Fraction Design Challenge
Plan a fraction-based design and justify its quantities with two models.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. A unit mosaic highlights 2/3 of its rows and 3/4 of its columns. What fraction overlaps?
c2. Half the display is green and one quarter is blue, without overlap. What share is colored?
c3. If 3/4 of the board is colored, what share stays blank?
c4. Three equal banners each use 2/5 meter of ribbon. Find total meters.
c5. A 5/6 meter strip loses 1/4 meter. What length remains?
c6. Two thirds of a 3/4 meter border is painted. How many meters are painted?
c7. Half a sheet is shared equally among three designs. What share of the original sheet is used by each?
c8. Two meters are cut into quarter-meter borders. How many borders can be made?
e1. Calculate 2/3 × 3/4. Show a model or your reasoning.
e2. Give two checks a partner can use on your design.
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
- Plan a one-square-unit mosaic with 2/3 of the rows and 3/4 of the columns highlighted.
- Compute the overlap and represent it with both a grid and fraction strips.
- Partners critique whether the two models show the same whole and final amount.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Plan a one-square-unit mosaic with 2/3 of the rows and 3/4 of the columns highlighted.
Compute the overlap and represent it with both a grid and fraction strips.
Partners critique whether the two models show the same whole and final amount.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 2/3 × 3/4. Show a model or your reasoning. Give two checks a partner can use on your design.
Watch for this misconception
Using different wholes or units in two supposedly matching models.
Label the whole, unit and quantity on every model.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. A unit mosaic highlights 2/3 of its rows and 3/4 of its columns. What fraction overlaps?
2/3 × 3/4 = 1/2. Multiply the numerators and denominators; interpret the groups or overlap.
c2. Half the display is green and one quarter is blue, without overlap. What share is colored?
1/2 + 1/4 = 3/4. Use equal-sized parts before combining or removing them.
c3. If 3/4 of the board is colored, what share stays blank?
1 - 3/4 = 1/4. Use equal-sized parts before combining or removing them.
c4. Three equal banners each use 2/5 meter of ribbon. Find total meters.
3 × 2/5 = 6/5. Multiply the numerators and denominators; interpret the groups or overlap.
c5. A 5/6 meter strip loses 1/4 meter. What length remains?
5/6 - 1/4 = 7/12. Use equal-sized parts before combining or removing them.
c6. Two thirds of a 3/4 meter border is painted. How many meters are painted?
3/4 × 2/3 = 1/2. Multiply the numerators and denominators; interpret the groups or overlap.
c7. Half a sheet is shared equally among three designs. What share of the original sheet is used by each?
1/2 ÷ 3 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c8. Two meters are cut into quarter-meter borders. How many borders can be made?
2 ÷ 1/4 = 8. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s1. Calculate 1/2 × 1/2. Show a model or your reasoning.
1/2 × 1/2 = 1/4. Multiply the numerators and denominators; interpret the groups or overlap.
s2. Calculate 1/2 + 1/4. Show a model or your reasoning.
1/2 + 1/4 = 3/4. Use equal-sized parts before combining or removing them.
s3. Calculate 1 - 1/4. Show a model or your reasoning.
1 - 1/4 = 3/4. Use equal-sized parts before combining or removing them.
s4. Calculate 2 × 1/4. Show a model or your reasoning.
2 × 1/4 = 1/2. Multiply the numerators and denominators; interpret the groups or overlap.
h1. Represent the 2/3 by 3/4 overlap with both grid and strip models.
Six of twelve grid cells and six twelfth-size strip sections both show one half.
- 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. Design a colored board with exactly 3/4 colored and two non-overlapping colors.
Color one half green and one quarter blue; one quarter remains blank.
- 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. State and check a material limit for your ribbon design.
A 2-meter supply covers three 2/5-meter banners and leaves 4/5 meter.
- 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 why matching numbers alone is not enough to match models.
Both models must refer to the same whole and quantity, such as area rather than length.
- 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 2/3 × 3/4. Show a model or your reasoning.
2/3 × 3/4 = 1/2. Multiply the numerators and denominators; interpret the groups or overlap.
e2. Give two checks a partner can use on your design.
Check equal parts and common wholes; check computed quantities against the stated material limits.
- 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 1/2 × 1/2. Show a model or your reasoning.
s2. Calculate 1/2 + 1/4. Show a model or your reasoning.
s3. Calculate 1 - 1/4. Show a model or your reasoning.
s4. Calculate 2 × 1/4. Show a model or your reasoning.
e1. Calculate 2/3 × 3/4. Show a model or your reasoning.
e2. Give two checks a partner can use on your design.
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Represent the 2/3 by 3/4 overlap with both grid and strip models.
h2. Design a colored board with exactly 3/4 colored and two non-overlapping colors.
h3. State and check a material limit for your ribbon design.
h4. Explain why matching numbers alone is not enough to match models.
e1. Calculate 2/3 × 3/4. Show a model or your reasoning.
e2. Give two checks a partner can use on your design.
Teaching notes & lesson sources
Designed for Grade 5. Plan a fraction-based design and justify its quantities with two models.
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.