Sorting and Classifying

You may observe children sorting toys and natural objects while they are playing. Adults love to sort too, and often do so on a daily basis! Sorting is a universal strategy for creating order; it is purposeful and can feel very satisfying. Children may sort their toys by colour, or by the ones they love and don't love anymore. They may sort this same group of objects differently on different days depending on the attribute they choose. This is a great opportunity to ask them about it, and to put our mathematical lenses on!

Same and different

Look closely at these Lego figurines.

How are they the same? How are they different?

We can see:

Six of them have hats.
Four of them have light blue pants.
They have white, yellow, brown, blue or grey hands.
Two of them have a beard.
Two are wearing the same clothes but have different emotions on their face.

You may have noticed many attributes that we haven't.

The bolded questions above can be used for any comparison activity or conversation. We want to build on children's natural desire to sort, prompting them to look for different attributes in the same group of items. These might be toys but could just as easily be natural materials, animals, clothing, themselves - anything they have an interest in. These comparisons require children to focus in on different attributes and features. This leads well into sorting and classifying.

Sorting then classifying

Sorting is the action. When you sort objects or ideas you put them together.

Classifying tells us the big overarching idea or concept. It could be considered the sorting rule. Classification can be tricky at first. A helpful prompt is being able to finish this sentence:

I have sorted them by...

We could sort the cars in this picture into groups of yellow, white, blue, pink purple, black, green and grey. The classification is colour.

If we sorted them into cars with 4 seats and 2 seats, then the classification would be number of seats.

There are many other attributes we could sort these cars by - which would you choose, and how would you classify this sorting?

Questioning prompts

girl wearing white blouse and blue jeans

Sorting and classifying is an open-ended task. This means there are many possibilities, not one right answer. Sorting items into groups then labelling that process promotes logical, creative and flexible thinking as children must ask themselves questions that start with how, why, and what if?

For example:

How can I sort these into groups so everything has something that is the same about it?
Why do these ones go together?
Why don't these ones fit in this group?
What if I put this one in the group?
What if I change the sorting rule.

We help build on these problem solving and reasoning processes when asking children to explain their sorting, justify why certain items are with each other, and how they made these decisions. We could probe with:

Tell me about your sorting
What is the same about all of the items in this group?
Can you sort them in a different way?

Focusing in on the mathematics

Asking children to sort the same items in many ways and tell you about that sorting will prompt them to look more closely at the items' attributes and features. But these sorting and classifying experiences may not have a mathematical focus. This is where we can become intentional, consider other ways they may be sorted and the mathematical language we would be looking for.

Given a pile of blocks like those in this picture, children will often sort by colour. This is our opportunity to put on our mathematical lenses and consider the potential for infusing language associated with 3D objects into the conversation. Prompted to sort again, children may notice: pointy bits (vertices), objects that roll (curved surfaces, or cylinders), flat parts (faces), boxes (prisms).

Children may notice or be interested in the 2D shapes on the faces of these 3D objects like triangles, rectangles, circles, and squares. Combining 2D and 3D, we start to introduce adjectives like triangular, rectangular, circular.

Infusing a multimodal approach by exploring how the objects look, feel, and are described by mathematicians, we are aiming to deepen children's conceptual understanding of 3D objects. Asking them to record their sorting adds to this multimodality.

assorted-color shape toy lot_edited_edit

Sorting or ordering?

While sorting, children may attend to an object's length, sorting by long ones and short ones, or tall ones and short ones. While this is an important feature to notice, sorting by length (height) has to have a comparison to help classify it. Prompting children's description with a comparative and the associated language i.e 'longer than' and 'shorter than' will help promote this sorting into one that can be classified, i.e. longer (or taller) than my finger.

Ordering items, like from from shortest to longest, is not sorting and classifying. Sorting requires children to put things in groups that have something that is the same about them.

Collaborating to promote hypothesising

A nice prompt when children are sorting and classifying the same objects many times is to ask children to choose and present their favourite sorting. Children can then visit the work of others and see if they can work out how they have sorted. This further promotes the mathematical processes of problem solving and collaboration as children verbalise their thoughts about how items are grouped and hypothesise about whether their first thoughts fit the rule. It is also a great opportunity to use and refine mathematical language as children describe what they see. The 'owner' of the sorting becomes the expert as others ask "are they sorted by...?"

Repeating patterns

Sorting and classifying is also a great precursor to generating repeating patterns as the elements that repeat are already clustered together, ready to place in the pattern. For example, a child might have sorted 2D shapes into two groups:

with vertices (corners)
without vertices (corners).

They could then choose one from each of these groups repeatedly to make a 2-part pattern:

Planning with Intentionality

As mentioned, sorting and classifying is a natural activity that builds on children's ability to match things that are the same, and identify when they are different. They may see this kind of organisation often as physical materials are often sorted and packed away in early childhood, home and school settings to make them easy to find and use. We may even classify and refer to some of these as building corner items, and/or counting materials.

We can build on children's interests as well as planning experiences that intentionally focus on mathematical concepts and language. For example, we might ask everyone to get a 3D object they can find in the room. Having one ready ourselves, and wanting to prompt some comparative language, we would ask:

How is your __ the same as mine?
How is it different?

As children respond, we would reinforce and record the mathematical language they are using. These prompts could then be used to stimulate further collaborative and/or scaffolded sorting and classifying activities.

"Which one of these is not like the others?" is a well known song on Australia's ABC Playschool program. This question playfully promotes comparing and contrasting, and the opportunity to sort and classify with a mathematical feature in mind.

Choosing objects or items that assist a focus on particular mathematical features and attributes will promote development of conceptual understanding. The open-endedness of sorting and classifying means such experiences can go beyond blocks to numbers, fractions, money, patterns, graphs etc.

Pulling it all together

You could try sorting and classifying children's names at the beginning of the year as they get to know each other. There will be many ways to sort these names - by the same first letter or ones with an S in them. If we put our mathematical lenses on, they could also be sorted into groups of names that have the same number of letters, same number of syllables (clap to find these out), or double letters etc.

We could then graph our data on a picture graph to show how many children have names with 3 letters, 4 letters, 5 letters etc. Noticing and wondering about these data would be fascinating!

Reading a picture book or hearing first hand stories about how children got their names would be an interesting cultural connection to the data generated.