Sharing and Partition up to 10

Sharing and partition is the idea of taking a total number of objects, up to 10, and splitting them equally among a set number of groups or people. Instead of counting how many groups of a certain size fit into a total, sharing starts with the number of groups you already know and asks how many objects each group gets.

For example, if you have 10 stickers and 2 friends, sharing and partition asks: if I hand out the stickers one at a time so both friends end up with the same amount, how many stickers does each friend get?

The easiest way to share a small set of objects, up to 10, is to hand them out one by one, going around each group in turn, until every object is gone. Since each object is given out fairly in order, every group ends up with the same amount at the end.

Sharing and partition is closely related to another way of splitting numbers up to 10 called grouping, covered in Grouping numbers up to 10. The difference is what you already know before you start:

• In sharing, you know the number of groups, and you are looking for how many objects go in each group.
• In grouping, you know the size of each group, and you are looking for how many groups you can make.

Both ideas describe the same total and lead to the same division fact, but they picture the problem in opposite ways. Once a total of up to 10 has been shared into equal groups, that result can be written as a division sentence, which is explored further in Dividing with digits up to 10.

Every equal sharing situation can be written using a division sentence. If 10 objects are shared equally among 2 groups, and each group ends up with 5 objects, this is written as \( 10 \div 2 = 5 \).

The parts of this sentence match the sharing story directly:

• 10 is the total number of objects being shared.
• 2 is the number of groups (or people) sharing the objects.
• 5 is how many objects each group receives.

Suppose there are 8 apples to share equally among 4 baskets. Hand out the apples one at a time, going around each basket in turn:

1. Give 1 apple to each of the 4 baskets. That uses up 4 apples, leaving 4 apples.
2. Give 1 more apple to each of the 4 baskets. That uses up the remaining 4 apples.
3. Every basket now holds 2 apples, and there are no apples left over.

This can be written as \( 8 \div 4 = 2 \), meaning 8 apples shared equally among 4 baskets gives 2 apples per basket.

Now share 9 marbles equally among 3 friends. Handing out one marble at a time to each friend for 3 full rounds uses all 9 marbles, with each friend receiving 3 marbles: \( 9 \div 3 = 3 \).

Not every set of up to 10 shares out so neatly. If 10 marbles were shared among 3 friends instead, each friend would get 3 marbles with 1 marble left over, since \( 3 \times 3 = 9 \) and one marble cannot be split evenly. Situations like this, where objects are left over after sharing, are studied in Remainders from division up to 10.

To check that a set has been shared correctly, multiply the number of groups by the amount each group received. The result should match the original total. For \( 8 \div 4 = 2 \), checking gives \( 4 \times 2 = 8 \), which matches the starting number of apples, confirming the sharing was done correctly.

Sharing equally is one of the earliest ways young learners meet division, long before they see the symbol \( \div \) written down. Practicing sharing and partition with totals up to 10 builds the everyday sense that division means splitting something fairly. These skills carry directly into solving real situations, such as those found in Division word problems up to 10, where sharing stories are described in words rather than pictures.

Related lessons

• Math 1