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Grade 5 · lesson 2 of 4

Predict Whether a Positive Quantity Grows or Shrinks

Compare the supplied positive multiplier with one.

About 20 minutes, plus any extended practice

Download the grade pack

Supplied materials

  • Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
  • Supplied worked-case record: For 12×3/4, the factor is less than one, so the product must be smaller than twelve.
  • All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Multiplication can shrink a positive quantity when its factor is between zero and one. A factor greater than one enlarges it, and a factor equal to one preserves it. This reverses the misconception that every multiplication must make numbers larger. The prediction should be made before calculating the exact product.

Compare the supplied positive multiplier with one. Predict smaller, equal, or larger than the original positive quantity. Explain the prediction using copies or parts of one copy, then calculate a check if desired.

Compare the multiplier with one before computing. Multiplication by a positive fraction below one makes a positive quantity smaller. Draw one reference bar and show the factor as part of or more than one copy.

  1. Draw one reference bar and show the factor as part of or more than one copy.
  2. Follow the worked example. Point to each number or shape feature and say what it tells you.
  3. Compare the supplied positive multiplier with one.
  4. Try the question and then the three practice questions. Check your answers and explain any change you make.
Worked example

See the method in action

For 12×3/4, the factor is less than one, so the product must be smaller than twelve. It equals nine. For 12×5/4, the factor exceeds one, giving fifteen. The operation is multiplication in both cases, while the factor controls the resizing direction. Compare the multiplier with one before computing. Multiplication by a positive fraction below one makes a positive quantity smaller. Draw one reference bar and show the factor as part of or more than one copy.

Your turn

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Helpful tips
  • Compare the multiplier with one before computing.
  • Multiplication by a positive fraction below one makes a positive quantity smaller.
For positive quantity 8, compare 8×2/3 with 8.

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

Smaller

Two thirds is a positive fraction below one.

Take it further

Predict 18×11/12 and 18×13/12. Expected: smaller and larger than 18.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.

More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. For positive quantity 15, compare 15×4/3 with 15.
Need a hint?
  • Compare the multiplier with one before computing.
  • Multiplication by a positive fraction below one makes a positive quantity smaller.
2. For positive quantity 6, compare 6×1 with 6.
Need a hint?
  • Compare the multiplier with one before computing.
  • Multiplication by a positive fraction below one makes a positive quantity smaller.
3. For positive quantity 20, compare 20×7/8 with 20.
Need a hint?
  • Compare the multiplier with one before computing.
  • Multiplication by a positive fraction below one makes a positive quantity smaller.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.