Garbage!

A thinking mathematically context for practise resource focussed on using counting sequences and knowledge of number relationships such as before, after and between

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
• MAE-RWN-01
• MAE-RWN-02

• MAO-WM-01
• MA1-RWN-01

Collect resources

You will need:

• playing cards A-10

• someone to play with.

Watch

Watch 'Garbage!' video (4:44).

Compete to create a sequence using number cards.

Transcript of 'Garbage!' video

[Text over a navy-blue background: Garbage! Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning Team (NSWMS PL team). In the lower right-hand corner is the red waratah of the NSW Government logo.

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

• Playing cards from Ace to 10

Speaker

To play, you'll need some playing cards from ace to ten, and someone to play with. You might even like to play in teams. OK, let's learn how to play.

[Text over a navy-blue background: Let’s play!

2 rows of 10 playing cards are laid out on the floor, one on top of the other. The rest of the deck sits in between the rows.]

Hi, Sam.

Hi.

Speaker

OK, so today we're going to share one of our favourite games with all the mathematicians out there, called...?

Garbage.

Speaker

And to play this game, we need a set of playing cards from ace through to ten. We've got cards that actually have the number one, so we'll be playing with that card set today, and you arrange them in two sequences. You can choose to change your number range if you wanted to, couldn't we, Sam?

Sam

Maybe like 11 to 20?

Speaker

Yeah, so if you had cards that showed 11 through to 20, then you could choose to do that today. We are choosing to stick with one through to ten. So, the aim of the game is to be the first to complete your sequence from one through to ten without getting too many garbage cards. So, over to you, Sam, you can start.

[Sam picks a card from the deck, turns it over to reveal a 5. He takes the 5.]

Oh, five.

Speaker

OK.

[Sam points to the middle two cards of his sequence.]

Sam

I know that these two cards are halfway.

Mmm.

Sam

Five and six , so...

Speaker

Mmm.

[Sam places the 5 over the fifth card. He takes the fifth card underneath and turns it over to reveal an 8.]

Sam

Oh, I got an eight.

[The Speaker points to the card furthest on the right.]

Speaker

So, Sam, sorry, is that number one there?

[Sam points to the card furthest on the left.]

Sam

I thought number one is over here.

[The Speaker points to the card furthest on the right.]

Speaker

Yeah, number one's over there for you, Sam.

[Sam takes the fifth card from the right out of the sequence. He places the 5 over the fifth card’s space. He reveals the fifth card – it’s a 7.]

Sam

Seven. Oh, no. Seven is two after five.

[Sam places the 7 over the seventh card in the row.]

Speaker

It's two more than five, that's a good strategy.

[Sam takes the card under 7.]

Sam

I know one is the first number.

[Sam takes his card, number one, over to the first card in the row. He takes the first card, and places the 1 in its space.]

Mm-hm.

Sam

Nine.

[Sam places 9 under the ninth card. He takes the ninth card and places 9 in its space.]

Sam

The number before ten.

Yes, I see.

Sam

Four, number before five.

[Sam takes the fourth card away and places 4 in its space.]

Speaker

Like how you're using all your relational knowledge there.

Sam

Ten at the very end.

[Sam takes the tenth card away and places 10 in its space.]

Speaker

You're on a good run, Sam.

Sam

Ten again, that's garbage.

[Sam places the 10 next to the deck.]

Speaker

Ah, your first garbage card. Alright, fingers crossed.

[The Speaker takes a card from the deck – it’s a 7.]

Speaker

Seven, OK, so, I know something about seven, it's over halfway, and I'm actually going to count back three. Ten, nine, eight, seven,

[The Speaker takes the seventh card and places the 7 in its space. She turns the seventh card over to reveal a 3.]

Speaker

There we go. Three, I know that is in the third position in my number sequence.

[The Speaker takes the third card away and places 3 in its space. She turns the third card over to reveal a 10.]

Speaker

Ten. I'm going to use your strategy of knowing that that is the last number in the sequence.

[The Speaker takes the tenth card away and places 10 in its place.]

Speaker

So, it must be in the last position.

[The Speaker reveals the tenth card - it’s a 1.]

Speaker

Number one, first position.

[The Speaker takes the first card away and places 1 in its space. She turns the first card over and reveals a 5.]

Speaker

Five. Ah, yes, two after three, and also two before seven.

[The Speaker takes the fifth card away and places 5 in its space. She turns the fifth card over and reveals a 4.]

Speaker

Exactly in the middle. Four.

[The Speaker takes the fourth card away and places 4 in its place.]

Speaker

Oh, goodness, Sam.

[The Speaker reveals a 7.]

Speaker

[The Speaker places 7 on the garbage pile, next to the deck.

Sam picks a card from the deck and reveals it’s a 3.]

Sam

Three. Well, right before four.

[Sam takes the third card away and places 3 in its space.]

Sam

Nine, oh.

[Sam places the 9 on the garbage pile.]

This is garbage.

Speaker

That is garbage.

[The Speaker takes a card from the deck.]

Speaker

One, garbage.

[The Speaker places the 1 on the garbage pile.

Sam takes a card from the deck and reveals it’s a 2.]

Sam

Two. Not garbage.

[Sam places the 2 over the second card.]

Speaker

Oh, well done, right in between one and three.

[Sam turns over the second card and reveals it’s a 4.]

Sam

Four, oh, that's garbage.

[Sam places the 4 over the garbage pile.

The Speaker takes a card from the deck and reveals it’s a 3.]

Speaker

Three. Garbage.

[The Speaker places the 3 on the garbage pile.

Sam takes a card from the deck and reveals it’s a 4.]

Sam

Four. Garbage.

[Sam places the 4 on the garbage pile.

The Speaker takes a card from the deck and reveals it’s a 5.]

Speaker

Five. Garbage.

[The Speaker places the 3 on the garbage pile.

Sam takes a card from the deck and reveals it’s an 8.]

Eight. Oh, yes.

Speaker

Oh, well done, right in between...

[Sam places the 8 under the eight card. He turns the eight card over to reveal a 6.]

SAM
And six.

Speaker

(GASPS) Oh, well done, Sam.

[Sam takes the sixth card away and places 6 in its space.]

Speaker

So, you are the winner because you are the first to complete your sequence. Well done!

[Sam arranges his cards. He picks up the deck.]

Sam

Well, we could also have played that there are knights.

[Sam takes a knight card from the deck.]

Sam

And these are wild cards. Say, if I still don't have a six.

[Sam takes the 6 card.]

Sam

And I really need it and I pick up this.

[Sam places the knight in the sixth card.]

Sam

I could say that that's gonna be my wild card and that will be the six.

[Sam takes the knight card away and puts the 6 back there.]

Speaker

Ah, yes, that makes sense. OK, so, you can choose to include some of your picture cards. So, if you had a standard deck, Sam, you might choose to include jacks, for example, yeah, as your wild. Great. Alright, congratulations, Sam.

[Sam puts the deck back down.]

Sam

Thank you.

[DESCRIPTION:
Text over a navy-blue background: What’s (some of) the mathematics?]

Speaker

So, what's some of the mathematics?

[A title on a white background reads: What’s (some of) the mathematics?

Text below reads: Games can provide a great opportunity to practice and use our understanding. In the game Garbage, we can use what we know about:

• The counting sequence from 1 to 10, and from 10 to 1. (Underneath: an image of Sam’s cards in sequence appears.)
• Important relationships like before, after and between. (Underneath: an image of the Speaker’s cards appears with the Speaker holding 4, along with a red speech bubble that reads: I know 4 goes here because it is between 3 and 5. I also know it goes here as 4 is the number before 5.]

Speaker

Well, games can provide a great opportunity to practice and use our understanding. In the game Garbage, we can use what we know about things like the counting sequences from one to ten and from ten to one. We can also use what we know about important relationships like before, after and between. So, for example, I know four goes here because it's between three and five. I also know it goes here as four is the number before five. OK, mathematicians, have fun playing Garbage.

[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

• Shuffle the cards and place the pile face down in the middle of both players.
• Each player draws 10 cards each.

• Players organise their 10 cards in a row in front of them face down.

• Player 1 draws a card from the middle pile.

• Player 1 places this card in the matching position in their row of 10.

• Player 1 then picks up the card in its place. For example, if a 4 is drawn, player 1 places the card in the fourth position and picks up the card in that position.

• Player 1 looks at the card and decides whether it can also be placed in their row.

• Player 1's turn is over when they can no longer place a card in their row. This card is thrown away as 'garbage'!

• Player 2 draws a card to begin their turn and follows the same steps as player 1.

• The first player to complete their entire row of cards is the winner!

Other ways to play

• Use a picture card that a player can use to represent any number.

• If a player puts their unwanted card in the garbage and the other player needs it, it can be picked up to use.

• A king can be played to turn back over another player's card.