L1 · Equivalent fractions: partitioning the whole

Learning goal

“I can make a new name for a fraction by cutting each equal part into smaller equal parts - the amount stays the same, and the point on the number line does not move.”

Numerator — the number of equal parts being counted or shaded.

Denominator — the number of equal parts that make one whole.

Partition — to cut a whole (or each of its parts) into equal smaller parts.

Equivalent fractions — different names for the same amount, like 1/2 and 2/4.

Worked example

Rename 1/2 with denominator 4. Step 1: Start with a bar cut into 2 equal parts. Shade 1 part: that is 1/2. Step 2: Cut EACH part in half. Now the bar has 4 equal parts, and the shaded part has become 2 shaded parts. Step 3: The amount shaded did not change: 1/2 = 2/4. Say why it works: each part got smaller (half as big), so we need twice as many parts to make the same amount. In fraction language: the numerator and the denominator were both multiplied by 2 (1 x 2 = 2, 2 x 2 = 4). Model both ways, side by side: the bar in halves beside the same bar in quarters (shaded amount identical) AND a pre-segmented 0-2 number line where 1/2 and 2/4 are marked at exactly the same point.

Check yourself — explain it

When each part was cut in half, why did we count MORE parts for the same amount?

Paired problem — example still visible

Rename 1/3 with denominator 6. -> Cut each third in half: 1/3 = 2/6

Faded completion — last step is yours

"Rename 2/5 with denominator 10: each fifth is cut into 2 parts, so the denominator is 5 x 2 = 10 and the numerator is 2 x 2 = ___." -> 4, so 2/5 = 4/10

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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