Would you teach the rule in this AI draft?
Check the lesson claim and decide what would show that pupils understood.
The question
You are preparing a primary maths demonstration. Pupils need to compare shaded areas and explain how the size of each whole affects the comparison.
One third of any rectangle covers more area than one quarter of any other rectangle.
| Rectangle A | Rectangle B | |
|---|---|---|
| Area of the whole in grid squares | 12 | 12 |
| Denominator of the shaded unit fraction | 3 | 4 |
Both diagrams use grid squares of the same area. One part is shaded in each rectangle.
“What would you keep, what would you change and how would you check learning?”
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A strong answer, step by step
Open each step in turn. This is one strong answer, not the only one.
Step 1: Name the learning goal
What would you do here? Open the move you’d make.
Ask pupils to explain the size of each whole.
The strong move. The goal asks for an explanation that connects the fraction and the whole.
Check whether pupils can recite which fraction has the smaller denominator.
Tempting, but it misses something. Reciting a denominator rule gives no evidence that pupils can compare the shaded areas in a model.
See how a strong candidate says it
“I want pupils to compare the areas and explain which whole each fraction refers to.”
Why it works: The goal asks for an explanation that connects the fraction and the whole.
Step 2: Check the first diagrams
What would you do here? Open the move you’d make.
Keep the diagrams and qualify the claim.
The strong move. The diagrams give both fractions equal-sized wholes.
Keep the word “always” because the example confirms it.
Tempting, but it misses something. Both rectangles in the draft are the same size. That leaves the claim about different wholes unchecked.
See how a strong candidate says it
“A third of 12 squares is 4. A quarter of 12 squares is 3. That comparison works when the wholes are the same size.”
Why it works: The diagrams give both fractions equal-sized wholes.
Step 3: Compare the new diagrams
A new exercise pairs one third of a 12-square rectangle with one quarter of a 20-square rectangle. Each square represents the same area in both diagrams.
What would you do here? Open the move you’d make.
Use the new pair to show why the whole matters.
The strong move. A fraction and the size of its whole together determine the shaded area.
Choose the third as the larger area because its denominator is smaller.
Tempting, but it misses something. One quarter of 20 is 5, which is more area than one third of 12.
See how a strong candidate says it
“The shaded areas are 4 and 5 squares. One third is the larger fraction. Here the quarter covers more area because it uses a larger whole.”
Why it works: A fraction and the size of its whole together determine the shaded area.
Step 4: Check what pupils learned
What would you do here? Open the move you’d make.
Use a new pair and ask for the reason.
The strong move. An independent response shows whether pupils can apply the idea to a new pair.
Show the corrected answer and ask if everyone understands.
Tempting, but it misses something. Agreement after seeing the answer leaves each pupil’s reasoning untested.
See how a strong candidate says it
“I’d give each pupil a fresh pair. I’d ask for the larger shaded area and an explanation that names the whole in each diagram.”
Why it works: An independent response shows whether pupils can apply the idea to a new pair.
The answer, in short
- Decision
- Keep the equal-whole example and add an unequal-whole example.
- Because
- The size of the whole changes the area each fraction represents.
- What would change it
- If the next explanations still rely on the denominator alone, revisit the two wholes.
Common traps
- Generalizing from one pair of diagrams.
- Using agreement as evidence of individual understanding.
Check your answer
- I named the goal.
- I checked the first model.
- I explained the new comparison.
- I asked for a fresh explanation.
Last reviewed Nov 11, 2026