Explaining Mathematical Reasoning · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Telling how you got your answer

Mathematics · Mathematical Thinking · ages 6-7
Name ______________________   Date ____________

  1. You are making ten to solve 9 + 3. How many of the 3 do you add to 9 to reach 10?

    Answer: ______________

  2. Which of these explains how you solved 9 + 4, instead of just giving the answer?

    • I made ten, then added the 3 left
    • I wrote 13 and stopped
    • I chose 13 because it is the number I like best

  3. If you check your answer a different way and get the same result, your first answer was probably right.

    Circle one:   True   False

  4. What can you use to show how you solved a problem?

    • Just the final number
    • A drawing or number sentence
    • Only a guess with no steps to check

  5. To explain 4 + 5, Jo starts with 4 + 4 = 8. How many more cubes must Jo add to the double?

    Answer: ______________

  6. Tom solves 8 + 4 by drawing 8 dots and then only 3 more. He counts 11. Which change makes his drawing match 8 + 4?

    • Remove a dot from the group of 8
    • Add a dot to the group of 3
    • Add a dot to each group
    • Remove a dot from each group

  7. Ava writes 7 + 5 = 12. To check, she writes 5 + 7 and copies 12 without working it out. Has she calculated the sum again?

    Circle one:   True   False

  8. To solve 6 + 8, Kai uses 4 of the added 8 to make 10. How many of the 8 are still left to add?

    Answer: ______________

  9. Zara says: 'I know 6 + 7 = 13, because 6 + 6 = 12, and 7 is one more than 6, so the answer is one more than 12.' Is this a good way to justify her answer?

    • No, keep the double's total
    • Yes, double 6 then add 1 explains the total
    • No, number steps cannot explain a sum without a drawing

  10. To explain 7 + 9, Leo adds 10 to 7 and gets 17. He then takes away the extra 1. What is his final answer?

    Answer: ______________

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Answer key

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

Telling how you got your answer W1-mt_kJ5wYzO8qC-s1

  1. 1 · 9 needs 1 more to reach 10. The other 2 are added next.
  2. I made ten, then added the 3 left · Explaining your steps means telling how you got the answer, like making a ten first.
  3. True · Matching answers support the check. Also check that both methods use the problem's numbers and valid steps.
  4. A drawing or number sentence · A drawing or number sentence shows your thinking, not just the answer.
  5. 1 · 5 is one more than 4. Add 1 cube to the double's 8 cubes.
  6. Add a dot to the group of 3 · The starting group already has 8. Add one dot to make the new group 4.
  7. False · She reversed the numbers but copied the answer. She has not done another calculation.
  8. 4 · Split 8 into 4 and 4. After using one group of 4, the other 4 remain.
  9. Yes, double 6 then add 1 explains the total · Starting from a known double and adjusting by one is a solid way to justify an answer.
  10. 16 · Adding 10 instead of 9 adds one extra. Take that one from 17 to get 16.
Worksheet · LightMySky