Choosing representations strategically · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Choosing the right tool for the job

Mathematics · Mathematical Thinking · ages 9-10
Name ______________________   Date ____________

  1. What is 25 x 40?

    Answer: ______________

  2. Which multiplication suits mental maths?

    • 25 x 40
    • 347 x 26
    • 458 x 37
    • 679 x 84

  3. Which is easier to solve in your head: 25 × 40 or 347 × 26?

    • 25 × 40
    • 347 × 26
    • They are equally easy

  4. Comparing fractions to a benchmark like 1/2 is one way to order them without finding a common denominator.

    Circle one:   True   False

  5. What is 347 x 26?

    Answer: ______________

  6. Look at the fraction bar. Is it less than half or more than half shaded?

    • Exactly half
    • Less than half
    • More than half

  7. You estimate an angle as 120 degrees. How do you check it properly?

    • Measure it with a protractor
    • Guess a second time
    • Ask a friend to guess
    • Measure it with a ruler

  8. Fred estimates an angle then verifies with a protractor. He says tools beat guessing. Is Fred right?

    Circle one:   True   False

  9. Sam always uses long multiplication on paper, even for 10 × 20. Is this the best choice?

    • Yes, paper is always more accurate
    • Yes, long multiplication is required for every problem
    • No, mental math is faster and just as accurate for 10 × 20

  10. Fractions 5/6, 2/3, 3/4 equal 10/12, 8/12, 9/12. How many of the three fractions are greater than 9/12?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Choosing the right tool for the job W1-mt_IwEOCN6bL1-s1

  1. 1000 · 25 x 40 = 1000.
  2. 25 x 40 · 25 x 40 uses friendly numbers; the rest need written methods.
  3. 25 × 40 · 25 × 40 has round, friendly numbers you can multiply mentally. 347 × 26 has too many digits to hold in your head.
  4. True · You can compare 3/8 and 5/8 to 1/2 to quickly tell which is bigger, without common denominators.
  5. 9022 · 347 x 26 = 9022.
  6. Less than half · 3 out of 8 shaded parts is less than half the bar. Comparing to the 1/2 benchmark like this can be faster than finding a common denominator.
  7. Measure it with a protractor · A protractor verifies angle estimates; rulers and guesses cannot.
  8. True · Fred is right: measurement confirms or corrects estimates.
  9. No, mental math is faster and just as accurate for 10 × 20 · For simple, round numbers like 10 × 20, mental math is quick and reliable. Save long multiplication for harder numbers.
  10. 1 · Only 10/12 beats 9/12, so 1 of the three.
Worksheet · LightMySky