Compose One
Compose and decompose one whole using same-denominator fractions.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. How much must you add to 3/8 to make one whole?
c2. How much must you add to 1/4 to make one whole?
c3. How much must you add to 2/5 to make one whole?
c4. How much must you add to 5/6 to make one whole?
c5. How much must you add to 7/10 to make one whole?
c6. How much must you add to 2/3 to make one whole?
c7. How much must you add to 1/8 to make one whole?
c8. How much must you add to 3/4 to make one whole?
e1. How much completes 3/8 to one?
e2. Why does the denominator stay fixed?
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
- Shade 3/8 of a strip. Identify the amount needed to finish the whole.
- Pair cards that sum to one and verify each with a strip.
- Write two different decompositions of one using eighths.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Shade 3/8 of a strip. Identify the amount needed to finish the whole.
Pair cards that sum to one and verify each with a strip.
Write two different decompositions of one using eighths.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
How much completes 3/8 to one? Why does the denominator stay fixed?
Watch for this misconception
Adding denominators when combining same-sized parts.
Name the unit fraction aloud while adding the counts.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. How much must you add to 3/8 to make one whole?
1 - 3/8 = 5/8. Use equal-sized parts before combining or removing them.
c2. How much must you add to 1/4 to make one whole?
1 - 1/4 = 3/4. Use equal-sized parts before combining or removing them.
c3. How much must you add to 2/5 to make one whole?
1 - 2/5 = 3/5. Use equal-sized parts before combining or removing them.
c4. How much must you add to 5/6 to make one whole?
1 - 5/6 = 1/6. Use equal-sized parts before combining or removing them.
c5. How much must you add to 7/10 to make one whole?
1 - 7/10 = 3/10. Use equal-sized parts before combining or removing them.
c6. How much must you add to 2/3 to make one whole?
1 - 2/3 = 1/3. Use equal-sized parts before combining or removing them.
c7. How much must you add to 1/8 to make one whole?
1 - 1/8 = 7/8. Use equal-sized parts before combining or removing them.
c8. How much must you add to 3/4 to make one whole?
1 - 3/4 = 1/4. Use equal-sized parts before combining or removing them.
s1. Find the missing share: 1/2 + ? = 1.
1 - 1/2 = 1/2. Use equal-sized parts before combining or removing them.
s2. Find the missing share: 1/3 + ? = 1.
1 - 1/3 = 2/3. Use equal-sized parts before combining or removing them.
s3. Find the missing share: 1/4 + ? = 1.
1 - 1/4 = 3/4. Use equal-sized parts before combining or removing them.
s4. Find the missing share: 2/4 + ? = 1.
1 - 2/4 = 1/2. Use equal-sized parts before combining or removing them.
h1. Decompose one into three positive eighths fractions.
1/8 + 2/8 + 5/8 = 8/8 = 1.
- 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. Why is 3/8 + 5/8 equal to 1 rather than 8/16?
We count eight eighth-size pieces; their size did not change.
- 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 a one-whole sum with quarters using a repeated addend.
1/4 + 1/4 + 2/4 = 1.
- 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. Explain the complement of 7/10 using a model.
Three more tenths fill the ten equal parts.
- 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. How much completes 3/8 to one?
1 - 3/8 = 5/8. Use equal-sized parts before combining or removing them.
e2. Why does the denominator stay fixed?
The size of each part stays the same while the counts combine.
- 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. Find the missing share: 1/2 + ? = 1.
s2. Find the missing share: 1/3 + ? = 1.
s3. Find the missing share: 1/4 + ? = 1.
s4. Find the missing share: 2/4 + ? = 1.
e1. How much completes 3/8 to one?
e2. Why does the denominator stay fixed?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Decompose one into three positive eighths fractions.
h2. Why is 3/8 + 5/8 equal to 1 rather than 8/16?
h3. Create a one-whole sum with quarters using a repeated addend.
h4. Explain the complement of 7/10 using a model.
e1. How much completes 3/8 to one?
e2. Why does the denominator stay fixed?
Teaching notes & lesson sources
Designed for Grade 4. Compose and decompose one whole using same-denominator fractions.
4.NF.B.3a 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.