Make the whole visible before naming the fraction
This classroom activity helps learners explain why one half and two quarters cover the same amount of an equal-sized whole. You need two identical rectangular paper strips, pencils and two colours. No cutting is required. The goal is an explanation supported by the paper, rather than memorising that multiplying two numbers produces an equivalent fraction. Adapt the pace to learners who already recognise equal parts.
Prepare two equal wholes
Place one strip directly over the other to check that their sizes match. Call each strip one whole. Fold the first strip in half by bringing its short ends together, then open it. Shade one of the two equal parts. Ask: “How many equal parts make the whole, and how many are shaded?” Record 1/2 and say one half.
Show the same amount in smaller parts
Fold the second strip in half and then in half again in the same direction. Open it to show four equal sections. Shade two neighbouring sections from the same end used on the first strip. Align the strips. The shaded endpoints should match: one of two equal parts covers the same length and area as two of four equal parts. Write 1/2 = 2/4. Explain that the whole stayed the same size while each part became smaller.
Ask learners to justify the match
Use the sentence frame: “These fractions are equal because the wholes are ___ and the shaded amounts ___.” A useful answer is “the same size” and “match when aligned.” If a learner says two quarters is larger because two is greater than one, return to the paper and compare the sizes of the parts. If folds are uneven, refold or provide prepared strips; do not treat an inaccurate model as evidence against the fraction relationship.
Introduce a deliberate mismatch
Show half of a long strip beside half of a shorter strip. Both are one half of their own whole, but they need not represent the same amount of paper. Ask what must be checked before comparing shaded quantities. The answer is the size of the whole. Keep this example separate from the original pair so learners can identify exactly what changed.
Check understanding without the folded model
Draw two equal rectangles. Divide one into two equal parts and the other into four equal parts. Ask learners to shade one half in both and explain their choice. Accept different orientations when the partitions have equal areas. Expected answer: one part in the first rectangle and two parts in the second. For an extension, divide another equal whole into eight equal parts; four eighths matches one half. Record whether the learner checked equal wholes, equal parts and equal shaded amounts. Use these observations to choose the next practice task.
This is an original classroom resource for Schoolizer. The cover illustrates paper folding; it is not the completed fraction model.
