# Closest to 100 (additive strategies)

Stages 2 and 3 – A thinking mathematically context for practise focussed on developing flexible additive strategies and reasoning

## 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-AR-01
• MA2-AR-02

• MAO-WM-01
• MA3-AR-01

## Collect resources

You will need playing cards from Ace to 9 (where Ace = 1) or a 4 sets of 1 to 9 cards you’ve made at home.

## Watch

Watch Closest to 100 video (1:18).

Use additive think to get close to 100.

### Speaker 1

[Screen shows a teacher and 4 students in pairs, sitting on the floor in a semi-circle with 2 mini whiteboards, playing cards and 2 markers in blue and green.]

OK, turn your cards over. Share them with your partner. Turn them over. Have a look.

[Screen shows student turning over the cards.]

Now who can remember, what is the target number?

### Speaker 2

100.

[Screen reads what are you thinking? Screen shows students sorting through the cards.]

### Speaker 2

So, 2 and 8 are 10. They are 10. And then these two [cards] are 10. So, these [cards] are 20 and we have this which is a 5.

So, we have 25.

[Screen shows students adding the numbers up on the cards. The cards are 2, 8, 5, 5, 4 and 1.]

### Speaker 1

Is that as high as you can get... to 100? Is there something else we could try?

### Speaker 2

We could make maybe 85.

### Speaker 1

Keep going Colin.

### Speaker 2

Oh yeah, 85. I'm thinking like we could go... Yeah 85...and with the 15. We need to use all of the cards.

We don't have to, I don't think.

Okay. So, you don't have to use all the cards.

Oh, ok! So, we are done. 85 plus 15. That's 15.

[Screen shows students shuffling cards around to total 100. The students lay the cards 8 and 5 next to each other to make 85 and then place the cards 1 and 5 next to each other underneath to make 15.]

That would make 100. We did it!

We did it!

[End of transcript]

## Instructions

• Players shuffle the cards and put them in a central pile. One person takes 6 cards and places them face up for everyone to see.
• The goal is to use addition and subtraction to get as close to a total of 100 as possible.
• Each card can only be used once. It can be used to form a 1- or 2-digit number.
• Players score 0 points if they are able to reach exactly 100. Otherwise, they work out their points based on the difference between their total and 100. For example, if a team created a total of 98, they would score 2 points.
• Keep a cumulative total of their difference to 100. The winner is the team to have the lowest points score at the end.

## Watch

Watch Closest to 100 – Sam's variation video (1:18).

Closest to 100 variation using 'wild' cards.

### Michelle

I'm back here with one of my favourite mathematicians again. Hi Sam.

Hi Michelle.

### Michelle

Now Sam, you were telling me that you have a different way of playing "How close to 100"

Hey.

### Michelle

So, you came up with this idea using UNO cards. Do you want to explain what your idea was with the wild card?

[Michelle places a deck of UNO cards down]

### Sam

So, we would say, you would go through them, you would keep all... you could, so you could keep all these.

Then you would deal it out you get 6 each.

[Sam deals the cards out and gives Michelle and himself 6 cards each.]

Mhm.

### Sam

Then, we would then if you got any like wild cards.

[Michelle displays a wild card.]

### Michelle

Oh yeah, I got one.

### Sam

Then you could, you can only use 2 at a time.

OK.

### Sam

Like in one game. So, so like if you want to, and like instead of having to put them all in how many players there are you, for each player, you would put in 2 wild cards.

### Michelle

Ok, what is a wild card let me do?

[Michelle places her cards down showing a 5, a wild card, an 8, 2, 6 and 9 playing card.]

### Sam

It lets you put down any number you want, but it can't be 100 or it has to be a two-digit number.

### Michelle

Alright, let's play.

Alright.

### Michelle

How many ways do you think you can?

I think I can make 100 using my cards because the numbers can represent ones or tens.

And I can definitely find one way and I think I might have 2 ways.

### Sam

80.

[Sam places his cards down, placing down an 8 followed by a one and then another one.]

### Michelle

So, you're saying 8 is 8 tens.

### Sam

Yes, 80, 10 and 10.

### Michelle

Oh yes because 8 tens and one ten and another 10 is 10 tens which we call 100.

[Michelle points to the 8, then the one and then the other one.]

OK, well, I could do 8 tens and 2 tens which we call 100 but I think I could also do something like, um, I'm wondering.

[Michelle moves her 8 and 2 playing cards up and then moves them back down.]

### Sam

You could do 92 and 8.

[Sam moves Michelle’s cards 9, 2 and 8 up into a horizontal row.]

### Michelle

Oh yeah, so I could say that's 9 tens and 2 more so 92 plus 8. And that's a really nice idea.

[Michelle then places the 2 on top of the 9 and moves the 8 to the side.]

I was also thinking about Sam, I could do something like, oh yeah, 9 tens plus 6 tens minus 5 tens.

[Michelle then places cards back in bottom row and then moves the 9, 6 and 5, Michelle then places the 3 cards back into the bottom row.]

Yeah, Oh yeah.

### Michelle

Yeah, because 90 plus 60 would be 150 minus 50 would get me to 100 again. What about your cards? Have you got another way?

### Sam

I think I could do 80 plus 50 minus 30.

[Sam places his 8, 5, and 3 playing cards in a row.]

Oh yeah.

And then. Yeah.

### Michelle

You could also just do this one 5 tens plus 5 tens is 10 tens.

[Michelle moves Sam’s card into a row of 8, 5, 5, and 3, she then pushes one of the 5 back from the row. Sam then moves a 5, a one and another one into a row.]

### Sam

Oh yeah or I could do.

Oh, 10 tens.

### Sam

50 times 2. It goes one and one equals 2.

Oh yeah.

### Sam

And then that would be 100.

### Michelle

Oh yeah, so you can use multiplication if you want to extend in your game too yeah.

So why is this your favourite game Sam?

### Sam

I just like to add to 100 and I really like addition and like all maths and stuff.

### Michelle

Yeah, does it make your brain think?

Yeah, I guess.

### Michelle

That's cool. Thanks for showing me your version of the game.

### Sam

Thank you.

[Sam gathers his card into a pile.]

### Michelle

Welcome.

[End of transcript]

## Discussion

What are some variations you could develop?