Task 5
Complements
Find the part needed to complete one length to another.
We do
Place orange and black side by side. Which rod must be added to black to make a train equivalent to orange? Light green.
k + g = o
Repeat with orange and dark green:
d + p = o
The missing rod is the complement: the part needed to complete the length.
Your turn — Find the missing rod
Use a blue rod as the target. Which rod completes each statement?
- y + ? = b
- t + ? = b
- r + ? = b
- k + ? = b
- g + ? = b
- p + ? = b
Build first, then record the complete equation.
Show answers
- y + p = b
- t + w = b
- r + k = b
- k + r = b
- g + d = b
- p + y = b
Feedback / teacher prompts
- Which complements did you begin to know without building?
- What relationships appear more than once?
- What do you notice when the order is reversed?
Your turn — Look first, then check
Place each pair side by side. Without moving them, decide which rod completes the shorter length to the longer. Then check by moving the rods.
- red and yellow
- pink and blue
- light green and black
- yellow and tan
- red and dark green
- white and pink
Record each relationship as an equation.
Partner challenge
Choose a rod, then a second shorter rod.
- Move the rods to find the complement.
- Repeat by looking but not touching until you are ready to check.
- Try to answer before placing the rods side by side.
Swap roles.
What could you change?
Change the target, use a train as the target, hide the target after a brief look, allow the missing part to be a train, or ask pupils to create missing-part challenges for each other.
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?