Justifying mathematical reasoning (age 8+) · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Explaining Why Your Math Works

Mathematics · Mathematical Thinking · ages 8-9
Name ______________________   Date ____________

  1. A pie is cut into 5 equal slices. Jo eats 1 slice. How many slices are left?

    Answer: ______________

  2. Why is 1/3 bigger than 1/5?

    • 3 is bigger than 5
    • Thirds are bigger pieces than fifths
    • Fifths are bigger pieces than thirds
    • Both are the same size

  3. Which fraction is bigger: 1/3 or 1/5?

    • 1/3
    • 1/5
    • They are the same

  4. Ben solves 52 − 27. He exchanges a ten to make 12 ones, does 12−7=5, then 4−2=2, and gets 25. Is Ben's work correct?

    Circle one:   True   False

  5. Use 6 x 10 = 60 and 6 x 2 = 12 to find 6 x 8.

    Answer: ______________

  6. Using 7×10=70 and 7×3=21, what is 7×7?

    Answer: ______________

  7. Where is the mistake in 42 - 17 = 35?

    • Left the tens at 4, not 3
    • 12 - 7 does not equal 5
    • 42 - 17 cannot be worked out
    • Exchanges are never needed

  8. Oscar reasons: 6 x 10 = 60 and 6 x 2 = 12, so 6 x 8 = 60 - 12 = 48. He says breaking 8 into 10 - 2 proves it. Is Oscar right?

    Circle one:   True   False

  9. Cody says: '1/9 is bigger than 1/2 because 9 is a bigger number than 2.' What is wrong with his reasoning?

    • He forgot fractions can be negative
    • He compared piece-count, not size
    • He should have added the fractions instead

  10. Work out 94 - 57 using exchanges.

    Answer: ______________

LightMySky · lightmysky.comW1-mt_a3dov8CZkq-s1

Answer key

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

Explaining Why Your Math Works W1-mt_a3dov8CZkq-s1

  1. 4 · 4 slices are left because 5 - 1 = 4.
  2. Thirds are bigger pieces than fifths · Thirds are bigger pieces than fifths is the reason: 3 parts per whole are chunkier than 5 parts.
  3. 1/3 · Thirds are cut into fewer, bigger pieces than fifths.
  4. True · He exchanged a ten to make 12 ones, then subtracted each column correctly: the answer is 25.
  5. 48 · 6 x 8 = 48 because 8 is 10 - 2, so 60 - 12 = 48.
  6. 49 · 7 is 10−3, so 7×7 = 70 − 21 = 49.
  7. Left the tens at 4, not 3 · Leaving the tens at 4 instead of 3 is the mistake: lending 1 ten leaves 3 tens, and 3 - 1 = 2.
  8. True · Oscar is right because 10 lots minus 2 lots leaves 8 lots, and 60 - 12 = 48.
  9. He compared piece-count, not size · More parts means smaller pieces, so 1/9 is actually much smaller than 1/2.
  10. 37 · 94 - 57 = 37 because the ones exchange gives 14 - 7 = 7 and the tens give 8 - 5 = 3.
Worksheet · LightMySky