Sorting and Grouping Objects

What you will learn

• Sort objects into groups using a rule.
• Check that every object is in one group and only one.
• Count each group and compare groups to answer questions.

Before you start: you should be able to count and add within $20$. See Adding Within 20 if you need to.

The idea

A toy box in a mess is hard to use. Sort the toys into cars, dolls and blocks, and you can find things at once. Sorting also lets you answer questions such as “are there more cars or more dolls?” That is the start of data: information that you collect and organise so that it can answer questions.

Choosing a rule

To sort, you need a rule that says which group each thing goes in. The rule can be about colour, shape, size, what it is made of, or what it does.

Good rules are clear. “Red or not red” is clear, because you can tell for every object. “Nice or not nice” is not clear, because people disagree.

One object, one group

A good sort has no object left out and none in two groups. If you sort buttons by colour, a button that is red and blue does not fit well. Choose a clearer rule, such as the colour you see most, and say so.

The same objects can be sorted in different ways. Shapes can be sorted by number of sides, or by colour, or by size. Each rule gives different groups.

Counting and comparing groups

Once sorted, count each group. Then you can compare. Which group has the most? Which has the least? How many more are in one group than another? To find how many more, subtract the smaller from the larger.

To find the total, add the groups together. If the groups add up to the number you started with, you did not miss or double-count anything.

Worked examples

Example 1: Sort and count

A tray holds: red, blue, red, green, blue, red, blue, red. Sort by colour and count each group.

1. Red: there are $4$.
2. Blue: there are $3$.
3. Green: there is $1$.
4. Check the total: $4 + 3 + 1 = 8$, and there were $8$ objects.

Answer: $4$ red, $3$ blue, $1$ green.

Example 2: How many more?

A class votes for a snack: $8$ choose fruit and $5$ choose crackers. How many more chose fruit?

1. Compare the groups: $8$ and $5$.
2. Subtract: $8 - 5 = 3$.

Answer: $3$ more children chose fruit.

Example 3: Find the missing group

There are $14$ marbles in a bag, some small and some big. $9$ are small. How many are big?

1. The small and big groups together make $14$.
2. Subtract the small group: $14 - 9 = 5$.
3. Check: $9 + 5 = 14$.

Answer: $5$ big marbles.

Make sure the groups have no overlap. If an object can be in two groups, the total of the groups may be bigger than the real number of objects.

Why it matters

Shops sort goods on shelves, libraries sort books by type and doctors sort patients by need. Every chart and graph starts with sorted data, so this lesson is the first step towards reading and drawing them. See Charts and Graphs for what comes next.