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. Which shows that 3/4 is greater than 2/3?

    • 9/12 is greater than 8/12
    • 8/12 is greater than 9/12
    • 3/4 equals 2/3
    • 6/8 is less than 6/9

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

    • 12
    • 6
    • 18

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

    • 1
    • 10
    • 15

  5. 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?

    • Shift the tens row left
    • Add correctly
    • Multiply the ones digit

  6. In 347 x 26, the first partial product is 347 x 6. What is it?

    Answer: ______________

  7. Hana proves 3/4 > 2/3 with twelfths and a bar picture. She says her picture shows the same winner as her twelfths. Is Hana right?

    Circle one:   True   False

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

    Answer: ______________

  9. 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

  10. A pupil lines up both partial products on the right with no shift. She says shifting never matters. Is she right?

    Circle one:   True   False

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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. 9/12 is greater than 8/12 · 3/4 = 9/12 beats 2/3 = 8/12.
  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. 10 · In 15, the 1 sits in the tens place, so it stands for 10, not 1.
  5. Shift the tens row left · The tens-digit product stands for tens, so it needs a shift before it gets added.
  6. 2082 · 347 x 6 = 2082.
  7. True · Hana is right: her twelfths say 9/12 beats 8/12, and her bars show the same winner, so the two match.
  8. 10 · 5/6 = 10/12, because 5 x 2 = 10 and 6 x 2 = 12.
  9. 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.
  10. False · She is wrong: the unshifted total mixes ones with tens.
Worksheet · LightMySky