Missing Number Bridges
Find missing numerators or denominators by using a multiplicative scale factor.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. 3/5 = ?/10. Enter the missing numerator.
c2. 2/3 = 8/?. Enter the missing denominator.
c3. 1/4 = ?/12. Enter the numerator.
c4. 5/6 = 10/?. Enter the denominator.
c5. 3/4 = ?/20. Enter the numerator.
c6. 4/8 = 1/?. Enter the denominator.
c7. 2/5 = ?/15. Enter the numerator.
c8. 6/9 = 2/?. Enter the denominator.
e1. Complete 3/5 = ?/10.
e2. Why must the same factor appear on both arrows?
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
- Write 3/5 on one card and ?/10 on another. Bridge the denominators with a times-two arrow.
- Apply the same arrow to the numerators. Check with a strip.
- Partners build bridges in both directions and explain why adding is not the rule.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Write 3/5 on one card and ?/10 on another. Bridge the denominators with a times-two arrow.
Apply the same arrow to the numerators. Check with a strip.
Partners build bridges in both directions and explain why adding is not the rule.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Complete 3/5 = ?/10. Why must the same factor appear on both arrows?
Watch for this misconception
Applying a scale factor to only one part.
Draw both arrows and label them with the identical factor.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. 3/5 = ?/10. Enter the missing numerator.
The denominator doubled, so the numerator doubles.
c2. 2/3 = 8/?. Enter the missing denominator.
Multiply both parts by four.
c3. 1/4 = ?/12. Enter the numerator.
Multiply by three.
c4. 5/6 = 10/?. Enter the denominator.
Multiply by two.
c5. 3/4 = ?/20. Enter the numerator.
Multiply by five.
c6. 4/8 = 1/?. Enter the denominator.
Divide both parts by four.
c7. 2/5 = ?/15. Enter the numerator.
Multiply by three.
c8. 6/9 = 2/?. Enter the denominator.
Divide both parts by three.
s1. 1/2 = ?/4. Multiply numerator by 2.
One times two is two.
s2. 1/3 = ?/6. Multiply numerator by 2.
One times two is two.
s3. 2/4 = 1/?. Divide denominator by 2.
Four divided by two is two.
s4. 1/4 = ?/8. Multiply numerator by 2.
One times two is two.
h1. Find two possible fractions equal to 3/5 with larger denominators.
6/10 and 9/15 use factors two and three.
- 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. Can 3/5 be written as a fraction with denominator 8 and an integer numerator?
No; 3/5 times 8 is 24/5, which is not an integer.
- 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. Repair 2/3 = 4/5 and describe the broken bridge.
Double both parts to get 4/6; adding two does not preserve value.
- 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. Create a bridge where the scale factor is 4.
2/3 = 8/12 multiplies numerator and denominator by four.
- 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. Complete 3/5 = ?/10.
Both numerator and denominator are doubled.
e2. Why must the same factor appear on both arrows?
Multiplying numerator and denominator by the same nonzero factor preserves the amount.
- 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. 1/2 = ?/4. Multiply numerator by 2.
s2. 1/3 = ?/6. Multiply numerator by 2.
s3. 2/4 = 1/?. Divide denominator by 2.
s4. 1/4 = ?/8. Multiply numerator by 2.
e1. Complete 3/5 = ?/10.
e2. Why must the same factor appear on both arrows?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Find two possible fractions equal to 3/5 with larger denominators.
h2. Can 3/5 be written as a fraction with denominator 8 and an integer numerator?
h3. Repair 2/3 = 4/5 and describe the broken bridge.
h4. Create a bridge where the scale factor is 4.
e1. Complete 3/5 = ?/10.
e2. Why must the same factor appear on both arrows?
Teaching notes & lesson sources
Designed for Grade 4. Find missing numerators or denominators by using a multiplicative scale factor.
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.