• MAO-WM-01 
• MA2-PF-01

• MAO-WM-01 
• MA3-RQF-01

Michelle

[Screen shows 2 Colour in Fractions game boards, a bunch of highlighters, a pen and 2 foam dice. One of the dice has numbers on it, the other has fractions.]

Hello everybody, welcome back to having some fun with mathematics! I'm here again with Ayesha and Barbara. Hi guys!

Ayesha

Hello!

Barbara

Hi Michelle!

Michelle

We're going to play a game today called colour in fractions and sometimes you can play this game by yourself. Sometimes you can play competitively against someone else, and sometimes you can play where is it 2 teams of 2. Today we were limited in our access to mathematicians, so it's Ayesha and Barbara versing me today.

So we have our game board. We've got lots of different markers. We each have a pen and we have our fancy dice which you could also use spinner as well if you don't have these, so, let's play!

Today we're playing a version of the game where we're each going to use the same numbers that roll to see what happens with our game. So what happens is I know this is going to tell me how much and this is going to tell me my unit size.

[Michelle rolls the dice and lands on 2 sixths.]

So what we have here guys is 2 sixths, so now you can form 2 sixths on your board in any way. So you could do something like... we'll,, I'll let you work it out.

Barbara

OK. What do you think Ayesha, should we colour in... these are sixths, should we in 2 of those?

Ayesha

Sounds like a plan!

So what I'm going to record here is what was rolled.

[Barbara highlights 2 sixths on her board whilst Ayesha records what was rolled and what was shaded.]

Barbara

And then we're going to shade 2 sixths. And I’m gonna put that there, so we know what we coloured in.

[Barbara adds an orange dot next to their first row on the gameboard.]

Michelle

[Michelle records her game board and shades 1 third as 2 sixths.]

So you guys had 2 sixths as 2 sixths, and I had 2 sixths as 1 third. And I know they're equivalent 'cause this line down here shows me that 2 sixths is equivalent in value to 1 third. You guys can roll.

Ayesha

[Ayesha rolls the dice and lands on 2 sixths.]

So we have, 2 sixths.

Barbara

So now, what should we do? Should we do what Michelle did last time? Or should we look for another way?

Ayesha

I'm thinking we look for another way.

Barbara

If we do a line straight through, we can either do 1 third... or we can do this one here, which is twelfths. So we could do 4 twelfths.

[Barbara highlights 4 twelfths whilst Ayesha records what was rolled and what was shaded.]

Ayesha

OK.

[No sound. Screen fast forwards to show Michelle, Barbara and Ayesha playing the game.]

Michelle

All right, over to mathematicians to have fun too!

Michelle

Hi everybody! We wanted to come back and explore this idea in our colouring fractions game of 2 halves being equivalent to 2 quarters, 2 eighths and 3 twelfths as we can see here.

So we wanted to show you a strategy that you can use to help prove that this is an accurate way of describing or renaming 2 halves. And so to help me do that, I've taken a copy of my game board and I have a pair of scissors and I'm just going to cut those sections out.

[Michelle cuts each of the sections from her gameboard out.]

Excellent! And so now what I have is part of what I said was 2 halves and the other part of what I said was 2 halves and I actually have inside of this 2 quarters, my 2 eighths and 3 of my twelfths. And if I take them and lay them over the top of the halves line I can see that 2 quarters is the same as one half and if I join 3 twelfths with 2 eighths, that also turns out to be equivalent to another half, and so that's how I can say 2 quarters and 2 eighths and 3 twelfths is the same as 2 halves, or in fact, how I can prove it.

Now what we're wondering is how many different ways could you make 2 halves?

Over to you!