# Mastermind

Stage 1 to 3 – A thinking mathematically context for practise resource focussed on developing one-to-one correspondence, counting sequences and reasoning with strategies

## 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-RWN-01
• MA1-RWN-02

• MAO-WM-01
• MA2-RN-01

• MAO-WM-01
• MA3-RN-01

You will need:

• a pencil

## Watch

Watch the Mastermind video (7:43).

Use place value understanding to guess a 3-digit number.

### Michelle

Hello mathematicians!

Hi everybody.

Hi Barbara!

Hi Michelle.

I am.

### Michelle

Okay, so we're gonna play a game today called Mastermind.

[Screen shows 2 A4 sheets of paper placed down beside each other in portrait orientation.]

### Barbara

Oh, sounds like me.

### Michelle

I think it sounds like me, but let's play. So, we each have a square of paper. Can you show your square? And on our square of paper, we need to write a 3-digit number.

[Screen shows 2 square sticky notes. One is green and one is orange.]

Okay.

### Michelle

But none of the digits can repeat.

### Barbara

Okay sounds good.

### Michelle

So, you write yours and I'll write mine, don't show me.

### Barbara

Okay.

[Michelle and Barbara write on their sticky notes off screen.]

### Michelle

Okay everybody here's my number. [Michelle holds up the number 462 on her green sticky note.] Okay and Barbara can you show everybody your number.

### Barbara :

Here's my number there [Barbara holds up the number 305 on her orange sticky note].

### Michelle

Okay, so now what we need to do is, we're gonna make up our game board, and so on it we want to record what the guess was. I'm gonna have 3 columns. In here we want to know, um, how many places, and how many digits.

[Michelle and Barbara create 3 columns on their page by drawing 2 vertical lines. In the first column they write ‘guess’, in the second column they write ‘places’, and in the third column they write ‘digits’.]

### Barbara

Okay, what does that mean?

### Michelle

So, you know how we just wrote a 3-digit number?

Yep.

### Michelle

So, I might say to you, hey Barbara, was the number 426?

Mm-hm.

### Michelle

And I would write 426 and then I'd say to you, oh we should have actually written that the other way around, digits.

Okay.

### Michelle

And places.

[Michelle and Barbara fix their game board. They write ‘digits’ in the second column and ‘places’ in the third column.]

Okay.

### Michelle

‘Cause then you would say to me there's one digit or 3 digits or 2 digits that, or no digits.

### Barbara

That are correct? Okay.

### Michelle

And then you would say to me, it's in, there's one of them is in the right place.

### Barbara

Okay, so places means in the right spot and digits means the digit is in the number.

### Michelle

That's right. Okay so let's play because that's the easiest way I always find to learn.

[Michelle and Barbara draw a horizontal line underneath their headings.]

Yeah, me too!

### Michelle

So how could we decide who goes first but what about the person with the longest, the most letters in their first name.

### Barbara

Okay I think I've got you because Barbara's got some extra letters in there. B, A, R, B, A, R, A so 7.

### Michelle

Well but Michelle has 8.

Oh no!

### Michelle

Thanks to the French. All right so, I'm gonna try to guess what your number is. Um, what about 753.

[Michelle writes down 753 in the first column under guess.]

### Barbara

753, okay, you've got one number correct.

### Michelle

Do you mean one digit?

[Michelle writes down the number one under the digits column.]

### Barbara

Sorry, one digit correct.

### Michelle

One digit correct, mm-hmm.

### Barbara

And, but it's, it's not, none are in the right place. It's not in the right place.

### Michelle

So, I'm writing one digit is in the number and none of them are in the right place.

[Michelle writes zero in the third column under places.]

That's right.

### Michelle

Okay, so it's your turn to guess.

### Barbara

Okay, so 624.

[Barbara writes 624 under her guess column. Michelle shows the number 462 on her green sticky note.]

### Michelle

Okay so I'm gonna show the guys at home. [Michelle holds up her sticky note with the number 462] Mm-hmm, so I'm gonna say to you that three digits are correct.

### Barbara

Oh okay!

[Barbara writes 3 under the digits column.]

### Michelle

And none of them are in the right place.

### Barbara

Okay, that's kind of useful because it means I've got to change everything.

[Barbara writes 0 down underneath the places column.]

Uh-huh.

### Barbara

Aha, I will have to do another line, ok.

[Barbara continues to draw the horizonal line across the whole page left to right.]

### Michelle

Okay, so now what I'm thinking about is, I know one of these is correct, so I'm gonna have to take a guess but I'm gonna use one of them again, but in a different place. So, I might say, for example, keep the 3, and say, 300 and something.

[Michelle gestures towards the one and zero in the digits and places columns to show her thinking before gesturing to the number 753.]

Okay.

### Michelle

Right, because, or I could say 500, but I wouldn't say 700 and something again, ‘cause you told me that one of the digits is correct, but it's not in the right place.

### Barbara

That's right, yeah.

### Michelle

So, I might say, 302.

[Michelle draws a horizonal line across the page under 753 and then writes 3 in the guess column.]

### Barbara

Oh, Michelle I made a mistake, you had 2 digits in the, you had 2 digits correct. Okay, but still, none of them are in the right place.

### Michelle

Oh okay.

[Michelle strikes out the number one in the first guess of the digits column and replaces it with the number 2.]

### Barbara

That changes things a little bit, I'll just remind everyone what the number was [Barbara holds up her sticky note with the number 305].

### Michelle

Well, I'm gonna keep 300 ‘cause I wrote it.

Okay.

### Michelle

Um but I wouldn't say 350 something.

[Michelle points to the number 753 and the number 3 on her sheet of paper.]

### Barbara

No because, because that'd be there.

### Michelle

Yeah, so I might say 370.

[Michelle writes 370 under her first guess, 753.]

### Barbara

So, 370? Okay, so you've got 2 digits correct.

### Michelle

Okay.

[Michelle writes 2 in the digits column.]

### Barbara

And you've got one in the right place.

### Michelle

Okay.

[Michelle writes one in the places column, then draws a horizontal line from left to right under that row.]

### Barbara

Okay, so now I've got to change everything around. So, I'm gonna say 462.

[Barbara writes 462 in her guess column and Michelle shows Barbara’s green sticky note with 462 written on it.]

### Michelle

3 digits correct, 3 digits in the right place.

### Barbara

Oh brilliant!

Oh fantastic. Yes!

[Barbara writes 3 in her first, second and third column. Michelle then places her sticky note over Barbara’s page.]

Do you wanna keep going with mine? Yeah, because something really interesting is happening, that I want to see how you go.

### Michelle

Okay, so, so what I don't know, I'm not sure whether it's the 7 or the zero is right.

[Michelle points with her finger to the 370 on her paper.]

Mm-hmm

### Michelle

But I'm, but, and I'm not sure if the three is in the right place, or the 7 is in the right place. So, I have to like, keep reasoning through, right, so I'm gonna hold this, this I'm gonna hold the 3 here, and then to test it I might say 307.

[Michelle points to each column on her piece of paper.]

Barbara

Okay, so in 307.

### Michelle

Do you want to show those guys?

[Michelle writes down 307 in the guess column then Barbara her sticky note with the number 305 written on it.]

### Barbara

Yep, here you go [Barbara shows her sticky note with the number 305 on it]. You've got 2 digits correct.

### Michelle

Uh-huh.

[Michelle writes the number 2 under her digits and places columns.]

### Barbara

And 2 digits are in the right place.

### Michelle

Oh okay, so now what I am thinking, is that I'm pretty confident the 3 is okay.

Mm-hmm.

### Michelle

I think the zero is okay, but it's not 7.

### Barbara

Okay, so if it's not, okay, I shouldn't give you any clues, but if it's not 7 what could it be?

### Michelle

Well, I'm actually wondering if it, I am wondering, still about this 5, as well. Because I guessed it was 7 but I could, it could still also be the 5, because I haven't checked, tested that.

[Michelle uses a marker to point to the numbers on her piece of paper.]

Yeah.

### Michelle

So, what I might do is now just test 305 to see whether it's the 7 or the 5 that I was guessing here, to confirm my thinking.

Okay.

### Michelle

So, and that will also then tell me if the 3 and the zero are in the right place and I'll have confirmation.

[Michelle writes 305 in her guess column and draws a line underneath it.]

Yeah.

### Barbara

3 digits correct.

### Michelle

Yes!

[Michelle writes 3 in the second row under digits.]

### Barbara

And how many do you think are in the right place knowing what you've seen?

Well now 3.

You're correct.

### Michelle

Yes!

[Michelle writes 3 in the third column under places and Barbara places down Michelle’s sticky note with the number 305 written on it.]

### Barbara

Well done!

Cool. I got really excited because, it looked like you were giving up on the 5 but then as you gave up, it looked like you were giving up on the 5, but you introduced the zero, which was in, which was actually part of my number, so that's why I wanted, even though I beat you and I like beating you. I really wanted to see you work it out.

[Barbara points at the numbers on Michelle’s piece of paper.]

### Michelle

Because you also sort of, not to take away from your win, because it was. It was a bit lucky.

It was lucky.

### Michelle

It was a bit lucky.

### Barbara

The first part was lucky, and then that was the first time I just thought, I'll just put the yeah 4 in the hundreds.

[Barbara points and moves her hands across the piece of paper indicating the numbers and pushes sticky notes to the side.]

Yeah.

### Barbara

I'll make it 462 but that, I got quite lucky, whereas you had to reason.

### Michelle

I had to reason through a bit more.

Anyway, mathematicians we hope you really liked this game Mastermind. You could play it with 4-digit numbers, with 2-digit numbers.

[Michelle picks up sticky note with 462 written on it and places it back down.]

### Barbara

Can you play where you repeat the digit or is that does that make it a bit?

### Michelle

Have a go and see what happens! Okay. Have fun!

[Screen reads over to you, mathematicians!]

[End of transcript]

## Instructions

• Each player writes down a 3-digit number (with no repeating digits).

• Each player draws up their game board (a table with 3 columns: 'guess', 'digits', 'places').

• Players take turns to guess a 3-digit number.

• Their opponent tells them how many digits are correct and how many are in the correct place.

• Players record their guess, the number of digits that are correct and the number of digits that are in the right place. Players then use this information to refine their guesses.

• The first player to correctly guess their opponents' number is the winner!

• Players can choose to play using 4-digit numbers, 5-digit numbers, 2-digit numbers. etc.