Equivalent Strip Lab
Build equivalent fractions by repartitioning the same whole.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. The strip shows 2/4. Enter the same amount as a fraction.
c2. Compare 1/2 and 2/4. Choose <, =, or >. The wholes are the same size.
c3. Compare 2/3 and 4/6. Choose <, =, or >. The wholes are the same size.
c4. Rename 3/4 as an equivalent fraction with denominator 8.
c5. Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size.
c6. Compare 2/5 and 4/10. Choose <, =, or >. The wholes are the same size.
c7. Write the value shown by eight of twelve parts.
c8. Compare 3/4 and 9/12. Choose <, =, or >. The wholes are the same size.
e1. Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size.
e2. Explain why 1/2 and 2/4 are equivalent.
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 strips of exactly the same length. Shade one half of the first.
- Divide the second into fourths and the third into sixths. Shade to the same endpoint.
- Pair up to explain what changed and what stayed equal. Repeat with two thirds and sixths.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw three strips of exactly the same length. Shade one half of the first.
Divide the second into fourths and the third into sixths. Shade to the same endpoint.
Pair up to explain what changed and what stayed equal. Repeat with two thirds and sixths.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size. Explain why 1/2 and 2/4 are equivalent.
Watch for this misconception
Adding the same number to numerator and denominator to make equivalents.
Repartition each original part by the same factor; compare endpoints.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. The strip shows 2/4. Enter the same amount as a fraction.
Two of four equal parts cover half of the same whole.
c2. Compare 1/2 and 2/4. Choose <, =, or >. The wholes are the same size.
1/2 = 2/4. Rename them as equal-sized parts or place them on the same unit number line.
c3. Compare 2/3 and 4/6. Choose <, =, or >. The wholes are the same size.
2/3 = 4/6. Rename them as equal-sized parts or place them on the same unit number line.
c4. Rename 3/4 as an equivalent fraction with denominator 8.
Split each fourth into two eighths: three fourths becomes six eighths.
c5. Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size.
3/6 = 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c6. Compare 2/5 and 4/10. Choose <, =, or >. The wholes are the same size.
2/5 = 4/10. Rename them as equal-sized parts or place them on the same unit number line.
c7. Write the value shown by eight of twelve parts.
Eight twelfths and two thirds share the same endpoint.
c8. Compare 3/4 and 9/12. Choose <, =, or >. The wholes are the same size.
3/4 = 9/12. Rename them as equal-sized parts or place them on the same unit number line.
s1. What amount is shaded? Count two fourths.
Two of four equal parts are shaded.
s2. Compare 1/2 and 2/4. Choose <, =, or >. Split each half into two equal parts.
1/2 = 2/4. Rename them as equal-sized parts or place them on the same unit number line.
s3. What amount is shaded? Count three sixths.
Three of six equal parts are shaded.
s4. Compare 1/3 and 2/6. Choose <, =, or >. Split each third into two equal parts.
1/3 = 2/6. Rename them as equal-sized parts or place them on the same unit number line.
h1. Give three different names for 2/3 and explain the common endpoint.
2/3, 4/6 and 8/12 cover the same share of equal-length strips.
- 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. A partner says 2/3 = 3/4 because both numbers increased by one. Give a counterexample.
Two thirds is 8/12 and three fourths is 9/12, so their endpoints differ.
- 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. How could you rename 3/4 using twelfths?
Split each fourth into three twelfths. Three groups of three make 9/12.
- 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. Can unequal-length strips prove equal physical amounts? Explain.
Equal fraction labels describe relative shares, but unequal wholes do not establish equal lengths.
- 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. Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size.
3/6 = 1/2. Rename them as equal-sized parts or place them on the same unit number line.
e2. Explain why 1/2 and 2/4 are equivalent.
Repartition the same whole: each half becomes two fourths, and the shaded endpoint 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.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
s1. What amount is shaded? Count two fourths.
s2. Compare 1/2 and 2/4. Choose <, =, or >. Split each half into two equal parts.
s3. What amount is shaded? Count three sixths.
s4. Compare 1/3 and 2/6. Choose <, =, or >. Split each third into two equal parts.
e1. Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size.
e2. Explain why 1/2 and 2/4 are equivalent.
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Give three different names for 2/3 and explain the common endpoint.
h2. A partner says 2/3 = 3/4 because both numbers increased by one. Give a counterexample.
h3. How could you rename 3/4 using twelfths?
h4. Can unequal-length strips prove equal physical amounts? Explain.
e1. Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size.
e2. Explain why 1/2 and 2/4 are equivalent.
Teaching notes & lesson sources
Designed for Grade 4. Build equivalent fractions by repartitioning the same whole.
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.