Number Line Launch
Locate fractions from 0 to 1 by counting equal intervals.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Write the fraction at the marked point.
c2. Write the fraction at the marked point.
c3. Write the fraction at the marked point.
c4. Write the fraction at the marked point.
c5. Write the fraction at the marked point.
c6. Write the fraction at the marked point.
c7. Write the fraction at the marked point.
c8. Write the fraction at the marked point.
e1. What fraction is at the marked point?
e2. Explain why we count spaces instead of tick marks.
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 a line from 0 to 1. Mark four equal intervals, not four interior points.
- Place a paper counter at each fourth. Say the distance from zero.
- Partners draw thirds and sixths and label the marked locations.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw a line from 0 to 1. Mark four equal intervals, not four interior points.
Place a paper counter at each fourth. Say the distance from zero.
Partners draw thirds and sixths and label the marked locations.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
What fraction is at the marked point? Explain why we count spaces instead of tick marks.
Watch for this misconception
Counting tick marks as fractional intervals.
Trace each space from zero to one and count the intervals.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Write the fraction at the marked point.
1 parts of size 1/4 represent 1/4.
c2. Write the fraction at the marked point.
3 parts of size 1/4 represent 3/4.
c3. Write the fraction at the marked point.
2 parts of size 1/3 represent 2/3.
c4. Write the fraction at the marked point.
1 parts of size 1/6 represent 1/6.
c5. Write the fraction at the marked point.
5 parts of size 1/6 represent 5/6.
c6. Write the fraction at the marked point.
3 parts of size 1/8 represent 3/8.
c7. Write the fraction at the marked point.
7 parts of size 1/8 represent 7/8.
c8. Write the fraction at the marked point.
2 parts of size 1/4 represent 2/4.
s1. Write the fraction at the marked point.
1 parts of size 1/2 represent 1/2.
s2. Write the fraction at the marked point.
1 parts of size 1/3 represent 1/3.
s3. Write the fraction at the marked point.
1 parts of size 1/4 represent 1/4.
s4. Write the fraction at the marked point.
2 parts of size 1/4 represent 2/4.
h1. Draw a number line with 0, 1/4, 2/4, 3/4 and 1.
Four equally spaced intervals connect zero to 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.
h2. Why do five tick marks make four intervals?
Intervals are the spaces between neighboring tick marks.
- 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. Show that 2/4 and 1/2 share a point.
Both are halfway from zero to 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.
h4. Repair a number line with uneven fourths.
Space all four intervals equally between zero and 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. What fraction is at the marked point?
Count three quarter-length intervals from zero.
e2. Explain why we count spaces instead of tick marks.
Each space is one equal unit fraction; a point itself has no 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.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
s1. Write the fraction at the marked point.
s2. Write the fraction at the marked point.
s3. Write the fraction at the marked point.
s4. Write the fraction at the marked point.
e1. What fraction is at the marked point?
e2. Explain why we count spaces instead of tick marks.
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Draw a number line with 0, 1/4, 2/4, 3/4 and 1.
h2. Why do five tick marks make four intervals?
h3. Show that 2/4 and 1/2 share a point.
h4. Repair a number line with uneven fourths.
e1. What fraction is at the marked point?
e2. Explain why we count spaces instead of tick marks.
Teaching notes & lesson sources
Designed for Grade 3. Locate fractions from 0 to 1 by counting equal intervals.
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.