You know that 8 + 3 = 11. Without doing any new calculation, what does the commutative property immediately tell you?
A3 + 8 = 11
B8 − 3 = 5
C11 − 8 = 3
D3 + 3 = 6
The commutative property says switching the order of addends never changes the sum: 8 + 3 and 3 + 8 are the same fact. Subtraction facts like 8 − 3 are separate and are NOT given to you for free — subtraction is not commutative.
Question 2 Multiple Choice
A student says: 'I know 4 + 7 = 11, but I still need to separately memorize 7 + 4 as a different fact.' What is wrong with this thinking?
AThe commutative property guarantees both expressions have the same sum, so knowing one gives you the other for free
BActually, 4 + 7 and 7 + 4 can give different answers depending on which number you count on from
CThe student is correct — they are different problems that require separate memory
DYou only need to memorize 7 + 4, not 4 + 7, because you should always start with the larger number
The commutative property means switching the order of addends never changes the sum. 4 + 7 and 7 + 4 are not two separate facts — they are one fact viewed from two directions. Knowing either one gives you the other automatically, which is why the property cuts memorization roughly in half.
Question 3 True / False
The commutative property of addition means that 9 + 6 has the same sum as 6 + 9.
TTrue
FFalse
Answer: True
Yes — this is exactly what the commutative property states. No matter which order you add the two numbers, the total is the same (15). The blocks don't change; only the direction you count them changes.
Question 4 True / False
Because of the commutative property, you primarily need to memorize half as many addition facts AND half as many subtraction facts.
TTrue
FFalse
Answer: False
The commutative property applies to addition, not subtraction. 9 − 3 = 6, but 3 − 9 is a different (negative) result — you cannot simply flip a subtraction problem. So the memorization shortcut applies only to addition facts, not subtraction facts.
Question 5 Short Answer
Why does the commutative property cut the number of addition facts you need to memorize roughly in half?
Think about your answer, then reveal below.
Model answer: Because every addition fact has a 'partner' fact with the same two numbers in the other order and the same sum. If you know 6 + 7 = 13, you automatically know 7 + 6 = 13 — you do not need to memorize them separately.
The commutative property means the sum depends only on which two numbers you add, not the order. Every pair of different addends (like 6 and 7) produces two equations (6+7 and 7+6) that share the same answer, so learning one teaches you both.