Back to routineTeacher answers · Choose the same paper size in the print dialog.

Fraction Classroom · 2.1.0 · Teacher answers & responses

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.

Run the short session

Grade 3 or a targeted review in Grades 4–5. Paper, pencil and a ruler. Use the timings as a guide; listen to explanations rather than rushing.

guide-1. 0–3 minutes: Ask d1–d3 without correction. Listen for marks counted as parts, zero counted as a step, or unequal gaps accepted as thirds.

guide-2. 3–6 minutes: Model w1. Ask the learner to trace each gap, starting the count after leaving zero. If gaps are unequal, measure and rebuild the unit first.

guide-3. 6–10 minutes: Use p1–p3. Fade the finger tracing and ask for a sketch and explanation.

guide-4. 10–12 minutes: Ask t1 independently. Use the next-step guide; a single wrong answer needs a follow-up question.

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: 4 equal intervals, although it has 5 marks.

Look for:

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

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

Look for:

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

Teacher response: 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: No. Thirds require three equal-length intervals.

Look for:

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

Teacher response: 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.

Look for:

  • Uses four equal intervals in the unit.
  • Locates the endpoint after three steps.

Teacher response: Likely difficulty: Placing 3/4 at the third mark when zero is counted as mark one. Response: Draw three travel arcs and read their endpoints: 1/4, 2/4, 3/4.

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: 4 marks.

Look for:

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

Teacher response: 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: 5/8.

Look for:

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

Teacher response: 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: 2/4, or 1/2.

Look for:

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

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

Look for:

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

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

Choose the next step

next-marks. Still counts marks or counts zero as one.

Teacher response: Return to d1 and w1. Trace arcs over the gaps and say the distance travelled before naming the endpoint. Recheck later with sixths.

next-equal. Counts gaps but accepts unequal intervals.

Teacher response: Compare the lengths with a ruler. Rebuild one whole with equal gaps before asking for a fraction label.

next-ready. Explains equal gaps and completes the transfer independently.

Teacher response: Continue with Number Line Launch or the Number Line Lab. Keep the 0-to-1 whole fixed when moving beyond 1.

Teaching notes