Maths Lab · Free lesson · 18 minutes
Different pieces, the same fraction
Explain equivalence using equal-sized parts of the same whole, compare fractions and recognise fractions greater than one.
Primary 6 · fraction foundations01 · Think first
Start with a question.
You share one loaf with a friend. Cutting your half into two pieces changes the number of pieces, but does it change how much bread you have? The size of the whole must stay fixed.
What you already know
- Recognise equal parts
- Multiply and divide whole numbers
- Locate 0 and 1 on a number line
02 · See it
Split each part; preserve the whole
Change the partition and count shaded equal parts. Doubling both counts preserves the length shaded. Compare only equal-sized wholes.
1/2 = 1/2. More pieces; the same shaded fraction of the same whole.
- Original fraction
- 1/2
- Each original piece split into 1
- 1/2
- Amount of the same whole
- one half
Use the justified worked steps below to explore this idea.
03 · Show steps · explain why
One justified step at a time.
- 1
1/2 = 2/4 = 4/8
Splitting every part into two doubles both the total number of parts and the shaded number. The amount of the original whole is unchanged.
04 · Mistake clinic
Find the first wrong idea.
1/8 > 1/4 because 8 > 4.
Compare the correction and its reason
For the same whole, 1/8 < 1/4.
A greater denominator divides a fixed whole into more, smaller pieces. Counting the denominator alone ignores the size of each piece.
Check: Draw equal-length bars, split one into four and one into eight, then shade one part of each.
A mistake is evidence about the next idea to repair. It is not a label for the learner.
05 · Your turn
Try first. Then use a hint.
06 · Check & reflect → next step
Understanding includes explaining.
Explain why equivalent fractions have different counts but the same value. Which whole did you use?
Use fraction meaning to understand percentages as parts per hundred. If comparisons are uncertain, revisit the equal-parts model first.
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JEM-P6-M03-001 · Phase 1 Primary6 Readiness and Core Mathematics · Lesson 5 · printed pp. 19–20
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