# Mancala

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

## Collect resources

You will need:

• game board (this can be created using an old egg carton, cups or by drawing on a piece of paper)

• 48 counters (or other items such as beans, dried pasta, building bricks, paper clips or buttons)

• someone to play with (you can also play this game in teams so you can share your brainpower!)

## Watch

Watch the Mancala video (6:01).

Empty your game board in an ancient game of strategy.

### Transcript of Mancala

[White text on a blue background: Mancala. An ancient game of strategy. In the bottom right corner is the red waratah logo of the NSW government. In the bottom left corner is the small font text: NSW Mathematics Strategy Professional Learning team (NSWMS PL team)]

### Michelle

Mancala, an ancient game of strategy.

[New slide. Text: You will need…

• A gameboard (we made ours using an old egg carton. You could also make it using cups or by drawing on a piece of paper).
• 48 counters (you can use dried beans, dry pasta, LEGO bricks, paper clips or buttons as your counters. For this game, they don’t all need to be the same object. Place 4 items in each hole.
• Someone to play with (you can also play this game in teams so you can share your brainpower!)

### Michelle

To play this game, you will need a game board. We made ours using an old egg carton. You could also make it using cups or by drawing on a piece of paper. 48 counters, you can use dried beans, dried pasta, LEGO bricks, paper clips or buttons as your counters. For this game, they don't all need to be the same object. Place four items in each hole. And then you need someone to play with. You can also play this game in teams so you can share your brainpower.

[New slide. Text: Let’s play!]

### Michelle

OK, let's play.

[An empty egg carton is on a flat surface. The top of the egg carton has been cut off and then cut in half short ways. The two halves have been placed underneath the bottom of the egg carton so that there is an overhanging receptacle on the left and the right.]

### Michelle

Hello everybody and hello Barbara!

### Barbara

Hi everyone! Hello Michelle! How are you?

### Michelle

I am fantastic. How are you today?

### Barbara

I'm very well, thank you.

### Michelle

I'm going to show you a new game today called Mancala. So, we're using an old egg carton and we each need to have four beans or beads in our six cups.

### Barbara

OK, before we start.

[Michelle and Barbara place 4 blue beans in each of the 12 cups.]

### Michelle

So, we're going to call these our cups, yeah. So, that means you'll have 24 beans in total.

### Barbara

Because six fours are at 24.

### Michelle

That's right. And if you have any spare, I think I need three more.

### Barbara

Oh, OK. I'll be nice.

Thanks.

### Barbara

OK, three more there.

[Michelle indicates that the top row of 6 cups is her side of the board, and the bottom row is Barbara’s.

She indicates that the receptacle on the left is her cup and the receptacle on the right is Barbara’s.]

### Michelle

Perfect. And this is my side of the board and that's your side of the board. And this is my cup that I'm collecting into and that's your cup. Would you like to start or should I start?

### Barbara

I think maybe you can start so I can watch.

### Michelle

So there's two ways that I can get these beans into my cup. And one is to just land, like, land your beans there. So, for example, I know something about the game, too, so I'll just show you as I do it. I've got four beans here.

[Michelle picks up the 4 beans from her fourth cup from the left. She places one bean in each of the 3 cups to the left and the then fourth been in her receptacle end zone.]

### Michelle

I have to spread one in each bean as I travel along, one in each cup. And when I land with one in here, I get to keep it there. But if it's my last turn, I also get to have another go. So, now these ones, for example, five, would have five in it. Well, not five, but it would have five and I could drop them off one here, here. And then I would have to drop one into your side but I wouldn't get to have another go.

### Barbara

Yeah. And I don't just get to keep it because I need to...

[Michelle picks up the now 5 beans from the second cup on the left. She places one bean in the cup on the far left, one bean in the end zone, and then the next 3 cups on Barbara’s side of the board from left to right.]

### Michelle

Yeah, you need to move it up to there. But I think I might use it from this cup just to show you that move. So, one for me, one in my keep cup and then one dispersed into your side of the board.

### Barbara

OK, so I've noticed something. I can't start where you started because I no longer have four in there, I have five. But what I can do is I can start from one back, right?

### Michelle

Yeah.

[Barbara picks up the 5 beans from her cup second from the left on the bottom row. She places one bean in the 4 cups on the right before the final bean is placed in her end zone.]

### Barbara

So, one, two, three, four, five.

### Michelle

Yeah, and now you get another go.

### Barbara

OK, now, no matter what I do... I'm going to end up giving you some, right?

Yeah.

### Barbara

OK, so I might just spread them around myself.

### Michelle

Yeah because you would then keep your own there.

I keep my own.

### Michelle

Yeah.

[Barbara picks up the 5 beans from her leftmost cup and places them one at a time in the 5 cups to the right.]

### Barbara

So, I've got five, one, two, three, four, five.

### Michelle

Oh, now this is actually good for me. I'm glad you did that.

Oh, really?

### Michelle

Yeah, because there's two ways that you get to keep stuff in here. One is to move through them or the other is to land in an empty... cup on your side that has something in the opposite side.

[Michelle picks up her 4 beans in her rightmost cup. She places them one at a time in the cups to the left. The second cup on the left of Michelle’s row now has one bean in it. The corresponding cup on Barbara’s row, the second from the left, also has one bean.

She takes both her bean and Barbara’s bean from the cups second from the left and places them in her end zone.]

### Michelle

So, because I have four beans here, I can go one, two, three, four and I landed in an empty cup. And you've got something in that cup. So, I get to keep both those beans. Yeah, cool, hey?

### Barbara

That's very cool.

[Michelle takes the 5 beans in her cup second from the right and places them one by one in the cups to the left. The last bean is placed in the end zone.]

### Michelle

But what I might do is take your strategy and just spread out my own. Oh, actually, no. This will give me a free one. Look, one, two, three, four, five, like that.

### Barbara

OK, great.

[Michelle picks up the 2 beans in the cup third from the right and places them in the 2 cups to the left.]

### Michelle

And then, yeah, I might just spread these ones out like this. Now, it's your go.

[Barbara points to Michelle’s leftmost cup.]

### Barbara

So, now it's a bit different because now you've got seven in here, which is what I was afraid of because I started counting. And if you got seven, then you would go...

### Michelle

Like this, one, two, three, four, five, six, seven. You've got to watch out, I might have eight in there.

### Barbara

Oh, you've got eight in there?

### Michelle

Well, if I did have eight, you have to be careful because I would go, one, two, three, four, five, six, seven, eight and then I'd be able to get all of those.

### Barbara

How many do you have? Oh, sorry. So, you've only got seven, but that's OK. It's still something that I need to be careful about.

[Barbara picks up her 6 beans in her right most cup. She places a bean in each of Michele’s cups, from right to left.]

So, I'm going to get rid of this because I'm quite scared of you landing there now. OK, so one, two, three, four, five, six.

### Michelle

Oh, OK. Alright, so mathematicians, this is a brief introduction of how to play Mancala. We're going to keep playing. The winner at the end, Barbara, is the person with the most beans in their tray. Over to you to have fun and over to you, Barbara, to get strategizing.

[White text on blue: What’s (some of) the mathematics?

New slide. Text: Mancala is a great ancient game of strategy and there’s a lot of mathematics we could talk about!

• For some of our younger mathematicians, Mancala can help us build confidence with counting as we drop each bean into one pit (or cup). This can help us build one-to-one correspondence. We can also practice saying the number word sequences and working out how many beans we have at the end of the game.

A graphic depiction of a Mancala game board appears. A red bean graphic appears in the bottom row cup third from left. Below the cup the text: one, appears. One by one 3 more beans are added to the next 3 cups on the right. The words: two, three and four appear under the corresponding cups.]

### Michelle

So, what's some of the mathematics? Mancala is a great ancient game of strategy, and there's lots of mathematics we could talk about. For some of our younger mathematicians, Mancala can help us build confidence with counting as we drop each bean into one pit or cup. This can help us build one-to-one correspondence. We can also practice saying the number word sequences and working out how many beans we have at the end of the game.

[New slide. Text:

• For some of our older mathematicians, Mancala can be used to develop computational thinking and investigate winning strategies. Can you find a way that if you start, you can never lose?

### Michelle

For some of our older mathematicians, Mancala can be used to develop computational thinking and investigate winning strategies. Can you find a way that if you start, you can never lose at Mancala?

[The NSW Government logo flashes on screen. Text below reads: Copyright, State of New South Wales (Department of Education), 2021.]

[End of transcript.]

## Instructions

• Each player sits opposite each other facing the long side of the game board (egg carton)
• Players place 4 beans into each of the cups.
• The collection cups (mancala stores), are placed at each end of the game board, and remain empty of beans.
• Player one grabs all the beans from one hole on their side of the gameboard and drops them, one by one, into each cup around the board going to the right. (This may take you around into the other player's side of the board).
• If the player passes over their collection cup, they get to place a bean in there.
• Once the player doesn't have any more beans in their hand, player 2 does the same sort of thing with a pile of beans from their side.
• If a player puts their last bean in their collection cup, they get an extra turn!
• If a player puts their last bean from a pile into one of their empty cups on their side, they get to reach across the game board and collect the beans from the opposite cup of their opposing player.
• Play continues in this way until a player's side of the game board is completely empty.
• The winner is the one with the most beans in their own collection cup!

## Discuss and reflect

What moves will increase your chances of winning?