# Strike it out (addition and subtraction to 20)

Stage 1 to 3 – A thinking mathematically context for practise focussed on communicating and exploring representations using additive 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-CSQ-01
• MA1-RWN-01
• MA1-RWN-02

• MAO-WM-01
• MA2-AR-01
• MA2-AR-02

• MAO-WM-01
• MA3-AR-01

## Collect resources

You will need:

• 3 colour pencils or markers
• paper.

## Watch

Watch Strike it out video (7:44)

Take turns to eliminate numbers 0 to 20 on a number line.

### Transcript of Strike it out video

[On a sheet of paper, is a handwritten title in the top left corner that reads: Strike it out!]

### Michelle

OK, I'm joined here with Barbara today. Hi Barbara.

Hi, Michelle.

### Michelle

And we wanted to play Strike It Out. Barbara, have you played this game before?

### Barbara

I haven't, will you teach me?

### Michelle

I sure will. Now, the first thing that we need to play is a number line as our game board for this game.

[In the middle of the sheet, Michelle draws a line across.]

### Michelle

So if I do this, it's got a bit of a bump in. It doesn't matter.

[On the left end of the line, she places a mark and labels it with the numeral 0. On the right end of the line, she places a mark and labels it numeral 20.]

### Michelle

It goes from 0 to 20 but we need to fill in all the other numbers.

### Barbara

Well, I've got an idea. If you look around the middle…

[Barbara points to the middle of the line.]

### Barbara

…you might be able to put 10.

### Michelle

Oh, that's a really good idea, because 10 is halfway between zero and 20.

[In the middle of the line, Michelle places a mark and labels it 10].

Yeah.

### Michelle

OK, and then we could use the same strategy. So from 0 to 10, halfway would be five.

[In between 0 and 10 on the line, Michelle places a mark and labels it 5].

### Barbara

And then halfway between 10 and 20 you'll have 15.

### Michelle

Yeah, so that's about halfway there, do you agree.

[In between 10 and 20 on the line, Michelle places a mark and labels it 15].

Yep.

### Michelle

Yep, and then we would need to fifth these components.

[Michelle points to the space between 0 and 5.]

### Barbara

I don't think I know how to fifth but we can halve it.

### Michelle

Well, I learnt this strategy from a professor, Professor (UNKNOWN) she, she showed us this strategy.

Oh, show me.

### Michelle

[With her left forefinger, Michelle traces the line from 0 across a few spaces.]

### Michelle

So she said you just sort of need to move your finger along and you can start to see that if I halve this section…

[She places her right forefinger halfway between the 0 and 5. Then moves it slightly to the left.]

### Michelle

…and halved it again…

[She wiggles her left forefinger along the line.]

### Michelle

…would that be about the same distance as my fingers moved here?

OK, yeah.

### Michelle

So if I move my finger and say if I halve there…

[She moves her right forefinger back in the middle of 0 and 5.]

### Michelle

…and I halve that again…

[She moves her right forefinger slightly to the left.]

### Michelle

…it would be, are they now about the same.

Yeah.

### Michelle

So if I go…

[She places a mark above her left forefinger.]

### Michelle

…that's about one fifth and then if I halve this…

[She places a mark in the middle of the previous mark and 5, a mark in the middle of the 2 marks and halfway to 5.]

### Michelle

…and have these portions, oh, that's a bit wonky on this side…

[She points to the space near 5.]

### Michelle

…but it's not bad for estimating and I can fill it in.

[Below the marks, she labels them 2, 3, and 4.]

### Michelle

Do you want to have a go.

### Barbara

OK, so I'm trying to imagine where the six would be…

[Barbara places her left forefinger on the line slightly after 5.]

### Barbara

…and then I'm halving and halving again and seeing if that's about the same.

Yeah.

### Barbara

So I'm pretty happy with that actually.

[She places a mark where her finger was.]

### Barbara

So then I can halve this…

[She places a mark in between the previous mark and 10.]

### Barbara

…and halve it again…

[She places a mark in the middle of the 2 marks, and then halfway to 10.]

### Barbara

…and then I can put six, seven, eight , nine, wow.

[Below the marks, she labels them 6, 7, 8 and 9.]

### Michelle

Yeah, because there are the numbers between five and 10. Here, you fill out the numbers between 10 and 15.

[Barbara repeats the process in between 10 and 15.]

### Barbara

OK, so I'll do the same thing. I'm still happy with that. OK, then halfway, half again. It's a little bit wonky, but that doesn't matter, does it?

[Below the marks, she labels them 11, 12, 13 and 14.]

### Michelle

No, because we're estimating.

### Barbara

OK, actually, that's pretty good.

### Michelle

It's pretty good. Yeah, alright, I'll do the last one.

[Michelle repeats the process in between 15 and 20.]

### Michelle

I reckon, about there and the numbers between 15 and 20…

[Below the marks, she labels them 16, 17, 18 and 19.]

### Michelle

…are 16, 17, 18 and 19. Alright, we're ready to play. So this is how you play. You can be blue, I will be orange and you just pick any two numbers that you'd like to make a number sentence with or an equation with. So, for example, you could say one plus two is three or five minus four is one, which is addition and subtraction. So what are you thinking you might like to start with and I'll show you how to record it.

### Barbara

OK, so I'm thinking maybe 10 plus five is 15.

### Michelle

Awesome, so you cross out the 10…

[Michelle points to 10 on the line, then crosses it with her finger.]

### Michelle

…or strike out the 10.

[She points to 5 on the line, then crosses it with her finger.]

### Michelle

Strikeout the five and circle the 15.

[She circles 15 with her finger. Barbara with a blue marker crosses out 10 and 5, and circles 15.]

### Barbara

OK, and it's equivalent value to 15 so I can circle that one.

### Michelle

So then you just need to record your move here.

[Michelle points to the space below the line on the left-hand side.]

### Barbara

OK. So I'm joining five…

[On the space, Barbara writes: 5.]

### Barbara

…and 10…

[Next to 5, Barbara writes: + 10 = 5.]

### Barbara

…and that's equivalent in value to 15.

### Michelle

Yeah, and so now I have to use the 15.

[Michelle points to 15.]

OK.

### Michelle

Yeah, and I have to see if I can use additional subtraction as well. So I can't do something like 20…

[Michelle points to 20, 15 and 5.]

### Michelle

…minus 15 is five because the five is used. So I have to only use unused numbers. I could do something like 15…

[Michelle points to 15, 14 and 1.]

### Michelle

…minus 14 is one. I could do something like 15…

[Using an orange marker, Michelle crosses out 15 and 4, and circles 19.]

### Michelle

…plus four is 19 and I'm going to record my go here.

[Below the line, on the right-hand side, Michelle writes: 15 + 4 = 19.]

### Michelle …

…15 combined with four is equivalent in value to 19 and now you have to use the 19. You're go.

### Barbara

OK so, I start from 19…

[Barbara points to 19.]

### Barbara

…so I strike it out?

### Michelle

Sure.

[Barbara crosses out 19.]

### Barbara

And I subtract 17.

[Barbara crosses out 17.]

### Michelle

Yeah, if that's what you want.

### Barbara

And then the answer is two…

[Barbara circles 2.]

### Barbara

…because 19 take away 17 is two. And now you need to start from two.

[Below her writing, Barbara writes: 19 – 17 = 2.]

### Michelle

I do. And the way you win is to be the last person that can record a go.

OK, so I can...

### Michelle

Eventually try to block people.

### Barbara

So I can think about being tricky here.

You can.

### Barbara

OK, because I like being tricky.

### Michelle

So do I. So I'm going to say two…

[Michelle crosses out 2 and 7, and circles 9.]

### Michelle

…plus seven is nine.

[Below her writing, Michelle writes: 2 + 7 = 9.]

### Michelle

So two combined with seven is equivalent in value to nine. You're turn.

### Barbara

OK. Alright, so I'm at nine. Oh, 20 is still available, isn't it?

[Barbara crosses out 9 and 11, and circles 20.]

### Barbara

OK, so I'm going to combine nine and 11 for a total of 20.

### Michelle

OK, record you're go.

### Barbara

Of course.

[Below her writing, Barbara writes: 9 – 11 = 20.]

### Michelle

OK, I still think there's, I'm trying to be strategic but I still think there's maybe too many numbers for me to find out what it is. So I'm going to say…

[Michelle crosses out 20 and 14, and circles 6.]

### Michelle

…20 subtract 14 is equivalent to six.

[Below her writing, Michelle writes: 14.]

### Michelle

So 14…

[She crosses out 14. Below Michelle writes: 20 – 14 = 6.]

### Michelle

…20 minus 14 is equivalent to six.

### Barbara

OK. Six and, I might just need some thinking time.

### Michelle

That's alright. We can work together too if you want. What are you thinking?

Do I trust you?

Maybe not.

### Barbara

So, I think I want to use some of these numbers up here. So I think that I...

### Michelle

Oh, yeah, there's a way.

### Barbara

So I want to go up from six. So I'm thinking 12 could work because if I combine six…

[Barbara crosses out 6 and 12, and circles 18.]

### Barbara

…and 12 then it's equivalent to 18.

### Michelle

Yeah, write it down.

[Below her writing, Barbara writes: 6 + 12 = 18.]

### Michelle

Oh, now this is going to be tricky, I think, for me, because from 18…

[Michelle points to 18.]

### Michelle

…and I only now have 16, 13, eight, three, one and zero. So if I did 18 minus one, that would be 17 which is in use. 18 minus 16 would be two, which has been used. 18 minus 3 would be five, it's been used. 18 minus 10 would be 10, that's been used. If I did 18 plus anything, it makes it bigger. So there's no options for me which means I think you might have won.

### Barbara

Oh, beginners luck.

### Michelle

Can you see anything?

### Barbara

Let's see. Um...no.

### Michelle

I wonder if anybody out there who's joining us can say anything. So over to you guys. Can you see, is there a way that I could possibly win or has Barbara got this one?

### Barbara

And I think I want to play this game lots of times because I think the more I play it, the more strategic I can be and the more I can trap you. I kind of trapped you by accident.

### Michelle

Alright, have fun.

[Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]

[End of transcript]

## Instructions

• Start by drawing a number line from zero to 20.

• The first player chooses two numbers from the number line and crosses them out.

• The same player then circles the sum or difference of the numbers and records the calculation.

• For example, in the demonstration video, the first go looked like this:

• The second player must start their turn by crossing out the number circled by the first player.

• The second player then crosses out a second number not already used.

• Player 2 then circles the sum or difference of the numbers and records the calculation.

• For example, in the demonstration video, the second go looked like this:

• The player who stops their opponent from being able to take a turn is the winner.

## Discuss

• Is there a way Michelle can still win?

• If not, what could Michelle have done differently in her game to increase her chances of winning?