AC9MFN06 · FOUNDATION · NUMBER

Sharing and Grouping

Share things out fairly and make equal groups — the everyday roots of division.

Children meet fairness early and feel it strongly. Hand a bag of biscuits to a group of friends and the first thing they want to know is whether everyone got the same. This unit takes that strong sense of fairness and turns it into mathematics: the idea of splitting a whole into equal parts. It is the everyday beginning of division, long before that word or its symbol appears.

There are two ways to make equal parts, and both matter. The first is sharing. You have a number of things and a number of people, and you deal them out one at a time — one for you, one for you, one for me — going round until they are gone. When the dealing is done, each person has the same amount, and that amount is the answer. Sharing twelve biscuits between three plates gives four on each plate.

The second way is grouping. Here you know how big each group should be, and you ask how many groups you can make. Take twelve pencils and bundle them into groups of four: you get three bundles. The question has flipped — in sharing you knew the number of groups and found how many in each; in grouping you know how many in each and find the number of groups. Both are ways of splitting the same twelve into equal parts.

The word that holds this unit together is equal. Sharing is only sharing if the parts are the same; three biscuits on one plate and five on another is not a fair share, it is just a split. Children need to see and say the difference — to look at two plates and judge whether they match. This habit of checking for equal parts is what separates true sharing from simply dividing things up any old way.

Sometimes things do not share out evenly, and that is worth meeting gently too. Share seven lollies between two bags and each bag gets three, with one left over. The leftover is not a mistake; it is simply what happens when a number cannot be split into equal parts of that size. Noticing the leftover — and that it is smaller than a full share — is an early, intuitive taste of what later becomes the remainder in division.

As with adding, children find the answers here by doing and then counting or subitising — dealing the counters out and counting what landed on each plate, or making the bundles and counting the bundles. They do not need the division symbol or a memorised fact. They need to act the situation out with real things and trust what they see. The understanding comes first; the notation comes much later.

None of this needs a worksheet to begin. Dealing out cards, splitting a snack between friends, or packing things into equal boxes all build the same sense. The five visualisations below let a child do exactly this on the screen: share biscuits fairly, make equal groups, judge whether a share is fair, see the two ways of splitting side by side, and pack party bags with a few left over. Each one returns to the same idea — equal parts, shared or grouped.

See it five ways

Check understanding