A thinking mathematically targeted teaching opportunity focussed on sorting and categorising objects
Syllabus outcomes and content descriptors from Mathematics K-10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2021
You will need:
- a collection of about 20 things to sort
- colour pencils or markers
- something to write on.
Watch Sorting 1 video (6:24) to learn about sorting collections.
Hello there, mathematicians.
We were tidying up at home and look at this box of things; it's quite a mess.
[Screens shows a box with varied items in it.]
I was wondering how could we sort it out? What are the different things that you can see in there?
Ah, I can hear you. Some of you were saying I can see some pencils.
[Presenter removes 6 pencils from the box and puts them down to the left of the box. There are 3 pink, 2 yellow and one green pencil. The presenter then places a sticky note under the pencils with writing displaying, “pencils”.]
I can put the pencils over here. What else can you see?
Oh, you can see some cars. Some of them are really fun cars, so I have some cars that I can put over here.
[Presenter removes 3 toy cars from the box and places to the left-hand side of the pencils in a vertical row and places a sticky note underneath them with writing displaying, “cars”.]
What else can you see in my box? Oh, you can see some animals.
Yeah, I can see some animals too; some cows, 2 sheep, one cow, a pig, and some little baby piglets. So, we could see some animals.
[Presenter removes animals from box: 2 sheep, one cow and a pig with 3 piglets, these are placed next to the pencils on the left-hand and then places a sticky note under animals with writing displaying, “animals”.]
And what else can you see in my box here? Oh! Some counters, yeah, I'm going to tip those out. Here I have all of these different counters.
[Presenter picks up box and tips remaining items which are just counters out and places them on the desk to the right of the animals and places a sticky note under the counters with writing displaying, “counters”.]
And if I have a look at them, look over here, I have three cars 1, 2, 3.
[Presenter points to the cars, touching each one with her finger.]
I have some pencils. Will you count them with me? Excellent. 1, 2, 3, 4, 5, 6 pencils.
[Presenter then points to the pencils and rolls them individually counting them.]
How many animals can you see?
[Presenter circles animals with her finger.]
And over here we have some counters. Can you see how many there are?
[Presenting points to counters with a circular motion with finger.]
Should we count them together? Let's try. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, counters.
[Presenter uses index fingers to move counters to the left as she counts them out.]
I wonder now if I just take my pencils, move away my counters and move away my animals, and move away my cars.
[Presenter moves the counters, animals and cars to the far right-hand side out of view.]
Now I just have my pencils. I'm going to think about sorting them, so I might put these ones together. And these ones together. And this one over here by itself.
[Presenter now moves pencils into the centre scatters them with her hand and places the 2 yellow pencils to the left the 3 pink pencils in the middle and the one green pencil on the right in a row.]
Can you think about why they've been grouped together like that?
Yeah, that's what I was thinking too, so I had the things the pencils that are the same colour and when we get things and we sort them out together, we call them a set.
[Presenter points to each of the coloured pencils with her index finger, she then sweeps the pencils away to the top out of view.]
But over here, I have a set of really cool rocks that we found the other day when we went out for a walk.
[Presenter picks up a plate with assorted rocks on it and moves it into the middle of the screen.]
Some of them are really big, some of them small little pebbles, and some of them are dark grey, and this one is, like a caramel colour, and some of them are white. But here I have a set of rocks.
[Presenter picks up pebbles describing colours sizes and places them back on the white plate. She then picks up the rocks and moves them out of view.]
And what about here? I found these when we were washing up, a set of spoons! Yeah! or things that you could eat delicious ice cream with.
[Presenter places down a bowl with several different types of spoons in it, picking up one spoon and then sitting it back into the bowl. She then moves the bowl out of view.]
And I also have a set of... toys!
[Presenter moves a box of toys into view, she then points to the dinosaurs and points to blocks and then picks up the dinosaurs and places them back.]
I know, they look a bit fun, don't they? Some dinosaurs and ponies and things that move and blocks to build, and you know it's always good, to have dinosaurs to play with. And so, when we make a set, we always make sure that they have something in common. And that's how we know that we're sorting a set, so let me show you some others and I'd like you to think about what do these things have in common? Because these are all things that we can play with.
[Presenter points to toys and picks up box, shakes and moves it out of view.]
So, what about these things? What do they all have in common? That's right! They're all dice, aren't they?
[Presenter places a box down which has different sizes and coloured dice in it. She then moves the box out of view.]
What about these things? What do these things all have in common? They're numbers. Shall we read them together? What's this one? 5, 8, 7, 4, 9 and zero.
[Presenter places a white plate down which has coloured numbers on it. She points to the number 5, then the number 7, then number 9 then number 4 and then 0. She then moves the plate out of view.]
What about these things? What does this set have in common?
[Presenter places down a container with has an assortment of pencils, pens, texters.]
Ooo, I can hear your brains thinking. That's right, there's some pencils and pens, some coloured pencils and lead pencils, a really fun bee pen. Yeah, they're things that you could write with, so that's what they have in common.
[Presenter points to the different pencils and pens explaining the different colours and styles.]
And what about this one? What does this collection or set have in common? What can you see there that's the same?
[Presenter places down some paper, bundle of 10 craft sticks, 2 sticky notes with ten written on it in word form and 10 written on another one in numeral form, a piece of paper with a tens frame (a rectangle box drawn with a horizontal line in the middle and 4 vertical lines creating 10 boxes) with a black dot drawn in each box and 1 multi-attribute block of ten.]
That's right, they are all representations of 10 Look. Here's the word ten. Here's the number 10. This is 10 on a ten frame, 10 craft sticks and 10 blocks 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
[Presenter now removes the last objects and puts aside.]
So, what I wonder now, little mathematicians, is if I come back to my box of things that I had at the beginning, that was that clunky sound when you heard me put my counters back in my box.
[Presenter now brings back the original box containing, pencils, cars, animals, and counters and scatters them with her hands in the box.]
Now what I wonder is, I wonder how many different ways we could sort this? Or you could go find your own bits and pieces at home and think about what are all the different ways that you could sort your things into sets and how would you describe them?
Over to you!
[Screen reads –
What are all the different ways you could sort my collections of things?
· Draw pictures of the different ways you found to sort them.
· You can also use your own collection of things if you prefer.]
[End of transcript]
Draw pictures of the different ways you organised your own collection of items or the collection of items in the video.
Now watch Sorting 2 video (2:44) to see some different ways that items can be sorted.
[Screens reads, here’s what we found with our collection of items…]
[Screen shows a box of assorted toys, in the box are, some coloured counters, 3 pink coloured pencils, animal felt fabric cut-outs, of a pig, piglets, 2 sheep and one cow. The 3 pink pencils, one pig and 3 piglets, and 6 pink counters are displayed on the table next to the box.]
I made a set of things from my box of goodies.
Can you work out how I organised my set?
[Barbara circles the group on the table with her finger.]
What thing they all have in common?
Ah, that's what I was thinking too.
They're all things that are pink.
Let's have a look at another way.
[The screen now changes and displays the group on the table now as one pig, 3 piglets, 2 sheep and one cow.]
Okay, can you see what I was thinking about this time?
They're all things that are animals and things that aren't animals, or you could say things that are living and things that aren't living.
[Barbara circles the group of animals and then circles the group of objects in the box.]
I wonder what else I could think about.
Oh, here's another way of thinking.
Oops. This one should go here too.
[Screen now changes to display a pig, 3 piglets, 2 sheep, one cow and 3 toy cars.]
Can you work out what I was thinking about what these things all have in common?
That's right, there's some animals and some cars.
Yeah, so if they were real animals and real size cars, they're all things that can move that's right cause sheep can walk and cows can walk, and pigs can...
[Barbara moves the animals to indicate they are walking, and she rolls the cars like they are moving.]
And piglets can walk and cows, oh sorry.
Cars can also move.
Here's another way we thought of to organise our things from our box into a set.
[Screen shows a box of assorted counters, toy cars, and animal cut-outs. On the table is a cow cut-out and underneath aligned to the cow’s length are 6 coloured pencils varying in length slightly, there are 3 pink, 2 yellow and one green pencil.]
Can you see what these things have in common?
[Michelle moves hand over items on the table.]
Yeah, that's what we were thinking too that all of these things are longer than the cow.
See if I measure the car that's shorter than the car than the cow.
[Michelle picks up a car from the box and lines it up next to the cow, showing that the car is shorter than the cow.]
One of these counters, I'll use one that you can see.
That's definitely shorter in length than the cow.
[Michelle picks up a green counter and places it next to the cow, showing that the cow is much longer, she places the counter back in the box.]
And even the pig, which looks pretty close is shorter in length than the cow.
[Michelle picks up the pig measures it against the cow, showing that the cow is still longer. She places the pig back in the box.]
And let's check the sheep.
[Michelle picks up the sheep and measures it against the cow, showing that the cow is still longer, she places the sheep back in the box.]
It's also shorter in length than the cow, but the pencils, they're all longer.
[Michelle now picks up the pencils and measures them against the cow, showing that the pencils are all longer in length.]
So, what's the mathematics that we are seeing here?
Items can be sorted in lots of different ways.
[Screen reads: We found 4 different ways to sort these items:
There are 4 pictures. The first picture is a box with assorted items and to the right is 3 pink pencils and one pink pig and 3 pink piglets and 6 pink counters. Underneath the picture the text says: we made a set based on the colour (we chose pink).
The second picture shows a box of assorted items. To the right there is one pig and 3 piglets, 2 sheep, one cow and 3 toy cars. Underneath the picture it reads: we made a set based on things that move, like cars and animals.
The third picture is a box of assorted items, and to the right is one cow and 6 pencils aligned in a row, showing different lengths. Underneath the picture it reads: we made a set based on things that are long or longer than the cow. We used length.
The final picture shows a box of assorted items. To the right is one pig and 3 piglets, 2 sheep and one cow. Underneath the picture, it reads: we made a set based on living and non-living things.]
So, we found just in this box of our things that we were tidying up, but there were 4 different ways that we could sort these items.
I wonder if you can think of some other ways to sort your bits and pieces.
Over to you, mathematicians.
[Screen reads: Over to you!
Find all of the different ways you can sort your collection.
Draw each of your sets and if you can, ask someone to help you label them.
[End of transcript]
- Find different ways you can sort your own collection of things.
- Draw pictures of the different ways you could sort your collection of items. Ask someone to help you label them.