Addition in any order
Understand and apply the commutative property of addition: addends can be added in any order
What a learner can do afterwards
- Explain that 3 + 8 gives the same answer as 8 + 3
- Use commutativity to choose the larger number to count on from
- Demonstrate that subtraction is not commutative (5 − 3 ≠ 3 − 5)
1 · Read
You already know how to put two groups together to add. It does not matter which number you say first. 3 + 8 and 8 + 3 both give the same answer, 11.
Mia picks 4 red apples and 5 green apples. She counts the red ones first: 4 + 5 = 9 apples. Next time she counts the green ones first: 5 + 4 = 9 apples. Same total, either way.
When you count on, start from the bigger number. It is faster. For 3 + 8, start at 8 and count on: 9, 10, 11.
Addition can flip, but subtraction cannot. 5 - 3 is not the same as 3 - 5. Order only stays free for addition.
Add numbers in any order and the answer stays the same, but subtraction always keeps its order.
More to read
Properties of addition
When you add numbers, there are some handy rules to know.
The first rule is the order rule. You can add numbers in any order and the answer stays the same. 4 + 2 is 6, and 2 + 4 is 6 too. Swapping never changes the total. This helps you pick the easy way: start with the bigger number and count on the smaller one.
The second rule is the grouping rule. When you add three numbers, you can add any two first. For 2 + 3 + 4, you can do 2 + 3 first, or 3 + 4 first. You get 9 either way.
The third rule is the zero rule. Adding 0 to any number changes nothing. 0 + 4 is just 4.
Visualizing the Commutative Property of Addition
This is a picture tool you can play with. It shows two groups of things being added, like 3 dots and 8 dots. Then it swaps the order and shows 8 dots and 3 dots. You can see with your own eyes that the total pile is the same size both times. Play with it to see that adding in any order always gives the same answer.
2 · Watch
به انگلیسیTake it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.