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Operations & Algebraic Thinking

Understanding Addition

Addition as putting together and adding to.

Foundational15 min lesson2 min readUpdated August 12, 2026Author not yet attributed

Putting Groups Together

You already know how to count a group of objects. Addition is what happens when you start with one group and put more objects with it. Once the groups are together, you count them all as one bigger group.

Definition — Addition

Joining two or more groups together to find the total number of objects. The answer to an addition problem is called the sum.

There are two ways to think about addition. 'Putting together' means you start with two separate groups, like 3 red blocks and 4 blue blocks, and combine them into one group. 'Adding to' means you start with one group and more objects join it, like 3 birds on a branch and 4 more birds landing.

Worked Example — Putting Together

There are 3 red blocks and 4 blue blocks on the table. How many blocks in all? Count the red blocks: 1, 2, 3. Count the blue blocks: 1, 2, 3, 4. Put the groups together and count everything: 1, 2, 3, 4, 5, 6, 7. There are 7 blocks in all, so 3 + 4 = 7.

Worked Example — Adding To

3 birds are sitting on a branch. 4 more birds land on the same branch. How many birds are on the branch now? Start at 3, the number already there, and count on 4 more: 4, 5, 6, 7. There are 7 birds on the branch, so 3 + 4 = 7.

Tip

Counting on from the bigger number is faster than counting both groups from the start. For 3 + 4, start at 4 and count on 3 more: 5, 6, 7.

Common Mistakes

  • Recounting the whole group from 1 every time, even when counting on from the larger number would be faster.

    Start at the bigger number and count on by the smaller number. For 2 + 5, start at 5 and count on 2 more: 6, 7.

  • Losing track of how many were counted on, and stopping too early or too late.

    Use fingers or a number line to keep track of each count while counting on, one finger per number said.

Key Takeaways

  • Addition joins groups together to find how many there are in all.
  • The answer to an addition problem is called the sum.
  • Counting on from the larger group is a fast way to add.

Summary

Addition combines groups into one bigger group. The next lesson looks at the opposite move — taking a group apart — which is called subtraction.

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