Number busting – number talk (renaming 7 and 8)
A thinking mathematically targeted teaching opportunity focussed on building knowledge of part-part-whole relationships to reorganise and rename seven and eight
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 number of the same items (for example, pasta pieces, counters, pencils or building bricks)
pencils or markers
something to write on.
Watch '7 is' video (4:46).
(Duration: 4 minutes and 46 seconds)
[Text over a navy-blue background: 6 is…. Small font text in the upper left-hand corner reads: NSW Department of Education. In the lower left-hand corner is the white waratah of the NSW Government logo.]
We can also investigate numbers using things like a ten frame...
[A large white sheet with a long line drawn in the upper-left corner.]
...which is just a structure that we use to help us understand a numbers relationship to other numbers and the numbers that sit inside of it. And I started to draw a ten frame here...
[The speaker points to the space under the line.]
...but I thought it might be good to show you what it looks like. You might also have a book at home about helping a child with literacy and numeracy that has a ten frame in the middle. But it's just a really big rectangle. So I’ve already drawn the first line, and in this case, today, I'm gonna draw mine like it's standing on a skinny edge so that it's vertical and I draw my rectangle...
[She draws a rectangle that is longer in height than length.]
...and then I need to partition it in half, this way.
[She draws a line down the middle of the rectangle.]
And now I know, because I've played around with them a lot, I need to do some internal lines…
[She gestures drawing lines across the rectangle.]
…so that I end up with five boxes on one side and five on the other. And so I know that means I need four lines.
[About less than a quarter down the rectangle, she draws a line across it. At the same length down each time, she draws 3 more lines across.]
So I'm gonna put them about here one, two, three, four. And I should have five boxes on this side.
[She points to the left half of the rectangle. Then counts the number of boxes down.]
One, two, three, four, five and five on this side.
[She points to the right half of the rectangle. Then counts the number of boxes down.]
One, two, three, four, five. Which means I should have ten all together.
[She counts the number of boxes down the left half of the rectangle, then the right half.]
One, two, three, four, five, six, seven, eight, nine, ten. Which is why it's called a ten frame. So what I thought we could play around with is seven...
[She brings over purple pompoms over the ten frame.]
...and explore different ways of thinking about seven today. So seven is...
[Next to the ten frame, she writes: 7 is…]
...and I could represent it like this.
[She places a pompom into all left frames, and 2 in the top right frames.]
And what I see here is seven is one column of five-
[She points to the left half of the rectangle. Then points to the 2 buttons on the right.]
...and two more. So seven is...
[Under the text, in purple she writes: 5 and 2.]
...five and two. Do you have another way, Ash, that you could arrange it?
Sure, so I'm going to have a look at seven as four and three.
[Ash places a pompom across the top 2 rows of the frame. She skips a row. She adds a pompom in the next frame, skips a frame, and adds one in each of the bottom frames.
...OK. So seven is four and three.
[Under the text, the speaker writes: 4 and 3.]
And you know what else I'm saying? If I move this one…
[She moves the pompom in the bottom-right corner to the left middle row.]
…that helps me, I can also say that there's three blank spaces.
[She points to the empty frames on the right half of the rectangle.]
So seven is three less than ten cause it's a ten frame.
[Under the text, she writes: 3 less than 10.]
Do you think there's another way we could say seven?
So if I move this one over here…
[She takes the pompom from second last left row and places it in the right middle row.]
…I can say six and one more. Which makes seven.
Do you know what we could do? Because mathematicians sometimes use colour. So if I swap to this one here…
[She removes the pompom in the bottom corner frame. She replaces it with a blue pompom.]
…for a blue one. Does that help you see your six…
[She circles the pompoms in the top frames. Then circles the pompom in the bottom corner.]
It does. It does make it clearer.
So we could even record it like that, too. So we could say…
[Under the text, in purple she writes: 6, in black she writes: and, in blue she writes: 1.]
…six and one. So we can see the different colours are corresponding to our pretend counters, OK. Now that we're doing this, I could do something else. I'm gonna use these two…
[She brings 2 green pompoms over the frame. She takes away 2 of the purple pompoms.]
…and say in this case what I'm saying, I can still see your six and your one.
[She circles the pompoms in the top frames. Then circles the pompom in the bottom corner.]
…But the six is actually a four and a two.
[She circles the pompoms in the 2 top frames. Then circles the pompoms in the frames below.]
…So I could say seven is four and two and one.
[Under the text, in purple she writes: 4, in black she writes; and, in green she writes: 2, in black she writes: and, in blue: she writes: 1.]
Seven is four and two and one more.
Oh, I can say something else that I'd like to share. So in this four…
[Ash circles the pompoms in the top frames. Then circles the pompoms just below.]
…I can see two and two. So if I…
[She takes the bottom two purple pompoms away and replaces them with 2 orange ones.]
…set those out.
[She points to each row with a pompom.]
I can say two and two more and another two more is six and one more make seven.
So seven is…
[Under the text, in purple she writes: 2, in black she writes: and, in orange she writes: 2, in black she writes: and, in green she writes: 2, in black she writes: and, in blue she writes: 1.]
…two and two and two and one more. Does that represent your thinking, Ash?
It does. I can see how the colours are shown by the ten counters.
And you know what else we could do for this one…
[She traces the last text with her finger.]
…is we could actually say that this is three twos and one more…
[Under the text, in black she writes: 3 twos and 1. She points to each row.f]
…because there's one two, a second two and three twos, one two, a second two, three twos. And one more. There's a lot of things about seven. I wonder if you can find any extras.
[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]
- Choose a number such as 7.
- Get the amount of items for that number (for example pasta pieces, counters or pencils).
- Organise your items.
- Describe your collection.
- What other ways you can organise your items?
- Describe your other ways.
- You may like to use a mathematical structure such as a ten-frame to help you.
Here is another way we can play number busting using building bricks. Watch Number busting with bricks (2:26).
(Duration: 2 minutes and 56 seconds)
[A long, flat brick of green Lego 16 studs long and 8 studs wide is on a piece of butcher’s paper. A narrow brick of brown Lego only one stud long and 8 studs wide is connected to the top edge of the green brick. The speaker is off-screen.]
So we were thinking about number busting and we thought we could probably do some number busting with Lego or investigate part, part, whole number knowledge onto Lego.
And so I've got a board here, my Lego board and I've got an 8 brick and what we were wondering is can we use the Lego then to show us different ways of thinking about or renaming 8.
Oh, good idea.
So Barbara, have you got some bricks that you could use that would fit into there?
So, and I could record it for us.
So I can say 8 is....
Well ,I know that 8 is also 4 and 4.
[Michelle writes the heading ‘8 is…’ and then ‘4 and 4’ underneath. Two blocks comprising of 4 are placed on the LEGO mat.]
Ok. 4 and 4. Ayesha, have you got any?
I've got some Lego here that can make 8. So it's 2 and 2 which is 4. And 2 more, which is 6 and 2 more which makes 8. So 2 and 2 and 2 and 2.
[Underneath the heading, Michelle writes ‘2 and 2 and 2 and 2’. Ayesha places 4 blocks comprising of 2 on the LEGO mat.]
And if I wanted to I could look at it and say we've got one, 2, 3, 4 twos, so I could also describe that as 4 twos.
And mathematicians would call that multiplicative.
Can I have a go?
[Michelle also writes ‘4 twos’ underneath her list.]
Umm ok, what about this? What about a 4 and a 2 and a 1 and a 1. Or I should read it across this way. A 1 and a 1 and a 2 and a 4. 1 and 1 and 2 and 4. Do you have another way Barbara?
[1 and 1 and 2 and 4 is written in the list. Blocks comprising of 2 ones, a 2 and a 4 are placed on the LEGO mat.]
I do. So this one actually uses a 3, which we haven't used yet. 3 and 2 and 2 and then 1 more.
[Silent placing of bricks for 3 rows.]
So, I've got a 2 and a 6.
[Michelle writes ‘2 and 6’ underneath her list as a block comprised of 2 and 6 is placed on the LEGO mat.]
And then I think, yep, that's different, a 3, a 4 and one more.
[Michelle writes ‘3 and 4 and 1’ under her list. She places blocks comprised of 3 and 4 and 1 onto the LEGO mat.]
I wonder, are there any others?
[The NSW Government logo flashes on screen. Text below reads: Copyright, State of New South Wales (Department of Education), 2021.]
[End of transcript.]
Can you try the same task using different equipment (for example, building bricks)
Draw and record 3 different ways you thought about your collection.
Were you surprised by all the different ways to make your number?
What did the different structures and patterns help you notice about your number? (For example, when we make 8 on a ten-frame, we can see things like 8 is 2 less than 10. When we make 8 using dice patterns, we can see things like 8 is made up of 3 and 5.)
What did you find interesting in this activity?