# Place value game

Stage 1 to 3 – A thinking mathematically context for practise resource focussed on using reasoning to create pathways to a target number

This task is from Dianne Siemon.

## 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

## Collect resources

You will need:

• Game board (you can make one using sticky notes or drawing boxes)
• 0-9 sided dice (you could also use 0-9 playing cards or a 0-9 spinner (PDF 199 KB))

• Marker or pencil.

## Watch

Watch the Place value game video (5:29).

Empty your game board in an ancient game of strategy.

### Transcript of Place value game

[Screen shows a title over a navy-blue background: The place value game. Below the title is text: By Professor Dianne Siemon.

A title on a white background reads: You will need…

A gameboard (you can make one by drawing boxes or using sticky notes).

2 markers

2 x 0 to 9 sided dice. You can also use a set of playing cards from Ace to 0 and the use Kings to represent zero. You can also use a spinner.

A maths buddy to play with!

On the right side is an image of a large blue board with pink sticky notes in a zig-zag pattern on it. The first note is labelled 0 and the last note is labelled 100.]

### Michelle

Before we play today, you will need a gameboard. You can make one by drawing boxes or using sticky notes. And Barbara and I will show you how to make a gameboard just before we start playing. Two markers, 2 dice that have zero to 9.

[Screen shows text over a blue background: Let’s play!]

### Michelle

Let's play.

We hope you're having a great day today. We thought we would play a game from Professor Dianne Siemon, it's called the Place Value Game, Barbara. What do you notice? You look curious.

[Screen shows 2 large blue boards. On each there are pink sticky notes in a zig-zag pattern. The first sticky note on the top left has the number 0, the final sticky note on the bottom of the page has the number 100.]

### Barbara

Well, I can see that our game boards, it looks a bit like a snake, but I can also see that they look the same.

### Michelle

All that would really matter actually is not that they occupy the same shape or space, but just that you have the same number of boxes. So, Barbara, you've got 2 zero to 9 dice, you're gonna roll them and I'll show you how to play. OK.

[Barbara rolls the dice.]

### Michelle

So, Barbara, you've got a 2 and a 2, they're your digits and you need to make a decision. In this case, you don't have one of whether you want this 2…

[Michelle points to the yellow dice at the bottom.]

### Michelle

…to be worth 2 tens or 2 ones. And this case…

[Michelle points to the blue dice at the top.]

### Michelle

…for this 10 to be 2 tens or 2 ones, but it doesn't sort of matter to you. Either way, you have to only make the number...

### Barbara

22.

[Michelle places the blue dice next to the yellow one.]

### Michelle

22. But what you do need to decide is where do you want 22 to go on your game board, knowing that as we need to be the first person to complete the board. And the numbers have to go in order between zero to 100.

### Barbara

Do you mind if I count them?

### Michelle

Sure. Yeah.

[Barbara points to each of the sticky notes on her game board.]

### Barbara

One, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. There's 13 spaces. So, 22 would be much closer to the zero than the 100. But I don't want to miss out on anyone-digit numbers if they come up or any sort of anything in the teens. So, I might put it, I'm thinking here or here.

[Barbara points to the last 2 sticky notes in the second and third row.]

Oh, yeah.

### Barbara

I might put it here.

[Barbara writes 22 in the second-row sticky note.]

### Michelle

OK. My go.

[Michelle picks up the dice and rolls it.]

Now, I got a 7 and a 9, so I can make a decision of whether I wanna have the value of the 7 as 7 tens or 7 ones. And the same with the 9. And I think I'm gonna make this 97.

### Barbara

That's what I would do.

[Michelle points to the sticky note next to 100 on her game board.]

### Michelle

Because I'm gonna probably put it right here next to the 100. Whereas if I made 79, I'd be making decisions about where I might put it. And I think that's the best place for me to move.

### Barbara

Yeah. You're so close to 100.

[Michelle writes 97 in the sticky note next to 100.]

### Michelle

97 'cause it's really close to 100. OK, over to you.

[Screen shows text over a blue background: A little while later…

Most of the sticky notes have numbers in them. The yellow dice shows a 3 and the blue dice shows a 5.]

### Barbara

So, 35 is not an option for me.

[Barbara moves the blue dice to the left of the yellow one.]

So, 53 is...

### Michelle

Oh, yeah. Oh, that's a good choice for you.

### Barbara

Yeah. 5 tens and 3 ones.

[Barbara writes 53 on the sticky note in the fourth row.]

### Michelle

Renamed 53, OK. Oh, yes.

[Michelle rolls a 0 on the yellow dice and a 4 on the blue.]

### Barbara

Oh, that worked out.

### Michelle

That's really nice. So, I can't make 4, but I can make 4 tens that we rename 40.

And I know that 40 is between 36 and 51.

[Michelle writes 40 in the middle third row sticky note.]

### Barbara

OK, so you've only got one number.

### Michelle

One number to go. Your go.

### Barbara

Well, I need to roll, one of my numbers needs to be a 1 or a zero.

### Michelle

Yeah. Or a 7 or an 8.

[Barbara rolls a 5 on the yellow dice and a 2 on the blue.]

So, bam bam.

You can't go.

### Barbara

I can't go. 25 doesn't work. 52 doesn't work.

### Michelle

OK, so I need a number that's maybe a 5. A 6 or 7 would be good. And maybe a 5. I'm gonna roll one at a time. Oh, no good.

[Michelle rolls a 4 on the yellow dice and a 5 on the blue.]

### Michelle

Oh! Was that a 4?

[Michelle points to the yellow dice.]

### Barbara

It was a 4. Yeah.

[Michelle moves the yellow dice on the right side of the blue dice.]

### Michelle

So, I got really lucky Barbara, because 54 is directly after 53, and it definitely is between 53 and 80.

So, for the first time in a very long time, I just won.

[Michelle writes 54 in the first sticky note of the fifth row.]

Congratulations!

### Michelle

Yay! Alright mathematicians, over to you.

[Screen shows text over a blue background: Over to you!

What's (some of) the mathematics?]

### Michelle

So, what's some of the mathematics here?

### Michelle

Well, one of the important things this game reminds us of is that the value of a digit is determined by its place, which is why we call it place value.

So, for example, when we rolled a 7 and a 9, we could choose to make the 9 have a value of 9 tens and the 7 be worth 7 ones. Or the 7 could have a value of 7 tens and the 9 could be worth 9 ones.

So, I don't have to write 9 tens and 7 ones, which is 13 symbols or 97, which is also pretty long. Mathematicians invented place value.

And so, I can simply write 97, these 2 symbols. Because the 9 is to the left of the 7, I know it has a value of 9 tens and the 7 has a value of 7 ones.

So, thank you mathematicians for your efficiency in recording numbers.

[End of transcript]

## Instructions

• This game is for 2 or more players.
• Make a gameboard for each player.
• Take turns to throw 2 x 0–9 sided dice (or spin your spinner).
• Use the numbers you roll to create a 2-digit number, for example a 5 and a 2 could be recorded as 25 or 52.
• Record your number somewhere along the path from 0 and 10.
• Numbers must be placed in order from 0–100 so you must think carefully about the best place to put your numbers.
• If numbers cannot be placed, you miss your turn.
• Continue taking turns to roll the dice, creating numbers and filling in the pathway on the gameboard.
• The winner is the first to fill all of the places.

## Another way to play

Players could use the same gameboard with two different coloured markers. The winner is the person who fills in the most numbers, or, who fills in the final place on the pathway.

## Reflection

1. Explain why you chose to create a particlar number. For example, when you rolled 5 and 2, why did you choose to create 52 instead of 25?

2. What thinking did you do to decide where to place numbers on the gameboard?

3. Imagine you have a space available between 34 and 41. What are all of the possible numbers that could be placed on those two spaces? What are you hoping to roll to fill it?

4. What numbers, if any, could you make where you know exactly where to put them almost every time? Which numbers are they? Where would you out them? And Why?

5. If you were to replay this game, are there any things you would do differently? Why?