Justifying mathematical reasoning · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Checking if a maths argument makes sense

Mathematics · Mathematical Thinking · ages 7-8
Name ______________________   Date ____________

  1. Work out 246 + 135 using column addition. What is the total?

    Answer: ______________

  2. In the usual column-addition method, why do we finish the ones before the tens?

    • It lets us add any carried ten when we reach the tens
    • It lets us ignore the tens until the hundreds are finished
    • It lets us add ones digits as if each one were ten
    • It lets us avoid carrying whenever the ones pass nine

  3. You add two two-digit whole numbers in columns. The ones total more than 9. What should you do?

    • Write the ones digit and carry one ten
    • Write both digits together in the ones place
    • Write the ones digit and drop the extra ten

  4. If two whole numbers are both even, adding them always gives an even number.

    Circle one:   True   False

  5. Nia joins 9 counters and 6 counters. After making as many pairs as possible, how many counters are left without a partner?

    Answer: ______________

  6. Which pair shows that two odd numbers can add to an even number?

    • 3 and 5
    • 3 and 4
    • 2 and 4

  7. For 467 + 258, the tens step is 6 + 5 + 1 = 12 tens. We write 2 tens and carry 1 to the hundreds. What does that carried 1 mean?

    • It means 10 ones moved into the hundreds column
    • It means 1 one moved into the hundreds column
    • It means 1 hundred made by grouping 10 tens
    • It means 12 hundreds made by grouping 12 tens

  8. Tom gets 79 for 35 + 24 using two methods. Both times he copies 24 as 44. Do the matching answers show that his answer to 35 + 24 is correct?

    Circle one:   True   False

  9. Ravi sets out 68 + 7 with 7 under the 6. He adds 6 + 7 = 13 tens and keeps 8 ones, giving 138. Which step first changes the value of 7?

    • Keeping 8 as the ones digit of the total
    • Putting 7 in the tens column
    • Adding 6 + 7 after treating both digits as tens

  10. A child writes 506 - 278 = 232. Check by adding the answer to the amount taken away. What is 232 + 278?

    Answer: ______________

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Answer key

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

Checking if a maths argument makes sense W1-mt_pyMD_SIiYO-s1

  1. 381 · The ones make 11, so carry one ten. The tens make 8 tens and the hundreds make 3 hundreds. The total is 381.
  2. It lets us add any carried ten when we reach the tens · Adding the ones may make a ten. Starting there lets us include that ten when we add the tens.
  3. Write the ones digit and carry one ten · Ten ones make one ten. Write the remaining ones digit and include that ten in the tens column.
  4. True · Each even amount forms complete pairs. Joining the amounts keeps every counter paired, so the total is even.
  5. 1 · Nine counters leave one after pairing, and six leave none. Together, 15 counters form seven pairs with one counter left.
  6. 3 and 5 · 3 and 5 are both odd. Their sum is 8, which is even. This example shows that two odd numbers can have an even sum.
  7. It means 1 hundred made by grouping 10 tens · Ten tens have the same value as one hundred. Regrouping 12 tens gives one hundred and two tens.
  8. False · Both methods use the same copied number. They find 35 + 44 = 79, but the question asks for 35 + 24 = 59.
  9. Putting 7 in the tens column · The number 7 means 7 ones. Putting it in the tens column treats it as 70. It belongs under the 8, and 68 + 7 = 75.
  10. 510 · 232 + 278 = 510. Adding back should give 506, so the check shows that the stated subtraction answer needs fixing.
Worksheet · LightMySky