per class (optional)
Activity
- Draw three groups of 2/5 on strips. Count all fifth-size pieces.
- Write both repeated addition and multiplication for the same model.
- Partners model four groups of 3/4 and explain how groups can exceed one.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw three groups of 2/5 on strips. Count all fifth-size pieces.
Write both repeated addition and multiplication for the same model.
Partners model four groups of 3/4 and explain how groups can exceed one.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 3 × 2/5. Show a model or your reasoning. What does the whole-number factor count?
Watch for this misconception
Multiplying the denominator by the whole-number group count.
Count the unchanged fractional unit across all groups.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Calculate 3 × 2/5. Show a model or your reasoning.
3 × 2/5 = 6/5. Multiply the numerators and denominators; interpret the groups or overlap.
c2. Calculate 4 × 3/4. Show a model or your reasoning.
4 × 3/4 = 3. Multiply the numerators and denominators; interpret the groups or overlap.
c3. Calculate 2 × 5/6. Show a model or your reasoning.
2 × 5/6 = 5/3. Multiply the numerators and denominators; interpret the groups or overlap.
c4. Calculate 5 × 1/3. Show a model or your reasoning.
5 × 1/3 = 5/3. Multiply the numerators and denominators; interpret the groups or overlap.
c5. Calculate 6 × 2/8. Show a model or your reasoning.
6 × 2/8 = 3/2. Multiply the numerators and denominators; interpret the groups or overlap.
c6. Calculate 3 × 3/7. Show a model or your reasoning.
3 × 3/7 = 9/7. Multiply the numerators and denominators; interpret the groups or overlap.
c7. Calculate 4 × 2/9. Show a model or your reasoning.
4 × 2/9 = 8/9. Multiply the numerators and denominators; interpret the groups or overlap.
c8. Calculate 2 × 7/10. Show a model or your reasoning.
2 × 7/10 = 7/5. Multiply the numerators and denominators; interpret the groups or overlap.
s1. Calculate 2 × 1/2. Show a model or your reasoning.
2 × 1/2 = 1. Multiply the numerators and denominators; interpret the groups or overlap.
s2. Calculate 3 × 1/4. Show a model or your reasoning.
3 × 1/4 = 3/4. Multiply the numerators and denominators; interpret the groups or overlap.
s3. Calculate 2 × 1/3. Show a model or your reasoning.
2 × 1/3 = 2/3. Multiply the numerators and denominators; interpret the groups or overlap.
s4. Calculate 4 × 1/4. Show a model or your reasoning.
4 × 1/4 = 1. Multiply the numerators and denominators; interpret the groups or overlap.
h1. Draw 3 × 2/5 as repeated groups.
Three groups each show two fifths; six fifths is 1 1/5.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h2. Explain why 4 × 3/4 equals three wholes.
Twelve fourth-size pieces regroup into three wholes.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h3. Create two stories for 5 × 1/3.
Five bags each hold a third cup, or five walks each cover a third mile.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h4. Correct 3 × 2/5 = 6/15.
Three groups add fifths, so the result is 6/5; the fifth-size unit stays fixed.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
e1. Calculate 3 × 2/5. Show a model or your reasoning.
3 × 2/5 = 6/5. Multiply the numerators and denominators; interpret the groups or overlap.
e2. What does the whole-number factor count?
It counts the number of equal fractional groups.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
s1. Calculate 2 × 1/2. Show a model or your reasoning.
s2. Calculate 3 × 1/4. Show a model or your reasoning.
s3. Calculate 2 × 1/3. Show a model or your reasoning.
s4. Calculate 4 × 1/4. Show a model or your reasoning.
e1. Calculate 3 × 2/5. Show a model or your reasoning.
e2. What does the whole-number factor count?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Draw 3 × 2/5 as repeated groups.
h2. Explain why 4 × 3/4 equals three wholes.
h3. Create two stories for 5 × 1/3.
h4. Correct 3 × 2/5 = 6/15.
e1. Calculate 3 × 2/5. Show a model or your reasoning.
e2. What does the whole-number factor count?
Teaching notes & lesson sources
Designed for Grade 4. Interpret a whole number times a fraction as repeated groups.
4.NF.B.4b curriculum reference
Version 1.0.0. Original, AI-assisted lesson content. Free local classroom use; public reuse terms have not yet been assigned.
These lessons have not yet been field-tested in classrooms. Use the exit ticket and student explanations to decide what to revisit.