Benchmark Sort
Use one half as a benchmark to classify and compare fractions.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Compare 7/12 and 1/2. Choose <, =, or >. The wholes are the same size.
c2. Compare 3/8 and 1/2. Choose <, =, or >. The wholes are the same size.
c3. Compare 4/8 and 1/2. Choose <, =, or >. The wholes are the same size.
c4. Compare 5/6 and 1/2. Choose <, =, or >. The wholes are the same size.
c5. Compare 2/5 and 1/2. Choose <, =, or >. The wholes are the same size.
c6. Compare 6/10 and 1/2. Choose <, =, or >. The wholes are the same size.
c7. Compare 3/7 and 1/2. Choose <, =, or >. The wholes are the same size.
c8. Compare 5/10 and 1/2. Choose <, =, or >. The wholes are the same size.
e1. Compare 7/12 and 1/2. Choose <, =, or >. The wholes are the same size.
e2. How does twice the numerator help?
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 columns below, equal to, and above one half.
- Place fraction cards by comparing twice the numerator with the denominator.
- Partners explain a tricky card with a model rather than a decimal approximation.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw columns below, equal to, and above one half.
Place fraction cards by comparing twice the numerator with the denominator.
Partners explain a tricky card with a model rather than a decimal approximation.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 7/12 and 1/2. Choose <, =, or >. The wholes are the same size. How does twice the numerator help?
Watch for this misconception
Assuming all fractions above half are equal.
Use the benchmark for a first sort, then compare more closely.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Compare 7/12 and 1/2. Choose <, =, or >. The wholes are the same size.
7/12 > 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c2. Compare 3/8 and 1/2. Choose <, =, or >. The wholes are the same size.
3/8 < 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c3. Compare 4/8 and 1/2. Choose <, =, or >. The wholes are the same size.
4/8 = 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c4. Compare 5/6 and 1/2. Choose <, =, or >. The wholes are the same size.
5/6 > 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c5. Compare 2/5 and 1/2. Choose <, =, or >. The wholes are the same size.
2/5 < 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c6. Compare 6/10 and 1/2. Choose <, =, or >. The wholes are the same size.
6/10 > 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c7. Compare 3/7 and 1/2. Choose <, =, or >. The wholes are the same size.
3/7 < 1/2. Rename them as equal-sized parts or place them on the same unit number line.
c8. Compare 5/10 and 1/2. Choose <, =, or >. The wholes are the same size.
5/10 = 1/2. Rename them as equal-sized parts or place them on the same unit number line.
s1. Compare 1/4 and 1/2. Choose <, =, or >. The wholes are the same size.
1/4 < 1/2. Rename them as equal-sized parts or place them on the same unit number line.
s2. Compare 2/4 and 1/2. Choose <, =, or >. The wholes are the same size.
2/4 = 1/2. Rename them as equal-sized parts or place them on the same unit number line.
s3. Compare 3/4 and 1/2. Choose <, =, or >. The wholes are the same size.
3/4 > 1/2. Rename them as equal-sized parts or place them on the same unit number line.
s4. Compare 1/3 and 1/2. Choose <, =, or >. The wholes are the same size.
1/3 < 1/2. Rename them as equal-sized parts or place them on the same unit number line.
h1. Explain where 7/12 belongs without dividing.
Half of twelve is six; seven twelfths is above 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. Name two fractions below half with different denominators.
1/3 and 3/8 are both below 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.
h3. Can the benchmark alone compare 3/4 and 5/6?
It shows both exceed half, but more reasoning is needed; 9/12 is below 10/12.
- 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. Invent a fraction between one half and one.
3/5 is greater than half and less than one.
- 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 7/12 and 1/2. Choose <, =, or >. The wholes are the same size.
7/12 > 1/2. Rename them as equal-sized parts or place them on the same unit number line.
e2. How does twice the numerator help?
Compare two copies of the fraction with one whole; twice the numerator versus the denominator gives the relation.
- 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. Compare 1/4 and 1/2. Choose <, =, or >. The wholes are the same size.
s2. Compare 2/4 and 1/2. Choose <, =, or >. The wholes are the same size.
s3. Compare 3/4 and 1/2. Choose <, =, or >. The wholes are the same size.
s4. Compare 1/3 and 1/2. Choose <, =, or >. The wholes are the same size.
e1. Compare 7/12 and 1/2. Choose <, =, or >. The wholes are the same size.
e2. How does twice the numerator help?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Explain where 7/12 belongs without dividing.
h2. Name two fractions below half with different denominators.
h3. Can the benchmark alone compare 3/4 and 5/6?
h4. Invent a fraction between one half and one.
e1. Compare 7/12 and 1/2. Choose <, =, or >. The wholes are the same size.
e2. How does twice the numerator help?
Teaching notes & lesson sources
Designed for Grade 4. Use one half as a benchmark to classify and compare fractions.
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.