Checking if a maths argument makes sense

Mathematics · Mathematical Thinking · ages 7-8

Name ______________________ Date ____________

Work out 246 + 135 using columnar addition. What is the total?
Answer: ______________
Why does columnar addition start with the ones column?
- So that any regrouping moves left into the tens
- Because the ones are the biggest digits
- Because hundreds can never be added
- Because the answer is always even
In columnar addition, the ones add up to more than 9. What should you do?
- Carry the extra ten into the tens column
- Ignore the extra amount and move on
- Write both digits in the ones column
If two numbers are both even, adding them always gives an even number.
Circle one: True False
Add two even numbers: what is 24 + 36?
Answer: ______________
Which pair of numbers proves that adding two odd numbers can give an even number?
- 3 and 5
- 3 and 4
- 2 and 4
A pupil works out 467 + 258 = 615, saying no regrouping is needed. Which total is correct?
- 615
- 625
- 725
- 6150
Tom says columnar addition works because each column adds ones with ones and tens with tens. Is Tom right?
Circle one: True False
Ravi says 68 + 27 = 815. He added the ones as 8 + 7 = 15 and the tens as 6 + 2 = 8. What exactly went wrong in his reasoning?
- He should have added the tens column first, not the ones
- He never carried the ten hidden inside 15 into the tens column
- He should have added 68 and 27 as one long number
A pupil writes 506 - 278 = 232. To check, work out 232 + 278. What do you get?
Answer: ______________

Answer key

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

381 · Ones 6 + 5 = 11, tens 4 + 3 + 1 = 8, hundreds 2 + 1 = 3, so 381.
So that any regrouping moves left into the tens · Regrouped tens move left, so you must finish the ones first.
Carry the extra ten into the tens column · Ten ones make a ten, so that ten needs to move into the tens column, or the total will be too small.
True · Even numbers split into pairs with nothing left over. Joining two even amounts still leaves nothing left over, so the sum is even.
60 · 24 + 36 = 60, and 60 is even, as the sum of two evens always is.
3 and 5 · 3 and 5 are both odd, and 3 + 5 = 8, which is even. This one example supports the idea.
725 · Both the ones and tens regroup, giving 725.
True · Tom is right. Matching place values column by column is exactly why the method gives the correct answer.
He never carried the ten hidden inside 15 into the tens column · 15 contains a ten. That ten has to join the tens column before adding 6 + 2, or the tens total is missing a whole ten.
510 · 232 + 278 = 510, not 506, so the subtraction answer 232 was wrong.