Separating Parts with Objects Up to 10

When we separate parts, we take one group of objects and split it into two smaller groups. If a child has 7 blocks, those 7 blocks can be pushed apart into a group of 3 and a group of 4, or a group of 5 and a group of 2, or several other combinations. Every way of splitting still uses all 7 blocks, just arranged into two different piles.

This idea is the mirror image of combining together with objects up to 10, where two small groups are pushed together to make one bigger group. Separating starts with the whole and pulls it apart, while combining starts with the parts and pushes them together. Learning both directions helps children see numbers as flexible, not fixed.

Being able to separate a set into parts is one of the earliest building blocks of subtraction. Before children ever write \( 7 - 3 = 4 \), they need hands-on experience physically pulling a group apart and seeing what is left. Separating also shows that the same total, like \( 6 \), can be broken into more than one pair of parts: \( 1 + 5 \), \( 2 + 4 \), or \( 3 + 3 \). Noticing all these possibilities is the heart of decomposing numbers.

The most reliable way to separate parts is with real, touchable objects such as counters, buttons, or small toys.

1. Count out the whole group of objects, for example 8 counters, and say the total out loud.
2. Slide some of the counters away from the rest to form two separate piles.
3. Count each pile on its own: "This pile has 5, this pile has 3."
4. Check that the two counts still make the original total by counting all the objects again.

Doing this several times with the same starting number, but sliding a different amount away each time, shows that one number has many possible pairs of parts.

A simple picture called a part-part-whole diagram helps children see the relationship between the whole group and its two separated parts. The whole sits on top, and the two parts sit underneath it.

Notice that the two parts, 3 and 4, still combine to make the same whole, 7. Saying it as \( 3 + 4 = 7 \) connects the picture directly to a number sentence, which students explore further in writing an addition statement up to 10.

A great practice activity is to take one number, such as 6, and find every possible way to separate it into two parts using objects.

• \( 6 = 1 + 5 \)
• \( 6 = 2 + 4 \)
• \( 6 = 3 + 3 \)
• \( 6 = 4 + 2 \)
• \( 6 = 5 + 1 \)

Lining up the counters for each pair side by side lets children physically see that as one part grows, the other part shrinks, but the total never changes. This is exactly the kind of flexible thinking that later shows up in solving addition word problems up to 10, where knowing a number's parts helps figure out a missing amount.

Suppose a child has 9 crayons and wants to separate them into two groups to share with a friend.

Step 1: Count all 9 crayons and place them in one pile.

Step 2: Move some crayons into a second pile, for example moving 4 crayons away.

Step 3: Count each pile: the first pile has 5 crayons, the second pile has 4 crayons.

Step 4: Check the parts against the whole: \( 5 + 4 = 9 \), so the separation is correct.

If the child instead moved 6 crayons into the second pile, the parts would be 3 and 6, and checking again gives \( 3 + 6 = 9 \). Both separations are valid ways to break apart the same total of 9.

Use small everyday items like snacks, buttons, or toy cars so the activity feels playful rather than like a worksheet. Ask questions such as "If we split these into two groups, how many could go in each group?" and let the child try more than one answer. Always finish by counting the parts together to confirm they still add back up to the original whole.

Related lessons

• Kindergarten