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.
Paper, pencil and a ruler. Read the prompts aloud or download the student pages. No student device is needed.
Ask the three diagnostic questions. Keep the first explanation before offering help.
Trace each equal gap in the worked example. Zero is the starting place, not the first step.
Use the three selected practice tasks. Ask the learner to explain what the denominator counts.
Give the new situation independently, then use the next-step guide below.
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.
Read aloud, copy onto a board or use the separate student download. Open an answer only when you are ready to discuss it.
Try all three. Explain with words, a sketch, or objects.
4 equal intervals, although it has 5 marks.
Follow-up: Likely difficulty: Counting endpoint marks as fractional parts. Response: Slide a finger across each gap, starting the first count after leaving zero.
The next mark is 1/6 because only one sixth-length interval has been traveled.
Follow-up: Likely difficulty: Including zero as a traveled step. Response: Ask what distance has been traveled before taking the first step.
No. Thirds require three equal-length intervals.
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.
Trace each equal gap as you count.
Worked example: 3/4 is the endpoint after three fourth-length steps from zero.
Draw or explain your thinking.
4 marks.
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.
5/8.
Follow-up: Likely difficulty: Swapping the traveled steps and unit partition counts. Response: Name the step size first, then count five copies.
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.
Try this new situation without help.
5/6 is 10 cm from 0. Six 2 cm intervals require seven marks including the endpoints.
Follow-up: Likely difficulty: Using endpoint count to determine the denominator. Response: Build the line with six 2 cm steps, then count endpoints separately.
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 →Measure or copy one interval. Rebuild equal intervals before naming fractions.
Revisit equal parts →Move to independent model building and ask the learner to preserve the same unit beyond one.
Open the Number Line Lab →