A ready-to-run fraction substitute lesson

prepare. Materials: pencils, plain paper and a board, or printed student pages. Download the teacher HTML before going offline. This review assumes learners can identify halves, thirds and fourths of equal-sized wholes; if they cannot, use the halves-and-fourths support route throughout.

run-1. 0–5 min · Settle and start. Put the two warm-up prompts on the board or hand out the student pages. Learners sketch equal-length wholes and answer quietly.

run-2. 5–12 min · Show one example. Draw two equal-length rectangles. Shade half of each. Split each half of the second rectangle into two equal parts. Read the worked example together; the shaded endpoint stays fixed.

run-3. 12–22 min · Compare with a partner. Use c3 and c6. One partner draws; the other checks the whole and equal parts. Swap roles. Ask both to explain the equal sign.

run-4. 22–34 min · Work independently. Use c7 and h2. Learners may draw strips. If stuck, return to halves and fourths. Early finishers find a third name for 2/3.

run-5. 34–40 min · Discuss the useful error. Discuss h2: adding one to each number changes 2/3 to 3/4. Use same-sized wholes split into twelfths to compare 8/12 and 9/12.

run-6. 40–45 min · Collect an exit ticket. Ask e1 and e2 independently. Keep the two answers together and leave the brief handover notes for the class teacher.

c1. The strip shows 2/4. Enter the same amount as a fraction. Strip model: 1 same-sized whole, each divided into 4 equal parts; 2 parts are shaded altogether.

Answer: 1/2

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

c2. Compare 1/2 and 2/4. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

example. Show why 1/2 = 2/4 using two same-sized rectangles.

1. Draw two rectangles of the same length and width.
2. Divide each into two equal parts and shade one half.
3. Divide both halves of the second rectangle in half again.
4. It now has four equal parts and two are shaded. The shaded amount has not changed.

Worked example: 1/2 = 2/4. The whole and shaded amount stayed the same; only the number and size of the parts changed.

c3. Compare 2/3 and 4/6. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

c6. Compare 2/5 and 4/10. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

c7. Write the value shown by eight of twelve parts. Strip model: 1 same-sized whole, each divided into 12 equal parts; 8 parts are shaded altogether.

Answer: 2/3

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

h2. A partner says 2/3 = 3/4 because both numbers increased by one. Give a counterexample.

Answer: Two thirds is 8/12 and three fourths is 9/12, so their endpoints differ.

Look for:

• Reject 2/3 = 3/4.
• Provide evidence of different values, such as 8/12 versus 9/12.
• Explain that adding one to both counts does not preserve the fraction as multiplying both by the same factor does.

Teacher response: Adds the same number to numerator and denominator and claims the fraction stays equal. Put 2/3 and 3/4 on the same twelfths strip: 8/12 and 9/12 have different endpoints. Contrast this with 2/3 = 4/6, where both counts are multiplied by two.

e1. Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

e2. Explain why 1/2 and 2/4 are equivalent.

Answer: Repartition the same whole: each half becomes two fourths, and the shaded endpoint stays fixed.

Look for:

• Keep the whole fixed when moving from halves to fourths.
• Split each half into two equal fourths, giving 1/2 = 2/4.
• Explain that the shaded amount or endpoint stays unchanged.

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

support. If learners cannot yet draw equivalent fractions:

Teacher response: Keep both wholes the same size. Work only with 1/2 and 2/4. Draw the new partition through both shaded and unshaded halves. Ask what changed and what stayed fixed.

extend. If learners finish early, ask for three names for 2/3 and why they match.

Answer: For example, 2/3 = 4/6 = 8/12. Splitting each third into two or four equal pieces preserves the shaded amount.

handover. Leave on paper for the class teacher: Sections completed: ______. Could learners keep the same whole? ______. Could they explain e2? ______. Error to revisit: ______. Suggested next step: ______.

Teacher response: Use anonymous class or group observations. If equivalence is still fragile, revisit Equivalent Strip Lab; if only the whole is unclear, use Whole Size Matters.