Fraction Classroom · 2.0.0 · Teacher answers & responses
Number Line Launch: teaching companion
Read a fraction as an equal distance from zero, counting intervals. Student pages include two diagnostic probes, a reteaching check, and the original exit ticket. The teacher copy includes the complete lesson preparation, teaching sequence, diagnostic responses, all original question guides, and updated rubrics.
Complete lesson preparation
Grade 3 · 45 minutes. Locate fractions from 0 to 1 by counting equal intervals.
materials. Materials: Pencil: 1 per student; Plain paper sheets: 2 per student; Projector: 1 per class (optional).
activity-1. Draw a line from 0 to 1. Mark four equal intervals, not four interior points.
activity-2. Place a paper counter at each fourth. Say the distance from zero.
activity-3. Partners draw thirds and sixths and label the marked locations.
phase-1. 5 min · warmup: Look at the first model or task. What is the whole? What do you notice?
Answer: Students: Sketch an initial prediction and explain it to a partner.
phase-2. 8 min · model: Draw a line from 0 to 1. Mark four equal intervals, not four interior points.
Answer: Students: Follow the model; label the whole and the equal parts.
phase-3. 10 min · partner: Place a paper counter at each fourth. Say the distance from zero.
Answer: Students: Work in pairs. One models, the other checks; switch roles.
phase-4. 7 min · discussion: Partners draw thirds and sixths and label the marked locations.
Answer: Students: Compare two solutions and explain the relationship.
phase-5. 10 min · practice: Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Answer: Students: Solve independently, then compare the reasoning.
phase-6. 5 min · exit: What fraction is at the marked point? Explain why we count spaces instead of tick marks.
Answer: Students: Complete the two exit questions independently.
Diagnostic probes
Explain or draw your reasoning. Your teacher will use these responses to choose what to revisit.
d1. A 0–1 line has five equally spaced marks including its endpoints. What is the size of one interval?
Answer: 1/4: five marks bound four equal intervals.
Teacher response: If the learner answers 1/5 by counting the marks. Draw one curved jump over each gap. Start the first jump at zero and count four jumps to one.
d2. On that line, a point is three intervals from zero. Name the point and justify the denominator.
Answer: 3/4; three quarter-steps from zero, with four equal intervals per whole.
Teacher response: If the learner answers 4/5 by counting both boundary marks. Place a counter at zero without counting a step, then move and count only completed intervals.
Check after reteaching
Complete this check independently after discussing the model.
r1. A 0–1 line has six equal intervals. What point is four intervals from zero?
Answer: 4/6, equivalent to 2/3.
Exit ticket
Complete both original exit questions independently. Use a drawing or explanation when asked.
e1. What fraction is at the marked point? Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 3 intervals from zero.
Answer: 3/4
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
e2. Explain why we count spaces instead of tick marks.
Answer: Each space is one equal unit fraction; a point itself has no length.
Look for:
- Identify a space as a length or jump representing one unit fraction.
- Explain that a tick mark marks a position rather than a length.
- Relate the count of spaces from 0 to the fraction at the endpoint.
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
Focused reteach
Read a fraction as an equal distance from zero, counting intervals.
teach-1. Mark 0 and 1 on a line and transfer four equal lengths from a folded strip.
teach-2. Label each jump 1/4 and count the completed jumps from zero.
teach-3. Place a point at three jumps and connect the distance to three shaded fourths in a strip.
Use the exit evidence
A wrong answer invites a follow-up probe; it does not by itself establish a particular misconception. Check e1 and e2 separately.
next-1. e1 meets its criterion: e1 labels the marked point 3/4. e2 also meets its criterion: e2 explains that spaces represent equal lengths and tick marks represent positions.
Teacher response: Continue to the linked next lesson. Continue the same interval size and count beyond the point labeled one. Next original lesson: /lessons/beyond-one-walk/.
next-2. e1 does not yet meet this criterion: e1 labels the marked point 3/4.
Teacher response: Ask the learner to explain the attempt, then use the matching diagnostic probe to identify the difficulty. Work through the focused reteach below and its check. Use the linked short intervention if the difficulty persists; retry e1 and e2 before moving on. Short intervention: /interventions/intervals-not-points/.
next-3. e1 meets its criterion, but e2 does not yet show this evidence: e2 explains that spaces represent equal lengths and tick marks represent positions.
Teacher response: Ask the learner to demonstrate one jump and one mark on e1, then explain why only a completed jump adds to the numerator. Short intervention: /interventions/intervals-not-points/.
Original question guide and updated rubrics
Use these question-specific teaching responses alongside the original lesson. Accept other mathematically valid open responses that meet the criteria. The original question wording and mathematical answers are retained; model descriptions below make their references readable offline.
c1. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 1 intervals from zero.
Answer: 1/4
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
c2. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 3 intervals from zero.
Answer: 3/4
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
c3. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 3 equal intervals. The marked point is 2 intervals from zero.
Answer: 2/3
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
c4. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 6 equal intervals. The marked point is 1 intervals from zero.
Answer: 1/6
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
c5. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 6 equal intervals. The marked point is 5 intervals from zero.
Answer: 5/6
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
c6. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 8 equal intervals. The marked point is 3 intervals from zero.
Answer: 3/8
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
c7. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 8 equal intervals. The marked point is 7 intervals from zero.
Answer: 7/8
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
c8. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 2 intervals from zero.
Answer: 2/4
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
s1. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 2 equal intervals. The marked point is 1 intervals from zero.
Answer: 1/2
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
s2. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 3 equal intervals. The marked point is 1 intervals from zero.
Answer: 1/3
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
s3. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 1 intervals from zero.
Answer: 1/4
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
s4. Write the fraction at the marked point. Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 2 intervals from zero.
Answer: 2/4
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
h1. Draw a number line with 0, 1/4, 2/4, 3/4 and 1.
Answer: Four equally spaced intervals connect zero to one.
Look for:
- Place 0 and 1 at the endpoints of one unit.
- Draw four equal intervals and five boundary marks.
- Label the internal points 1/4, 2/4, and 3/4 in order.
Teacher response: Accepts uneven spacing on a fraction number line. Fold a paper strip into four equal lengths and transfer the fold positions to a 0–1 line. Compare every neighboring gap with the first gap before labeling fourths.
h2. Why do five tick marks make four intervals?
Answer: Intervals are the spaces between neighboring tick marks.
Look for:
- Distinguish a tick mark from the space between two neighboring marks.
- Count four spaces when five marks are in order.
- Explain that the first mark starts the first interval rather than creating an extra interval.
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
h3. Show that 2/4 and 1/2 share a point.
Answer: Both are halfway from zero to one.
Look for:
- Keep the 0–1 unit the same for both fraction names.
- Locate 2/4 and 1/2 halfway from 0 to 1.
- Show or explain that both names refer to the same point.
Teacher response: Treats different fraction names as different positions despite equal distance from zero. Align the zero and one of a halves strip and a fourths line. Transfer the halfway endpoint to the line and label the same point 1/2 and 2/4.
h4. Repair a number line with uneven fourths.
Answer: Space all four intervals equally between zero and one.
Look for:
- Keep the endpoints 0 and 1 fixed.
- Reposition the internal marks to make four equal spaces.
- Label the repaired marks in quarter-step order.
Teacher response: Accepts uneven spacing on a fraction number line. Fold a paper strip into four equal lengths and transfer the fold positions to a 0–1 line. Compare every neighboring gap with the first gap before labeling fourths.
e1. What fraction is at the marked point? Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 3 intervals from zero.
Answer: 3/4
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
e2. Explain why we count spaces instead of tick marks.
Answer: Each space is one equal unit fraction; a point itself has no length.
Look for:
- Identify a space as a length or jump representing one unit fraction.
- Explain that a tick mark marks a position rather than a length.
- Relate the count of spaces from 0 to the fraction at the endpoint.
Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
Teaching notes
- Teaching supplement version 2.0.0. Original lesson questions and PDF materials remain version 1.0.0. Original PDFs contain their original teaching notes and rubrics; use this supplement for the updated diagnostic guidance.
- Short intervention: /interventions/intervals-not-points/. Use its model for the identified difficulty, then return to this lesson’s check and exit ticket.
- Next original lesson: /lessons/beyond-one-walk/. Continue the same interval size and count beyond the point labeled one.
- Open responses are reviewed by a teacher using the specific criteria. These materials have not been field-tested in classrooms.