# Doubles fill

A thinking mathematically context for practise focussed on developing fluency with double facts

## Syllabus

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, 2023

• MAO-WM-01
• MA1-FG-01

You will need:

## Watch

Watch Doubles fill video (8:10).

Learn how to play

### Transcript of Doubles fill video

#### Michelle

Hi there Barbara.

#### Barbara

Hi Michelle, how are you?

#### Michelle

I'm very well how are you?

#### Barbara

I'm very well too. Oh, this looks fun.

[A game board is shown with headers that read ‘Student 1’ and ‘Student 2’. Underneath each header are 4 columns which read: rolled, spun, product, and code. Underneath those are 2 spinners. On the left there is a doubles spinner in the shape of a hexagon with each triangle reading different values such as double, twos and times 2. The second spinner is a standard 0-9 spinner.]

#### Michelle

I know, so you know that game Multiplication Toss that we play.

#### Barbara

I love that game.

#### Michelle

Yeah, so this is a version of that, but it's really focusing on working with doubles.

Ok.

#### Michelle

Yes, it really helps you with those skills, so um, we'll just play and then we'll talk about how to play as we're playing.

Ok sounds good.

#### Michelle

So, we use the same game board for this one and we need the spinner or a dice from zero to 9 and this special spinner.

So, spin both Barbara.

#### Barbara

Ok. So, 6.

[Barbara spins a 6 on the spinner and a double on the doubles spinner.]

#### Michelle

And then you've go to work out what to do with it over here. So.

Oh ok.

So double 6.

#### Michelle

Ok, so I'm going to say you're not student one you're Barbara. And you rolled a 6 and you spun double and what is double 6?

[Michelle draws a line through student 1 and writes Barbara. She then fills in the game board writing the number 6 under rolled, the word doubles under spun and the number 12 under product.]

Double 6 is 12.

#### Michelle

Uhm so then where would you like to go on the game board? Where would you like to put your double 6?

#### Barbara

Ahh, can I start on the top left?

So over here?

Yeah.

#### Michelle

And then do you want to go 6 this way and this way or across?

Ok, so 2 sixes.

#### Barbara

Two sixes, so double 6, yeah.

#### Michelle

Four, 5, 6. Double 6. And Barbara, if you weren't sure if it was 12, you could use that to help you.

Oh yeah, 'cause it could make 6 and then the other 6 and then count or.

[Michelle draws an outline around 12 squares, from the top left-hand corner, 2 squares down and 6 across.]

#### Michelle

And because it says to me a code down here, I'm going to do this to say that's that move.

Oh, Ok.

#### Michelle

Yeah, and then it's my turn.

#### Michelle

Ok.

Now may I have the spinner, the special spinner pen? And I'll start with my number. And I have zero.

Zero, Ok.

#### Michelle

And a times 2, so zero times 2 is zero 'cause zero twos is zero. So, I'm student 2. Can you record for me in the red?

[Barbara, writes zero under rolled, times 2 under spun and zero under product.]

#### Barbara

Sure.

Ok, so you rolled a 2.

Yeah.

#### Barbara

Sorry you rolled a zero.

#### Michelle

A zero. And then you spun.

#### Michelle

Times 2. And then the product is zero.

#### Michelle

Is zero. And then I don't need a code because the code could be nothing.

#### Michelle

Yes, cause I got nothing.

#### Barbara

Ok, my turn. Alright, so. Ok 7, 7 times 2.

[Barbara rolls a 7 and spins a times 2.]

#### Michelle

Ok, you got 7 times 2 and the product of that?

[Michelle, writes 7 under rolled, times 2 under spun and 14, under product.]

#### Barbara

Um, well actually, if double 6 is 12, then I just need 2 more, so 14.

#### Michelle

And where would you like it to go?

#### Barbara

So can I put it anywhere.

#### Michelle

Anywhere on the game board. The goal is at the end to be the person who's covered the most area.

#### Barbara

Oh ok, right.

So, then all my stuff will be the blue things and yours will be the things in red. Ok, um, alright, Well let's go with um, maybe just underneath it 'cause we can actually use what we know about 6. You know that that's 7 and do one more.

#### Michelle

And do the one more. Like this. So that's 7 times 2, and I might do stripes like this to show that's what you were thinking there.

[Michelle draws an outline on the game board from the left third and fourth squares down and 7 across. She draws stripes across the shape and labels the shape 7 times 2. She uses the same stripes in the code column.]

Ok, my go.

Good luck.

#### Michelle

Come on magic spinner.

#### Barbara

I hope you get a 9.

#### Michelle

So, do I. And I got a one. I think 'cos your hope wasn't very generous. It wasn't an accurate reflection of how you felt.

[Michelle and Barbara are laughing.]

#### Michelle

So, I rolled a one.

[Michelle rolls a one.]

So.

#### Michelle

And I spun twos.

[Michelle spinner lands on twos.]

#### Barbara

1 times 2, so one twos.

#### Michelle

Which is 2. Cause 1 times 2 is 2. And I would like my 1, 2 please, to go on the end of your double 6.

[Barbara, writes one under rolled, twos under spun and 2 under product. On the game board, Barbara draws an outline around 2 of the squares at the end of her ‘double 6’ square. In the centre of the shape, she writes 1 twos.]

#### Barbara

So that, that we then have a, across like that?

#### Michelle

No, the other way, so we then have a square array.

#### Barbara

Oh, ok, that could be 4 sevens actually.

#### Barbara

And will I write it this way?

Sure.

Ok, 'cause then.

#### Michelle

Yeah, it matches the array actually that way. Alright, your go. I'm glad my contribution is so enormous.

#### Barbara

Ok, Alright. So, 2 and 2 twos.

#### Michelle

Two, twos. And the product of that?

[Michelle, writes 2 under rolled, twos under spun and 4 under product.]

Ah, 4.

#### Michelle

Four and where would you like? What area would you like to block out?

#### Barbara

Um, I think next to your one 2. I think.

#### Michelle

So, like a square?

[On the game board, Michelle draws an outline around the eighth and ninth top 2 squares and the 2 underneath. In the centre of the shape she writes 2 twos and creates swirls to use as her code.]

#### Barbara

Yeah. Two twos would always be a square, wouldn't it, or is it yet 'cause I can't? I can't break it up.

#### Michelle

You can if you want.

Oh, ok.

#### Michelle

It's in the game.

#### Barbara

Ok, but I'm happy with that.

#### Michelle

Um, and I'm going to do swirls.

#### Barbara

Oh yeah, I didn't give you a little code, so I might give you dots for the first times 2.

#### Michelle

Ok, maybe I should say, come on, unlucky spinner. And off then. Oh, no still, still unlucky.

#### Barbara

Do you want to spin again?

#### Michelle

No, but thank you for that generosity, Um, 1, 2 please.

[Michelle spins a one and lands on twos.]

#### Barbara

Ok, 1 times 2.

[Barbara, writes one under rolled, twos under spun and 2 under product. On the game board she draws an outline next to the previous square. In the middle of the shape she writes one twos and draws stripes as her code which she writes on her game board under the heading ‘code.’]

#### Michelle

May I have the spinner please?

Sure.

#### Michelle

I'm going to try to go backwards.

[Michelle spins a 9 and lands on twos.]

#### Barbara

That worked. Yes, 9. Twos.

#### Barbara

9 twos. Ok, so, and what is that product of 9 twos.

[Barbara, writes 9 under rolled, twos under spun and 18 under product.]

18.

Ok.

#### Michelle

But because I know I can do this and now you've made me start thinking about being evil. I would like 2 of my 9 twos to go here.

Ok, where?

#### Michelle

Up here.

[Barbara outlines 4 squares, in the eighth row down, fifth and sixth squares across and the 2 directly under them. She labels the shape 2 twos and in brackets she writes 9 twos.]

#### Barbara

Ok, so that's 2 twos.

Yeah.

#### Barbara

Ok, do I write 2, twos in it? Ok.

#### Michelle

And then maybe put in brackets 2 nines, 9, twos so that we know that it's part of the 9, twos collection.

#### Barbara

Ok, yeah. So, 9 twos in here.

#### Michelle

Cause I still have 7 twos left that I can use.

Yep.

#### Michelle

So, I might use 3 twos down here.

Oh wow!

OK.

#### Michelle

Yeah. And then I'll pattern that the same way so we can all tell.

[Barbara now draws an outline around 6 squares, the fifth and sixth columns across and 8 and 9 rows down. She now writes 3 twos in the centre and 9 twos in brackets.]

#### Barbara

Ok, so that's 3 twos.

Of my 9 twos.

That's right.

#### Michelle

So that's 5 twos all together. So, I still have 4 more 2 twos to go.

#### Barbara

And you could go this way and that would make it kind of pretty.

#### Michelle

I could but I don't want to do that.

#### Barbara

You don't want to make it pretty Ok.

#### Michelle

I want to go. I'll just do 4 twos down here.

#### Barbara

In there?

[Barbara now she draws an outline around 8 squares in the eighth and ninth columns across and in the third, fourth, fifth and sixth rows. She now writes 4 twos in the center and 9 twos in brackets.]

Yeah.

#### Barbara

Ok.

I wonder if you're doing this on purpose, like leaving this weird little thing that?

Yeah.

#### Barbara

Oh ok. That's great, Ok, 4, 2 twos of your 9 twos. Now I need to be careful with how I showed that this is all the same term.

#### Michelle

So, it might be worth putting a little like asterisk or something.

[Barbara draws an asterisk in the square of 4 twos.]

Oh, yeah?

#### Michelle

And then saying down the bottom write it as 3 twos plus 2 twos plus 4 twos.

#### Barbara

Then I might put a little asterisk here as the code. Ok, so down the bottom?

[Barbara also draws an asterisk underneath the game board squares and writes, 3 twos plus, 2 twos plus 4 twos (equals 9 twos.).]

Yeah.

#### Barbara

So, I'll put in 3.

#### Michelle

Twos plus 2 twos plus 4 twos. And I really did that to show you that you can break it up as much as you like, and you can be quite silly.

#### Barbara

Equals 18, but I'll put in here, equals 9 twos. Yes, 'cause that's actually what you rolled, 9, twos. Ok?

#### Michelle

Well right over to you mathematicians to have fun playing Doubles Fill. Have fun.

[End of transcript]

## Instructions

• Players take turns to spin the 9 spinner. or roll a dice, and spin the doubles fill spinner.
• If a player spins a 6 and spins ‘double’, they double 6 to make 12, explaining their thinking to their partner who records the number sentence.
• The player then colours in a corresponding array.
• Then players swap roles.
• If there is no space on the grid, players miss a turn.
• Play continues until no one is able to add another array.
• Players then calculate the number of squares they covered and the person with the largest area is the winner.

## Other ways to play

• Use materials to work out double facts.
• Make up ‘codes’ to show the order in which they made the arrays.
• Students can rotate and rename the array to use the commutative property, e.g. change 5 twos into 2 fives and colour the corresponding array.
• Change the spinner to include repeated doubling.