Building and critiquing a mathematical argument · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Building a Strong Math Argument

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

  1. In 46 x 15, what does the 1 in 15 actually stand for?

    • 1
    • 10
    • 5

  2. Which number is a common denominator for 5/6 and 3/4?

    • 6
    • 7
    • 12

  3. If you tear off the three corners of a triangle and line them up, they form a straight line.

    Circle one:   True   False

  4. After rewriting, 5/6 = 10/12 and 3/4 = 9/12. Which fraction is greater?

    • 5/6
    • 3/4
    • They are equal

  5. Rewrite 5/6 as a fraction with denominator 12. What is the new numerator?

    Answer: ______________

  6. Nadia works out 34 x 12. Her lines are 34 x 2 = 68 and 34 x 1 = 34, and she adds them to get 102. What did she forget to do?

    • Add correctly
    • Shift the tens-digit product one place left
    • Multiply the ones digit

  7. Kofi says 3/4 > 2/3 because 3 > 2 and 4 > 3, so bigger numbers must make a bigger fraction. Is his reasoning correct?

    • Yes, his reasoning proves it
    • No, comparing numerators and denominators separately does not prove which fraction is bigger
    • No, because 3/4 is actually smaller than 2/3

  8. Zara tears the corners off a square instead of a triangle and lines them up. They cover more than a straight line. What does this tell you about a square's angles?

    • They add up to less than 180 degrees
    • They add up to more than 180 degrees
    • They add up to exactly 180 degrees, like a triangle
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Answer key

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

Building a Strong Math Argument W1-mt_2ESZh70NyS-s1

  1. 10 · In 15, the 1 sits in the tens place, so it stands for 10, not 1.
  2. 12 · 12 is a multiple of both 6 and 4, so both fractions can be renamed using twelfths.
  3. True · That straight line measures 180 degrees, which shows the three angles add up to 180 degrees.
  4. 5/6 · 10/12 is more than 9/12, so 5/6 is the greater fraction.
  5. 10 · 5/6 = 10/12, because 5 x 2 = 10 and 6 x 2 = 12.
  6. Shift the tens-digit product one place left · The tens-digit product stands for tens, so it needs a shift before it gets added.
  7. No, comparing numerators and denominators separately does not prove which fraction is bigger · Kofi's rule does not always work. Comparing fractions correctly needs a common denominator, like showing 9/12 > 8/12.
  8. They add up to more than 180 degrees · A square's four corners cover more space than a straight line, so their angles add up to more than 180 degrees.
Worksheet · LightMySky