Combining Together with Objects Up to 10

Combining objects together means taking two separate small groups and pushing them into one single group, then counting how many objects are in that new, bigger group. This is one of the very first ideas behind addition, and in kindergarten it is done entirely with real or pictured objects, no plus signs or number sentences required yet. The total number of objects always stays at 10 or fewer, so every combination stays easy to count on fingers or with counters.

Think of it like this: if there is a group of buttons and another group of buttons sitting nearby, combining them just means sliding all the buttons into one pile. Once they are one pile, the only job left is to count them all, one by one, starting from one.

Before a child can understand what \( 3 + 4 = 7 \) means, they need to physically experience what happens when 3 things and 4 things become one group. Combining objects together builds that understanding through touch and sight instead of symbols. Once a student is confident joining groups and counting the total, they are ready to move on to writing an addition statement up to 10, where the same action gets its own number sentence.

Follow the same three steps every time:

1. Look at the first group and count how many objects are in it.
2. Look at the second group and count how many objects are in it.
3. Push both groups together into one group, then count every object in the new group starting from one.

The picture below shows a group of 3 dots and a group of 4 dots being combined into one group of 7 dots.

Counting the bottom row one object at a time gives 1, 2, 3, 4, 5, 6, 7. Since the two starting groups had 3 and 4 objects, the combined total is 7 objects, and this can later be written as \( 3 + 4 = 7 \).

Suppose there are 5 red counters on one side of a table and 2 blue counters on the other side. To combine them, slide the 2 blue counters over so they sit next to the 5 red counters, forming one group of 7 counters. Counting the whole group from 1 to 7 confirms the total. Since 5 plus 2 objects never goes past 10, this combination fits comfortably within the up-to-10 range used at this stage.

Fingers work the same way as counters. Hold up 6 fingers on one hand pattern and 3 fingers on another, then count every raised finger together, starting from one, all the way to 9. This shows that combining a group of 6 with a group of 3 gives a group of 9.

Every combining task in this lesson is built so the joined group never has more than 10 objects. That means the two starting groups will always be small enough to add together and land on a number from 1 through 10. If counting the combined group ever passes 10, it is a good sign to recount each starting group separately, since a mistake in counting is more likely than a total that goes beyond the range being practiced.

Once combining objects feels natural, the next step is connecting that action to numbers and symbols. Practicing with addition statements with images helps bridge the picture of two combined groups to the matching number sentence, and addition word problems up to 10 shows how this same combining action shows up in everyday stories, like putting together toys or snacks. Every one of these skills starts with the same simple action practiced here: push two groups together, then count the whole thing.

Related lessons

• Kindergarten