# Counting game (by multiples of 5)

Stage 2 – A thinking mathematically context for practise resource focussed on counting forwards and backwards by fives

## 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
• MA2-MR-01

## Collect resources

You will need:

• pencils or markers

• something to write on.

## Watch

Watch Counting game (multiples of 5) video (3:35).

Reach the target number by counting forwards and backwards by fives.

### Michelle

OK Barbara, how are you today?

[Screens shows a blank piece of A4 paper.]

### Barbara

I'm good, how are you, Michelle?

### Michelle

Very well thank you. I thought today we could play one of my favourite games of strategy

that you can play pretty much anywhere.

Ok.

### Michelle

So, we just call it the counting game.

You can play it in lots of different ways using any number that you like.

So, today to get us started. I'd like you to think about the target number.

Let's make it. We want to count by 5s today so it has to be a number that would be in the counting sequence by 5s. And your favourite 2-digit number.

### Barbara

Oh, I have lots of favourite 2-digit numbers, but my favourite today is 85.

### Michelle

So, I know that's going to be a 5 number 'cause it ends in a 5 by 5 or zero, so 85 is our target and then we play it just by counting together all the way up to 85.

[Michelle writes ‘85’ and circles it at the top of the paper in the centre.]

But when you count, you can either say one number word, 2 number words or 3 number words.

So, you could say 5 or 5, 10 or 5, 10, 15.

Ok.

### Michelle

We take it in turns and you win if you're the person that gets to say the target number.

### Barbara

And I should say it because I chose it.

### Michelle

I'm hoping to get.

Yeah. Ok.

### Michelle

And because we're mathematicians. We're also going to record our thinking so when the numbers that you say I'll record that in my marker and you can record my moves too, so let's just have a go and you'll learn through playing.

Can I start?

Of course.

### Barbara

I'm going to say. 5, 10.

[Michelle writes 5, 10 in orange marker on the left side of the page.]

### Michelle

Alright, I'm going to say 15, 20, 25 and.

### Barbara

Ok where do I write that?

Underneath.

### Barbara

Ok.

[Barbara writes 15, 20 ,25 in blue marker underneath the 5, 10.]

### Barbara

Of course. I will say 30, 35, 40.

[Michelle writes 30, 35, 40 in orange marker underneath the previous numbers.]

### Michelle

I will say 45.

[Barbara writes 45 in blue marker underneath the previous numbers.]

### Barbara

I wonder why you only choose one? I'm going to say 50, 55.

[Michelle writes 50, 55 in orange marker underneath the previous numbers.]

### Michelle

Sixty.

[Barbara writes 60 in blue marker underneath the previous numbers.]

### Barbara

Just 60. Now we're getting quite close, so I think that now I need to start really thinking about this.

But because it's a new game I think because I'm not sure what to do next, so I'm going to say.

Oh, hold on a minute. I'm thinking now that if I get you to close, you'll be able to win, so I don't want to get you that close.

So, I don't want you to say OK. I'm only going to choose a few numbers to so I can.

Ok.

### Barbara

[Michelle writes 65 in orange marker underneath the previous number.]

### Michelle

Ok. And I'm going to say 70.

[Barbara writes 70 in blue marker underneath the previous number.]

### Barbara

And I am going to say... I'm very excited because I can say 75, 80, 85. Which means I win!

[Michelle writes 75, 80, 85 in orange marker and circles the 85.]

### Michelle

Congratulations, you're the winner today.

Wow.

### Michelle

But now that we've got our recording, we could also go and investigate. Is there a way that you can either guarantee you win or at worse that you never lose?

Yeah, of course.

### Michelle

Off you go let's go see what happens.

### Michelle

Let's explore.

[End of transcript]

## Instructions

• Select a target number for example, 85.

• Then select a unit value for example, fives.

• The goal is to be the player who says the target number.

• Players can count on by saying the next 1, 2 or 3 number words in the fives 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 85

Player A : 5, 10,

Player B: 15, 20, 25...

Player A: 30, 35, 40...

Player B: 45...

Player A: 50, 55

Player B: 60

Player A: 65,

Player B: 70, 80, 85!

• Player B collects a counter (or tally mark!)

## Reflection

• Is there a way to play so that you never lose?
• I wonder if Michelle could have changed her moves in any way to win. Could you give Michelle some advice? If she had said different number words, how could she have won?