Equal Parts Workshop
Distinguish equal-size parts from unequal parts before naming a fraction.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Are the parts in this strip equal in size?
Choices: Equal parts / Unequal parts
c2. Are the parts in this strip equal in size?
Choices: Equal parts / Unequal parts
c3. What fraction is shaded? Write its value.
c4. What fraction is shaded? Write its value.
c5. What fraction is shaded? Write its value.
c6. What fraction is shaded? Write its value.
c7. What fraction is shaded? Write its value.
c8. A rectangle has four pieces, all with the same area. Is each piece one fourth?
Choices: Yes / No
e1. Three unequal pieces are each one third. Is that correct?
Choices: Yes / No
e2. Explain the mistake in calling any one of four unequal pieces one fourth.
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
- Fold a paper rectangle in halves, then fourths. Open it and trace the folds.
- Draw a second rectangle split at 1/4 of its width. Compare the two piece sizes.
- Partners sort the drawings into equal and unequal parts. Give a reason for each choice.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Fold a paper rectangle in halves, then fourths. Open it and trace the folds.
Draw a second rectangle split at 1/4 of its width. Compare the two piece sizes.
Partners sort the drawings into equal and unequal parts. Give a reason for each choice.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Three unequal pieces are each one third. Is that correct? Explain the mistake in calling any one of four unequal pieces one fourth.
Watch for this misconception
Naming a fraction from the count of pieces alone.
Compare piece areas, then count only equal-sized pieces.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Are the parts in this strip equal in size?
Choices: Equal parts / Unequal parts
Each part has the same width.
c2. Are the parts in this strip equal in size?
Choices: Equal parts / Unequal parts
One part has width 1/4 and the other 3/4.
c3. What fraction is shaded? Write its value.
1 parts of size 1/3 represent 1/3.
c4. What fraction is shaded? Write its value.
1 parts of size 1/4 represent 1/4.
c5. What fraction is shaded? Write its value.
2 parts of size 1/4 represent 2/4.
c6. What fraction is shaded? Write its value.
1 parts of size 1/6 represent 1/6.
c7. What fraction is shaded? Write its value.
1 parts of size 1/8 represent 1/8.
c8. A rectangle has four pieces, all with the same area. Is each piece one fourth?
Choices: Yes / No
Four equal areas make fourths.
s1. What fraction is shaded? Write its value.
1 parts of size 1/2 represent 1/2.
s2. What fraction is shaded? Write its value.
1 parts of size 1/3 represent 1/3.
s3. What fraction is shaded? Write its value.
1 parts of size 1/4 represent 1/4.
s4. What fraction is shaded? Write its value.
2 parts of size 1/4 represent 2/4.
h1. Draw a four-part rectangle that does not show fourths. Explain.
Three narrow pieces and one wide piece are not fourths because the areas 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.
h2. Two equal-area pieces have different shapes. Can each be a half?
Yes. Equal area matters, even when shapes 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. Repair an unequal two-part strip without changing its whole.
Move the partition to the midpoint so both parts have half the area.
- 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. How could a partner verify that your six pieces are sixths?
Compare their areas or fold them onto each other; six equal pieces fill the whole.
- 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. Three unequal pieces are each one third. Is that correct?
Choices: Yes / No
Thirds must be equal in size.
e2. Explain the mistake in calling any one of four unequal pieces one fourth.
The count is four but the areas are not equal.
- 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 fraction is shaded? Write its value.
s2. What fraction is shaded? Write its value.
s3. What fraction is shaded? Write its value.
s4. What fraction is shaded? Write its value.
e1. Three unequal pieces are each one third. Is that correct?
Choices: Yes / No
e2. Explain the mistake in calling any one of four unequal pieces one fourth.
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Draw a four-part rectangle that does not show fourths. Explain.
h2. Two equal-area pieces have different shapes. Can each be a half?
h3. Repair an unequal two-part strip without changing its whole.
h4. How could a partner verify that your six pieces are sixths?
e1. Three unequal pieces are each one third. Is that correct?
Choices: Yes / No
e2. Explain the mistake in calling any one of four unequal pieces one fourth.
Teaching notes & lesson sources
Designed for Grade 3. Distinguish equal-size parts from unequal parts before naming a fraction.
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.