# Counting game (by multiples of 10)

Stage 1 and 2 – ​A thinking mathematically context for practise resource, focussed on counting forwards and backwards by multiples of 10

## 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
• MA1-FG-01

## Collect resources

You will need:

• pencils or markers

## Watch

Watch Counting game 110 video (3:35).

Reach the target of zero counting down using multiples of ten.

### Michelle

All right, hi everybody, I'm here with Ayesha today. Hi Ayesha.

[Screen shows bundles of craft sticks in a pile and an A4 piece of paper with a zero written at the top in the middle of the page.]

### Ayesha

Hi Michelle, how are you today?

### Michelle

I am excellent because we're about to play one of my favourite Maths games. How are you?

### Ayesha

I'm very excited too this sounds good.

Michelle

OK, so I know you've been playing the counting game, but I think you've been playing it so you're always counting up to a number?

That's correct.

### Michelle

And today what we were thinking about is we could show how you can also play it in the reverse, so our target today is zero.

[Michelle points to zero written at the top of the piece of paper.]

OK.

### Michelle

And also, we wanted to show you how when you're playing this game you can use some equipment to help you. So, I've got these bundles of paddle pop sticks over here. Um now I know how much is in them because I've made them, but what do you think when you see this?

[Michelle picks up bundles of craft sticks and puts back down, and then picks up one bundle and puts back down.]

### Ayesha

Hmmm, I think there might be ten in there. So, I might double check that if that's OK.

### Michelle

Of course, it's exactly what mathematicians should do.

### Ayesha

So, I can see that there's three and two more, which is 5. I'm noticing there's another five there, and together that's 10, so I trust that these are going to be 10.

[Ayesha picks up one bundle of craft sticks, spreads them in a fan displaying them individually and counts the craft sticks in the bundle. Ayesha puts the bundle back in the pile.]

### Michelle

Because if you laid them alongside you can see that pretty much 10. So, we need to work out how many we have. But because we've been learning about other ways of determining how many without having to count, we could organize our collection so that we can see how many that we have and use our skills of looking at thinking.

[Michelle picks up a bundle and displays next to the other bundles indicating the same amount in each bundle.]

### Ayesha

What a great idea!

I've got an idea. Ok. Why don't we use a ten frame.

### Michelle

Great idea!

[Ayesha moves bundles into 2 vertical rows, 5 bundles on the top row and 6 bundles on the bottom row.]

### Michelle

Oh, I can see what you're imagining in your brain there is Ayesh is that there's like a 10 frame around that. Is that right?

[Michelle draws a rectangle around the 10 bundles and a horizontal line along the middle making 2 boxes of 5, she then draws 4 vertical lines, creating a ten-frame. One bundle of craft sticks sits out of the ten-frame to the right.]

Spot on.

### Michelle

Aww and I know then I can go like this. That will mean that I have 10 boxes or rectangles uh-huh and so one whole ten-frame, and one more than 11 and eleven 10s.

[Michelle circles the bundles in the ten-frame with her pencil in the air and then points to the one bundle to the right.]

### Ayesha

We rename that is 110.

### Michelle

Alright, so that's where we're starting from today, 110. So, Ayesha when you play you can take away one, 2 or 3 of our bundles and we count back at the same time, and you can start because I'll also show you how we can record our thinking.

[Michelle picks up 3 bundles and places back down in position.]

### Ayesha

Sounds good. So, I will take 2 bundles away, so that's 100. 90.

[Ayesha removes 2 bundles from the screen and Michelle writes down on piece of paper 100, 90 in orange marker.]

### Michelle

Ok. And I think I might say, um, take away two also, so now 80 and 70. And can you record my thinking there Ayesh?

[Michelle removes 2 bundles from screen and Ayesha writes down 80, 70 in blue maker underneath the 100, 90.]

### Ayesha

I'm going to take away three bundles, so 30, 50, 40.

[Ayesha removes 3 bundles and Michelle writes 60, 50, 40 underneath the previous numbers.]

### Michelle

And, ok, I'm going to take away one more, so it is down to 30 three tens. 30.

[Michelle removes one bundle and Ayesha writes down 30 underneath the previous numbers.]

### Ayesha

And I can take away the three 10s that are the left, so 20, 10, zero.

[Ayesha removes the last 3 bundles and Michelle writes down 20, 10 and zero underneath the previous number. Michelle circles the zero and writes 3 exclamation marks next to it.]

Congratulations.

Good game!

### Michelle

Alright now what I wonder Ayesha is if our friends at home would like to have a play, you can start from any number that you like. We started at 110 today but I also wonder if I could have done something differently to have won.

### Ayesha

Wonder what you could have done?

Over to you.

[End of transcript]

## Instructions

• Select a starting number, for example 110.
• Then, select a unit value, for example tens.
• The goal is to be the player who says zero.
• Players can count back by saying the next 1, 2 or 3 number words in the tens sequence.
• Players collect a counter (or a tally mark) if they say the target number.
• A new target number is chosen and players play again.

### For example

• Target number 0 (starting at 110 and counting in tens).
• Player A: 100...
• Player B: 90, 80...
• Player A: 70...
• Player B: 60...
• Player A: 50, 40...
• Player B: 30, 20, 10...
• Player A: zero!
• Player A collects a counter (or tally mark!)

## Discuss

• What would happen if I had said... instead of ...? (Identify a point time, when playing the game, to ask this question.
• How could we change the game to make it more/less challenging?
• What did you notice about playing the game by counting backwards? Did it make your brain work harder or was it less difficult?
• Did you work out a way to play this game so that you didn’t lose? What was your strategy? Did it work?