Numberblocks – Stampolines follow up
A thinking mathematically targeted teaching opportunity focussed on investigating how a quantity can look different but be the same amount
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:
- 6 blocks
- pencils or markers
- your mathematics workbook.
Watch the Numberblocks Stampolines follow up video (4:03).
[Bold, white text on a dark blue background: Numberblocks: Stampolines follow up. In the bottom left corner is the white waratah logo of the NSW Government. In the top left corner in small font is the text: NSW Department of Education.
On a table are two sheets of A4 paper. The speaker’s hands are visible.]
Hi there mathematicians. Let's start investigating some ideas together. So you might have just seen an episode of Numberblocks. It's OK if you haven't seen it yet. You can still join with us today and play with us. But in the episode of Numberblocks, we had some of our little characters.
[The speaker places 4 Numberblocks on the table. Each Numberblock is made up of a different number of blocks. A red Numberblock is just one block, an orange Numberblock is made of 2 blocks. A yellow Numberblock is 3 blocks and a green Numberblock is 4 blocks. Each Numberblock is connected top to bottom so that they make rectangles.]
Yes, I made these because I really like them. I know, and Four's other eyebrow came off, but we won't worry about that. And in the episode of Numberblocks, some of the blocks were playing a game called Stampolines. Yes, and so what was happening was the shapes were coming along, doo, doo, doo, doo, doo, doo, doo, doo, doo. Jumping into a thing of paint, and splashing onto the wall. And they were leaving a shape behind them.
[The speaker picks up the green Numberblock, Four, and lands him on the top right corner of the paper. She draws Four’s outline in green marker, including the outline of each individual block.]
Mm-hm. So in this case, Four's shape looked a bit like this... where we could see the four blocks. Yes. And then sometimes Four could reform. So along he would come, doo, doo, doo, doo, doo, and he would jump into the ink and splash up onto the wall.
[The speaker takes off Four’s bottom block and places it to the side so that Four now forms an L-shape. She draws the outline of this new shape.]
Yes, and so this time, he's making a different shape. It's a bit hard to trace around, so I'll just draw them as squares. Like this. And I can still see there's four squares, because look, if I join that down there, it still makes four. But this time he has a different shape. Mm-hm.
[She re-connects Four’s bottom block.]
So what I was wondering about today is what would the Stampolines look like if it wasn't One, or Two, or Three, or Four, or Five that were playing Stampolines, but what would it look like if instead it was Six who was playing?
[The speaker places the other Numberblocks to the side and places a purple, 6 block Numberblock on the table. Each individual block has a number like a dice on it. She replaces the sheet of paper with the green drawing on it.]
Yeah, so what's one way you can think of already? Oh, I can think of that one too. He comes along, jumps in, and makes a big long rectangle.
[She gets a purple marker and draws the shape and the 6 individual blocks beside the Numberblock in the top right of the new sheet.]
So I'm going to record this way. Now I could trace around it if I like, or I could draw next to it. My long rectangle and it's got six blocks. So I'll halve it and then a third it.
[She places the Numberblock on the drawing.]
And that's one way, yeah. And what's another way? Oh OK, let's do a tricky one. Ready? Doo, doo, doo, doo, doo, jumps into the ink.
[The speaker removes the bottom three blocks. She places 2 blocks beside the remaining 3 and the last block beside the 2. This forms a staircase shape. She draws the shape, outlining the individual blocs.]
Splat onto the wall. Oh, yeah, it looks like a staircase. And I'm gonna move it over so I can draw it next to it. So three blocks down the middle, one block here... two blocks there, and then three blocks here. Ah-ha!
[She re-connects all the blocks to Six.]
OK, I can reform Six as one big rectangle. And now, mathematicians, it's over to you. What are all the different Stampolines that you could imagine that Six could make as she jumps into the paint and forms shapes on the wall?
[White text on a blue background: Get making! What are all the different shapes Six could make playing Stampolines? See if you can come up with at least 5 different (and new) ways. Over to you!
See if you can come up with five different ways or more. Over to you, mathematicians.
[New slide: What’s the mathematics?]
And before you go, what's some of the mathematics here?
- This task helps us notice the smaller parts that make up the bigger whole of 6.
- This task also helps us build our knowledge of shapes, deepened our reasoning skills and improves our skills at communicating like a mathematician.]
Mm-hm, so this task helps us to notice the smaller parts that make up the bigger whole of six. This is really important knowledge for us as mathematicians. It also helps us build our knowledge of shapes, deepen our reasoning skills, and improve our skills as communicating like mathematicians. Have fun Stampolining.
[The NSW Government logo flashes on screen. Text below reads: Copyright, State of New South Wales (Department of Education), 2021.]
[End of transcript]
- What are all the different shapes 6 you could make when playing Stampolines?
- Can you come up with at least 5 different ways?
- Record your thinking in your student workbook.