A thinking mathematically targeted teaching opportunity focussed on sorting, categorising and representing data using building bricks
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:
- coloured blocks
- pencils or markers
- a ruler.
Watch the brick data video (9:49).
[A title over a navy-blue background: Lego data. Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the lower left-hand corner is the red waratah of the NSW Government logo.]
Hey mathematicians. Today we're going to explore data by looking at some Lego bricks.
[A title on a white background reads: You will need…
Bullet points below read:
- Lego or coloured blocks
- pencils or a marker
- a ruler
Next to the points is an image of lego blocks next to a marker and ruler.]
You will need Lego or coloured blocks, pencils or a marker, a ruler and some paper.
[Text over a blue background: Let’s talk!]
[A blue paper covers a table. On top of the paper are some Lego blocks.]
Hi mathematicians. We've been sorting our Lego out this weekend and we were wondering how many pieces of each colour did we have and what would be a really good way for us to see how many we had of each colour just by looking and thinking. It's really hard for me to tell right now. I can see there is a lot of brown, but they're scattered all around. I wonder if you can think of a strategy that might help me. Alright, well let's try organise by colour to start with.
[The speaker picks out the brown blocks and sets them aside to the left.]
So, we'll put all the brown bits together…
[She picks out the green blocks and sets them aside over the top right side.]
…put all the green bits together…
[She picks out the pink blocks and sets them aside to the bottom right side.]
…they're some pink bits…
[She picks out the yellow blocks and sets them aside around the bottom centre of the sheet. She places one red block on the left of the yellow blocks.]
[She gathers the tan blocks in the centre, the blue ones in the top left corner and one purple block above the tan ones.]
[She moves a brown piece with the others.]
And there's the last piece of brown. What do you notice about the Lego pieces now that we've sorted them? We can tell that there are more brown over here.
[She circles the brown blocks with her finger.]
What else can you see? Yeah, we can see there's one red and one purple.
[She points to the red and purple blocks.]
Though we're wondering, is there a way that we can organise them so that we can check how many more brown? Maybe we could line them up…
[She places the brown blocks in one column.]
…like this in columns. Line my brown one's up.
[Next to the brown block column, she places the red block.]
My one red here…
[Next to the red block, but slightly higher, she lines the yellow blocks in a column.]
…put my yellow ones up here. Tan, purple.
[She lines up the rest of the blocks in a column.]
OK. What do you think now? Do you think this might be a better way of organising my Lego pieces so that I can see how many I have, just by looking and thinking? When I look at my yellow and tan pieces up here, it looks to me that they have the same amount. But if I put my subitising eyes on, I can tell that there are three yellow and I can see that there are two tan and another two tan, which is four. So, I don't think that these two should be lined up. Do you notice what the problem is with my data display? Yeah.
[She moves the bottom yellow Lego to align with the other coloured Legos.]
They all need to be lined up along my baseline…
[She runs her finger from left to right of the space below the Legos lined up.]
…down here, so maybe I can help by drawing my baseline in.
[She places a ruler on the space.]
So, let's get a ruler and let's draw a line so that we can make sure…
[She draws a line against the ruler.]
…that our Lego pieces are all lined up in the same spot to help me.
[She aligns the Legos against the line.]
OK. So, this means now that they're all starting in the same position. But I'm looking here…
[She circles the yellow and tan Legos above the aligned ones.]
…still and I haven't quite got that right. Are you thinking what I'm thinking?
[She moves the yellow and tan Legos closer to the aligned ones.]
We need to line them up so that there's, or no big gaps and they're all lined up evenly.
[The baseline is clear except for the column of brown Legos without gaps on the left, and a red Lego next to it.]
So, now that I know it's important to stack my Lego along my baseline…
[She picks up the yellow Legos and aligns them in a column against the baseline.]
…I'm going to try again to keep my bricks nice and close together so they're all evenly spaced out.
[She takes the rest of the Legos, and aligns them to the baseline and the other Legos.]
And I'll be able to look and think to see how many I have of each colour. So, I wonder what you notice about my coloured bricks down. Yeah. Red and purple only have one.
[On a post-it note, she writes: Red and purple have 1.]
I wonder if there's another word that we could use to describe that, red and purple have one. And we can describe that one as…
[Under the text, she writes: They have the least.]
…they have the least.
[She places the post-it note in the top left corner of the sheet.]
So, now that I know that red and purple only have one, I wonder what else I know.
[She places another post-it note outside the left edge of the sheet.]
Looking along the line of my yellow bricks. I notice the yellow and pink have the same amount. I'm going to write that down on my post-it note.
[On the post-it note, she writes: Yellow and pink have the same.]
Is there a way that I can tell how many yellow and pink I have from looking at my purple and red?
And what I notice is, look here…
[She points to the space above the purple Lego.]
…there's two empty spaces. So, I know there must be two more than my purple brick here. So, that means I know that they must have three.
[On the post-it note, she writes: They have 3.
She places another post-it note outside the left edge of the sheet.]
I wonder if we can see some empty spaces anywhere else that might be able to help us find out how many of a colour we have. Yeah.
[She points to the space above the pink Lego.]
I can see another two blank spaces here, one, two. So, I know that green must be two more than pink.
[On the post-it note, she writes: Green has 2 more than pink.]
So, I know that pink has three and I know that two more than three is five.
[She writes: Green has 5.]
So, green has five. I'm really interested to find out though, how many brown bricks I have, 'cause I still know that it is more than all the other bricks. I'm wondering if I might be able to use the green bricks to work out how many brown bricks I have.
[With both forefingers, she points to the top green Lego. She moves her left finger across to the brown Lego.]
So, when I draw my line across here, my imaginary line, brown has five bricks. But I know that it has more than five bricks. I wonder how many more.
[She places another post-it note outside the left edge of the sheet.]
If I know that all of these…
[She places her left thumb against the bottom brown Lego and her forefinger against the fifth Lego up.]
…are five, because I checked it against my green bricks, I'm thinking to myself, does it look like brown has double the amount of green?
And I'm wondering if there's a way that I might be able to check that. Now, I already know that all of these are five. What if I move them out and bring them up here?
[She moves the bottom 5 brown Legos to the left of the brown Legos above.]
Look. I can see that my brown bricks actually have double the amount of the green bricks. I'm gonna write that down.
[On the post-it note, she writes: Brown has double the amount of green. She places the post-it note to the right the other ones.]
What a great noticing. Brown has double. So, I know that green has five. How many might brown have? Oh, good thinking. Double five is 10.
[On a post-it note, she writes: I have 10 brown bricks. She places the post-it note below the last one.]
I have 10 brown bricks.
[She returns the 5 brown Legos back under the other brown Legos.]
Now I can put these back down in my graph.
[Text over a blue background: What's (some of) the mathematics?]
What's some of the mathematics?
[A title on a white background reads: What's some of the mathematics? Text below reads: We created a graph today to see how many Lego pieces we had of each colour. We noticed that the Lego pieces were spread out in their columns, it was really hard for us to see if one colour had more than another. A point below reads: It is important that the Lego are spaced out evenly. We used a baseline to line the bricks up.
Under the point is a row of 3 images. On the left is an image of the blocks spread out in their columns. In the middle, is an image of the blocks with a baseline. The last image is of the blocks lined up without gaps.]
We created a graph today to see how many Lego pieces we had of each colour. We noticed that the Lego pieces were spread out in their columns and it was really hard for us to see if one colour had more than another. We know now that it's important for our Lego pieces to be spaced out evenly and we even used a baseline to line up our bricks so that they were in a really nice, neat and tidy straight line.
[A title on a white background reads: What's some of the mathematics? Text below reads: We used what we knew about numbers to decide if we had more or less. We could also think about how many more and how many less. A point below reads:
· We compared the columns and looked at the blank spaces to notice how many more pink bricks we had. We saw two blank spaces above the purple brick, so we knew that there were two more pink bricks.
Under the point, on the right hand side is an image of the lined-up Legos. A pink arrow points to the space above the purple Legos. The text inside the arrow reads: 2 blank spaces.]
We used what we knew about numbers today to decide if we had more or less and we could even think about how many more and how many less.
We compared the columns and looked at the blank spaces to notice how many more pink bricks we had. We saw two blank spaces above the purple brick. So, we knew that there were two more pink bricks.
[A title on a white background reads: What's some of the mathematics? Text below reads: We could see that there were lots of brown bricks. We used our mathematical imaginations to draw a line from the 5 green bricks over to the brown bricks. This helped us to notice that there were double the amount of brown bricks. We saw the 5 and then we saw that there were 5 more because we know that double 5 is 10.
Under the text are images. On the left is an image of the lined-up Legos with a pink line that goes across the top of the green Legos and the middle of the brown Legs. A pink arrow points to the line. The text inside the arrow reads: Imaginary line. The image on the right are of the bottom 5 brown Legos against the brown Legos above.]
We could see that there were lots of brown bricks, but we used our mathematical imagination to draw a line from the five green bricks over to the brown bricks. And this helped us to notice that there were double the amount of brown bricks. We saw the five and then we saw that there were five more. And we know that double five is 10.
[Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]
[End of transcript]
- Grab two or three big handfuls of coloured bricks that are the same size.
- Sort the coloured bricks into colour groups.
- Use a ruler to draw a baseline on your piece of paper. Then line your bricks up in columns along the baseline. What do you notice?
- Describe or write what you can see in your graph.
- What colour do you have the most of?
- Do you have any columns with the same amount?
- Draw a picture of your coloured bricks graph.
- Why is it important to line up your coloured bricks? What did you notice when the bricks were not lined up evenly?
- Try taking a handful of coloured bricks with different sized pieces. How does that change the way you can sort your bricks?