Fraction Classroom
Teaching routines

Grade 3 · targeted review in Grades 4–5 · 12 minutes

A 12-minute number-line rescue

Count equal intervals instead of tick marks. Ask three short questions, model one example, practise three times, then check a new situation.

For a teacher working with a learner or small group after a number-line error.

Have this ready

Paper, pencil and a ruler. Read the prompts aloud or download the student pages. No student device is needed.

Teaching sequence

  1. 0–3 min

    Find the difficulty

    Ask the three diagnostic questions. Keep the first explanation before offering help.

  2. 3–6 min

    Model the distance

    Trace each equal gap in the worked example. Zero is the starting place, not the first step.

  3. 6–10 min

    Fade the support

    Use the three selected practice tasks. Ask the learner to explain what the denominator counts.

  4. 10–12 min

    Check transfer

    Give the new situation independently, then use the next-step guide below.

Materials for your group

Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.

The tasks, ready to use

Read aloud, copy onto a board or use the separate student download. Open an answer only when you are ready to discuss it.

0–3 minutes · Quick diagnosis

Try all three. Explain with words, a sketch, or objects.

d1. A number line from 0 to 1 has marks at 0, 1/4, 2/4, 3/4, and 1. How many equal intervals does it have?

Answer & teaching response

4 equal intervals, although it has 5 marks.

  • Counts 4 spaces.
  • Distinguishes 5 marks from 4 intervals.

Follow-up: Likely difficulty: Counting endpoint marks as fractional parts. Response: Slide a finger across each gap, starting the first count after leaving zero.

d2. Starting at 0 on a line divided into sixths, a student counts the zero mark as “one” and labels the next mark 2/6. Repair the label.

Answer & teaching response

The next mark is 1/6 because only one sixth-length interval has been traveled.

  • Labels the next mark 1/6.
  • Explains zero is the starting position.

Follow-up: Likely difficulty: Including zero as a traveled step. Response: Ask what distance has been traveled before taking the first step.

d3. A line from 0 to 1 has three gaps of different lengths. Can its marks be labeled 0, 1/3, 2/3, 1 in order? Explain.

Answer & teaching response

No. Thirds require three equal-length intervals.

  • Rejects the thirds labeling.
  • Requires equal interval lengths.

Follow-up: Likely difficulty: Treating any three consecutive gaps as thirds. Response: Measure or copy the first gap to check whether it fits the other two.

3–6 minutes · One worked example

Trace each equal gap as you count.

w1. Draw a line from 0 to 1 and locate 3/4.

  1. Mark and label 0 and 1 first.
  2. Partition their distance into four equal intervals; this needs five marks including both ends.
  3. Count three intervals from 0.
  4. Label the endpoint of the third interval 3/4.

Worked example: 3/4 is the endpoint after three fourth-length steps from zero.

6–10 minutes · Three practice tasks

Draw or explain your thinking.

p1. Draw a unit line with 3 equal intervals. How many marks are needed when both 0 and 1 are included?

Answer & teaching response

4 marks.

  • Draws three equal gaps.
  • Counts four marks including endpoints.

Follow-up: Likely difficulty: Assuming the mark count equals the interval count. Response: Start with the zero mark and add one endpoint for each of three steps.

p2. On a unit line split into eighths, what fraction is reached after five equal steps from 0?

Answer & teaching response

5/8.

  • Names eighths as the step size.
  • Labels 5/8.

Follow-up: Likely difficulty: Swapping the traveled steps and unit partition counts. Response: Name the step size first, then count five copies.

p3. A line has labels 0, A, B, C, 1, all equally spaced. Name B.

Answer & teaching response

2/4, or 1/2.

  • Identifies four equal intervals.
  • Names B as 2/4 or 1/2.

Follow-up: Likely difficulty: Using five letters or labels as the denominator. Response: Count the four gaps and mark the two that reach B.

10–12 minutes · Independent transfer

Try this new situation without help.

t1. A 12 cm line represents 0 to 1. Mark 5/6 and explain the difference between the number of marks and the number of intervals.

Answer & teaching response

5/6 is 10 cm from 0. Six 2 cm intervals require seven marks including the endpoints.

  • Locates 5/6 at 10 cm.
  • Distinguishes six intervals from seven marks.

Follow-up: Likely difficulty: Using endpoint count to determine the denominator. Response: Build the line with six 2 cm steps, then count endpoints separately.

Use what you notice

The learner counts marks or includes zero

Trace the spaces in the worked example. Ask how far they have travelled before the first step. Recheck with a different partition count.

Open the full number-line intervention →
The learner accepts unequal gaps

Measure or copy one interval. Rebuild equal intervals before naming fractions.

Revisit equal parts →
The explanation and transfer both hold

Move to independent model building and ask the learner to preserve the same unit beyond one.

Open the Number Line Lab →

The teacher download includes the full teaching notes and responses. Use explanations as well as correct answers to choose the next step.

Another classroom situation?