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Fraction Classroom · 2.0.0 · Student pages

Predict what a multiplier will do

Compare a positive multiplier with 1 to predict whether a length shrinks, stays the same, or grows.

Anonymous group code: __________   Date: __________

Quick diagnosis

Try all three. Explain with words, a sketch, or objects.

d1. Without calculating, compare 3/4 × 8 with 8. What does 3/4 tell you?

d2. Without calculating, compare 5/4 × 8 with 8.

d3. A student says 6/6 × 7 must be larger than 7 because the factor has a 6. Explain.

Worked examples

Study the example that matches the difficulty. Keep the other for a second session.

w1. A 12 cm ribbon is scaled by 2/3. Predict and calculate the new length.

  1. The factor 2/3 is less than 1, so expect a shorter positive length.
  2. Partition the 12 cm ribbon into three equal 4 cm sections.
  3. Take two sections: 2 × 4 = 8 cm.
  4. Compare 8 with 12 to check the prediction.

Worked example: The new length is 8 cm, less than 12 cm.

w2. Scale a 6 cm drawing by 3/2. Predict and calculate its new length.

  1. The factor 3/2 is 1 + 1/2, so expect more than the original length.
  2. Keep one full 6 cm copy.
  3. Add half of that copy, which is 3 cm.
  4. The result is 6 + 3 = 9 cm, matching the prediction.

Worked example: 9 cm, greater than 6 cm.

Practice

For a short session, choose three tasks. Use the others for a second try or follow-up.

p1. Compare 7/8 × 24 with 24 without multiplying. Explain.

p2. Compare 9/8 × 24 with 24 without multiplying. Explain.

p3. Choose the factor that keeps a 10 cm length unchanged: 3/4, 4/4, or 5/4.

p4. Scale 15 cm by 2/5. Predict first, then calculate.

p5. Which result is greater: 2/3 × 18 or 4/3 × 18? Explain using copies, then check.

p6. A 9 cm strip becomes 6 cm after scaling. Could the factor be 3/2? Give the correct factor.

Transfer check

Try one independently. Save the other for a later check.

t1. A machine enlarges a positive length with a factor of 1 1/4. An operator says the result is smaller because the factor contains 1/4. Explain and test the claim using 8 cm.

t2. Write one scale factor that shrinks a positive length, one that preserves it, and one that enlarges it. Does “a factor below 1 makes the result smaller” stay strictly true when the starting amount is 0?