• MAO-WM-01
• MA1-CSQ-01
• MA1-FG-01

[A title over a navy-blue background: Around the house. Below the title is text in slightly smaller font: Bay Williams and Kling. Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning Team (NSWMS PL team). In the lower right-hand corner is the white waratah of the NSW Government logo.

A title on a white background reads: You will need…
Bullet points below read:

• 1 or 2 markers
• A gameboard
• 3 x 0-6 dice or spinners (you could also use playing cards or numeral cards you make at home)
• Someone to play with (you could also play this game in teams so you can share your brainpower!)

On the right-hand side of the points is an image of the gameboard: an outline of a house with numbers 1-10 around it.]

Michelle

OK, mathematicians. To play this game, we will need one or two markers, a game board, and you can draw one that looks like ours, it's a house with the numbers of one to 10 around it. Three zero to six dice or spinners. You could also use playing cards or numeral cards you make at home. And someone to play with. You could also play this game in teams, so you can share your brain power.

[Text over a navy-blue background: Two variations you can try…]

Michelle

Now, before we play, we wanted to share two different variations that you can try with this game. So think about these as you're seeing how to play.

[A title on a white background reads: One variation you can try…
The bullet point below reads:

· Roll all 3 dice. Then, choose to use just 2 of the dice, or all 3. For example, you might roll 2, 2 and 5.

· You could choose to just use 2 of the dice. So we could do:

· 5 - 2

· 2 + 2

· 5 + 2

· 5 x 2

Next to the points is an image of a red, pink and green dice.]

Michelle

One variation you can try is that you roll all three dice and then choose to use just two of the dice or all three of them. So, for example, you might roll two, two and five. You could choose to just use two of the dice, so we could do 5-2 or 2 combined with 2, or 5+2 or five twos, 5*2.

[Below the bullet points, more bullet points appear:

· You can also choose to use all 3 dice, so we could do:

· 5 + 2 + 2

· 5 + 2 – 2

· 2 x 2 – 5.]

Michelle

We could also choose to use all three of the dice. So you could do 5+2+2, 5+2-2 or two twos minus five, or we could also rename that as 2*2-5. So one variation is you get to choose, do you use all three dice or just two? Up to you.

[A title on a white background reads: A different variation you can try…
A bullet point below reads:

· Instead of being able to use any operation (multiplication, division, subtraction, addition), just use addition and subtraction.]

Michelle

Another variation that you could try, is instead of using all of the operations like multiplication, division, subtraction and addition, just use addition and subtraction.

[Text over a navy-blue background: Let’s play!]

Michelle

OK, let's play.

[On a large sheet of paper is the gameboard: a green paper drawn with an outline of a house. Around the house are the numbers 1-10.]

Michelle

Hello there, mathematicians and hello, mathematician Barbara.

Barbara

Hello, mathematician Michelle.

Michelle

How are you today?

Barbara

I'm very well. I like the game board you've made.

Michelle

Oh, my gosh. This game. I love it for a few reasons, but one because it reminds me of that game you play with basketball when you play around the key.

Barbara

Yep.

Michelle

You know, and I love to always just think I'm like Mike. (LAUGHTER) Even though he's like a foot and a half taller than I am. Anyway.

But let's, let's learn how to play as we play.

[Michelle drops a red, pink and green dice below the gameboard.]

Michelle

So can you roll all three of those dice, please?

Barbara

Sure.

[Barbara rolls the dice. From the red dice, she gets a 2; from the pink she gets a 5; from the green, a 2. Michelle points to each dice.]

Michelle

OK. So you've got a two, a two and a five. And is there a way that you could make an equation that ends up with an equivalent value of one?

[Michelle points to the one on the gameboard.]

Barbara

Yes, I can start with five…

[Barbara points to the pink dice showing 5.]

Barbara

…and take away two…

[She points to the red dice showing 2.]

Barbara

…and then take away another two.

[She points to the green dice showing 2.]

Michelle

Yeah, OK.

[On the lower left-hand corner of the sheet, Michelle writes: 5 – 2 – 2 = 1.]

Michelle

So you would say, 5-2-2 is equivalent in value to one.

Barbara

Yes.

[Michelle crosses out the 1 on the gameboard.]

Michelle

Yep. So one is out of use. Can you use the same dice, Barbara, to make a value of two?

[Michelle points to the 2 on the gameboard.]

Barbara

Let me think. OK, so I can do something a little bit different.

[On the lower left-hand corner of the sheet above the text she’s just written, Michelle writes: Barbara’s ideas.]

Barbara

So I could do five take away two, which is three, but then three and two, I can't make... I don't think I can.

Michelle

No, and I thought about two divided by two would make one, but five minus one is four. OK, so I get to roll the dice now, if you can't go.

[Michelle rolls the dice. From the green she gets a 2, from the red: 3, from the pink: 3.]

Michelle

And I've rolled a three, a three and a two…

[She moves the two 3s together, and the 2 nearby.]

Michelle

…and I can make... Can I make that a two? I could make…

[Michelle moves the 3s down.]

Michelle

…double three is six divided by two…

[She moves the 2 near the 3s.]

Michelle

…is three.

[She pushes the 2 upwards. Then moves the red 3 below it.]

Michelle

I could make three minus two is one.

Michelle

Yes. So I could make it. So…

[She moves the pink 3 to the left, then the 2.]

Michelle

…3-2=1. And then the…

[She moves the red 3 under the other dice.]

Michelle

…3-1=2.

[On the lower right-hand corner of the sheet, below the gameboard, Barbara writes: Michelle’s ideas.]

Barbara

OK. So 3-2 =1?

[Under Michelle’s ideas, Barbara writes: 3 – 2 = 1.]

Michelle

Yeah. And then 3-1=2.

[Under the text, she writes: 3 – 1 = 2 .]

Barbara

OK. Cause you've still got the other three. OK, great.

Michelle

OK.

[Michelle crosses out the 2 on the gameboard.]

Michelle

And then I need to see if I can make three, and I can do that actually…

[She moves the 3s to the left, then the 2 slightly down.]

Michelle

…because 3/3=1, and 1+2=3.

Barbara

Oh, I like your thinking.

Michelle

Or even actually, three thirds plus two.

[Michelle points to each of the dice.]

Michelle

Can you write it like that?

Barbara

Yeah.

[Under Michelle’s ideas, Barbara writes: 3/3 + 2.]

Michelle

Yeah, three thirds plus two.

Barbara

Oh, I like that.

Michelle

Is three. Which is the same as three divided by three, but we could just rename that as one. And then two more, which makes three.

Barbara

OK.

[Next to the formula, Barbara writes: 3.]

Michelle

Well, is equivalent in value.

Barbara

To three.

Michelle

OK.

[Michelle crosses out the 3 on the gameboard.]

Michelle

So now I need to see if I can make four. And can I make four? Yes.

Barbara

I was hoping you wouldn't see it.

Michelle

3*2=6 Oh, no. Three. 3*3=9-2. No. 3*2=6-3. No. 3+3. Oh, yeah. Why am I thinking it's hard?

[She moves the red 3 next to the pink 3. She points to both dice.]

Michelle

3+3, double three is six, minus two…

[She moves the 2 next to the other dice.]

Michelle

…is four. So 3+3-2, that makes four.

[Under Michelle’s ideas, Barbara writes: 3 + 3 - 2 = 4.

[Michelle crosses out the 4 on the gameboard.]

Michelle

Alright, now I need to see if I can make five. I could if I could just add three plus two. That combines to (CROSSTALK) dice. I gotta use all dice.

[Michelle points to each dice.]

Michelle

I could do 3*3=9-2=7.

[She points to the red 3 then green 2.]

Michelle

3*2=6.

No, I can't get there. I don't think I can do it. Can you see it? Oh, what about three halves is one and a half and one and a half times three? No, that won't make it, I think I can't go. So your go to roll.

[Michelle pushes the dice over to Barbara. Barbara rolls them. She gets a pink 4, red 3, green 4.]

Barbara

Alright. OK, so I'm going for five.

[She moves the green 4 closer to the pink 4.]

Barbara

So four, oh, great. Four plus, four and four is eight.

[Barbara points to the 3.]

Barbara

And then 8-3=5.

[On the lower left-hand corner of the sheet, under Barbara’s ideas, Michelle writes: 4 + 4 – 3 = 5.]

Michelle

OK, so 4+4-3 is equivalent in value to five. Yes?

Barbara

Perfect.

Michelle

Do you know what I could have also written…

[She writes under the text: 5 = 4 + 4 – 3.]

…is five is equivalent to four combined with four minus three?

[Michelle crosses out the 5 on the gameboard.]

Barbara

Yes, it's true. Because as long as both sides are equivalent, right?

Michelle

That's right, yeah.

[Text over a navy-blue background: A little while later…

Under the gameboard, there is a red 2, green 3 and pink 1 dice.

Under Barbara’s ideas: 6 = 3 threes x 1 and 1 + 2 + 3 have been added.]

Michelle

Alright. Can you make seven?

[Michelle points to the 7 on the gameboard.]

Barbara

Yeah, I've got to cross it out.

[Barbara crosses out the 6 on the gameboard.]

Michelle

Yeah, you didn't actually, rats.

Michelle

OK. Yes, I can. So similar to my thinking before, this time I'm going to say three twos.

[Barbara moves the 3 next to the 2.]

Michelle

OK. Three twos.

[On the lower left-hand corner of the sheet, under Barbara’s ideas, Michelle writes 7 = 3 twos + 1.]

Barbara

And plus one.

Michelle

Plus one. And I know you could also write that number sentence as…

[Michelle writes: 3 x 2 + 1.]

Michelle

…3*2+1. OK, you've got seven.

[Michelle crosses out the 7 on the gameboard.]

Michelle

Can you make eight?

Barbara

OK. I don't think I can. And even if I multiplied all of these together, I think the largest number I can get is six.

Michelle

The only way is if you wanted to argue the case that…

[Michelle points to the 3 and 2 dice.]

Michelle

…the two could also be representing squared or three could be cubing because then you could say three squared minus one.

[She points to the 1.]

Barbara

Do we want to say that?

Michelle

Let's try it. So eight is equivalent to three squared.

Barbara

Which is nine, yeah.

Michelle

Minus one.

Michelle

Perfect, OK.

Michelle

Can you make nine, then? Yes, you can.

Barbara

Yes, I can. Because...

Michelle

You could say.

Barbara

Nine is equivalent in value to three squared plus one.

Michelle

Or three squared multiplied by one.

Barbara

Oh, multiplied by one. But I can make 10. (LAUGHTER)

Michelle

You can too because...

Both:

Three squared, plus one.

Michelle

Which actually means, can you cross them out, eight, nine, 10.

[Barbara crosses out the 8, 9 and 10 on the gameboard.]

Barbara

Boom, boom, boom.

Michelle

You're the winner. Congratulations.

Barbara

Thank you.

Michelle

Alright. Over to you, mathematicians. Are there any numbers that we couldn't make that you could?

Barbara

And are there other ways to make these numbers?

Michelle

Are there other ways to make them and go play the game.

Barbara

I like this one. I think it's my new favourite game.

Michelle

Over to you.

[Text over a navy-blue background: What’s (some of) of the mathematics?]

Michelle

So what's some of the mathematics here?

[A title on a white background reads: What’s (some of) of the mathematics?
The bullet points below read:

Games can be really fun, but more importantly, great games are a great way to build our confidence and mastery with things like number facts and strategies. Games support our mathematical learning when:

• They provide opportunities for low-stress practice of number facts

• They provide opportunities for low-stress practice of strategies

• They provide opportunities to share our knowledge, understanding and thinking

• Have a balance of skill and luck

· We enjoy them (it's OK to like some games more than you like others.)

Great games can also be modified in lots of different ways so our brains are just the right amount of sweaty!]

Michelle

Well, games can be really fun, but more importantly, great games are a great way to build our confidence and mastery with things like number facts and strategies.

Games support our mathematical learning when they provide opportunities for low stress practice of number facts, they provide opportunities for low stress practice of strategies, when they provide opportunities to share our knowledge, understanding and thinking, when they have a balance of skill and luck and when we enjoy them, and it's OK to like some games more than you like others.

Great games can also be modified in lots of different ways, so our brains are just the right amount of sweaty. Alright mathematicians, over to you.

[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]