Task 7
Trains of one colour
Investigate which lengths can be composed from repeated equal rods, and what remains when they cannot.
We do
Take a dark green rod. Can you make an equivalent train using only reds?
Repeat with pink and yellow. Which rods can be made exactly from red rods?
Then investigate using only light-green rods. Which target rods can and cannot be made exactly?
Teacher note: This gives early exposure to factors, multiples, divisibility and remainders without needing to formalise those ideas immediately.
Your turn — Investigate one colour
Choose a red, light green, pink or yellow rod.
Using only rods of that colour, investigate target rods that are at least as long as your chosen rod.
- Which target rods can you make exactly?
- Which can you not make exactly?
- Record the equivalences you find using colour letters.
If a target cannot be made exactly, how close can you get without going past it? What is left over?
Organise your results so somebody else can see the pattern.
Feedback / teacher prompts
- Allocate different starting colours to different pairs, then compare findings.
- What patterns appear in the exact matches?
- What patterns appear in the leftovers?
What could you change?
Choose a different repeated colour, give the target and ask which single-colour trains can make it, ask pupils to predict first, or focus specifically on describing what is left over.
Rehearse the teaching
For a task worth practising, work in pairs. One person teaches while the other responds as a pupil using the rods. Model enough to get the pupil started, then stop explaining and question their thinking. Swap roles.
Reflect: What was harder to explain than you expected? Which wording or question worked well?