Using structure to calculate efficiently

Mathematics · Mathematical Thinking · ages 6-7

Name ______________________ Date ____________

Why is 9 plus 3 the same as 3 plus 9?
- 9 is odd
- 3 is small
- plus means take away
- order does not change total
Reorder 3 plus 9 as 9 plus 3. What is the total?
Answer: ______________
Which is the smart way for 4 plus 8?
- count all from 1
- guess
- start at 8, count on 4
- start at 4, count on 8
What is 34 + 10?
- 35
- 44
- 24
Which shape shares a square's pattern of having 4 sides and 4 right angles?
- Rectangle
- Triangle
- Circle
Use place value: 58 plus 10?
Answer: ______________
What is 26 take away 10?
Answer: ______________
What is 35 plus 20?
Answer: ______________
Zara says 29 + 10 = 39 because only the tens digit changes. Ben says 29 + 10 = 20 because you just add a zero. Who is right?
- Ben
- Zara
- Both
Ken is adding 7 + 15. He flips it to 15 + 7. Why does this still give the correct answer?
- Because 15 is even
- Because you always start with the smallest number
- Because addition gives the same answer in any order

Answer key

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

order does not change total · Commutative rule keeps total same.
12 · 9 plus 3 is 12.
start at 8, count on 4 · Start at larger number.
44 · Adding 10 only changes the tens digit. 3 tens becomes 4 tens, so 34 becomes 44.
Rectangle · A rectangle has 4 sides and 4 right angles too, just like a square.
68 · Tens 5 becomes 6.
16 · Tens drop 2 to 1.
55 · Tens add: 30 plus 20 is 50, plus 5 is 55.
Zara · 29 + 10 = 39. Only the tens digit changes, from 2 tens to 3 tens. The 9 ones stay the same.
Because addition gives the same answer in any order · Addition gives the same answer no matter which order you add in, so flipping the numbers never changes the sum.