Why splitting numbers works

Mathematics · Addition & Subtraction · ages 7-8

Name ______________________ Date ____________

Splitting 45 into 40 + 5 changes its value.
Circle one: True False
Jada splits 54 + 35 into tens and ones. She adds 50 + 30, then 4 + 5. What total does she get when she puts the parts back together?
Answer: ______________
In 45 + 32, why do we write a 7 in the ones place of the answer?
- Because 5 ones plus 2 ones is 7 ones
- Because 4 plus 3 is 7
- Because 7 is the biggest digit we can use
When you split 67 + 24 into 60 + 20 and 7 + 4, why does this still give the right answer?
- Because 67 and 24 are made of tens and ones, and each part can be added separately
- Because splitting numbers makes them smaller so there is less work
- Because addition only works with round numbers
Ben adds 56 + 38 by doing 56 + 40, then subtracting 2. He says his answer is still correct because he only fixed the extra he added.
Circle one: True False
Tom works out 82 minus 19. He says: '82 minus 20 is 62, then I add 1 back because I took away one too many.' Why does he add 1 back?
- Because he subtracted 20 instead of 19, which is 1 too many
- Because 62 is too small a number to be correct
- Because you must always add 1 at the end of a subtraction
Mia adds 48 + 29 the clever way. She knows 29 is 1 less than 30, so she does 48 + 30, then takes 1 away. What is the answer?
Answer: ______________
In the written method for 38 + 47, 8 + 7 = 15. Why do you write a 1 in the tens column instead of the ones column?
- Because the tens column is always left empty
- Because you can put any digit in any column
- Because 15 ones is the same as 1 ten and 5 ones, and only whole tens belong in the tens column
You are making two two-digit numbers that add to 75, and you can use each digit only once. Which pair works?
- 30 and 45
- 38 and 37
- 40 and 35
Mia says: 'For 56 + 27, I can split it into 50 + 20 and 6 + 7, but it doesn't matter how I split it because addition always works.' What is wrong with her thinking?
- Nothing, she is completely right
- Splitting only works because each part matches a place value, tens with tens and ones with ones; it is not just luck
- She should have split it into 5 + 6 and 20 + 70 instead

Answer key

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

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False · 40 + 5 is just another way of writing 45. The value never changes, only how it is written.
89 · 50 + 30 = 80 and 4 + 5 = 9. Putting the parts back together gives 80 + 9 = 89.
Because 5 ones plus 2 ones is 7 ones · In the written method, each column talks about one place. The ones column says 5 ones plus 2 ones, which is 7 ones, so a 7 goes in the ones place.
Because 67 and 24 are made of tens and ones, and each part can be added separately · 60 and 20 are both tens, and 7 and 4 are both ones. Adding tens with tens and ones with ones keeps the total correct.
True · True. 40 is 2 more than 38, so he added 2 too many. Subtracting 2 puts the total back to exactly 56 + 38.
Because he subtracted 20 instead of 19, which is 1 too many · 20 is 1 more than 19, so subtracting 20 removes 1 too many. Adding that 1 back fixes the total.
77 · Adding 30 instead of 29 means she added 1 too many, so she subtracts 1 to fix it. 48 + 30 = 78, and 78 - 1 = 77.
Because 15 ones is the same as 1 ten and 5 ones, and only whole tens belong in the tens column · 15 ones regroups into 1 ten and 5 ones, so the extra ten moves into the tens column, matching place value.
30 and 45 · 30 + 45 = 75, and the digits 3, 0, 4, 5 are all different. The other pairs repeat a digit or do not add to 75.
Splitting only works because each part matches a place value, tens with tens and ones with ones; it is not just luck · If the split mixed tens and ones together, the total would come out wrong. Splitting works because place value is kept matched.