Grouping numbers to add
Understand and apply the associative property of addition: when adding three numbers, any two can be added first
What a learner can do afterwards
- Solve 2 + 6 + 4 by first adding 6 + 4 = 10, then 2 + 10 = 12
- Explain that grouping addends differently gives the same total
- Choose which two numbers to add first to make the calculation easier
1 · Read
You already know you can add two numbers in any order. Grouping works in a similar way. When you add three numbers, you can add any two of them first, then add the third one. The total stays the same either way.
Ben adds 3 + 7 + 6. He notices that 3 and 7 make 10, an easy number. So he groups those first: 3 + 7 = 10. Then he adds 10 + 6 = 16. Grouping the numbers a different way did not change the answer.
Look for two numbers that make a friendly number like 10. Add those first, then add the last number. The total never changes, no matter which pair you pick first.
You can add any two numbers first when adding three of them, and the total always stays the same.
More to read
Properties of addition
Numbers like to team up in smart ways. Here are three helpful rules about adding.
Changing the order. You can swap two numbers when you add and the total stays the same. 4 + 2 is 6, and 2 + 4 is also 6.
Changing the grouping. When you add three numbers, you can pick which two to add first. The total never changes. (2 + 3) + 4 means add 2 and 3 first, then add 4. That is 9. And 2 + (3 + 4) means add 3 and 4 first, then add 2. That is also 9. Same numbers, same total.
This trick helps you add faster. If you see 7 + 8 + 2, look for a pair that makes 10. The 8 and the 2 make 10, so add those first. Then 7 + 10 is easy. It is 17.
Adding zero. When you add 0 to a number, nothing changes. 0 + 4 is just 4.
Try it yourself. Add 3 + 6 + 4. Can you find the pair that makes 10? Add that pair first and see how quick the rest feels.
Commutative and Associative Properties
There are two handy rules that make adding easier.
Swap rule. You can switch the order of two numbers you are adding and the answer stays the same. 5 + 3 is 8, and 3 + 5 is 8 too.
Group rule. When three numbers are being added, you can choose which two to add first. The answer stays the same. Write it like this: (a + b) + c = a + (b + c). The little letters stand for any numbers you like.
Why does this matter? Because some pairs are easier to add. If a pair makes 10, grab it first. Then the last step is simple.
Example. Try 6 + 7 + 3. The 7 and the 3 make 10. Add them first: 7 + 3 = 10. Then 6 + 10 = 16. Done, and it felt easy.
2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 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.