# Turn over 3 (using known facts to 20)

A thinking mathematically context for practise focussed on reasoning and using known facts to combine quantities

## 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-CSQ-01

## Collect resources

You will need:

• playing cards (ace to 10 representing 1-10 and the jokers representing zero)

## Watch

Watch Turn over 3 video (5:58).

Find doubles, near doubles and combinations to 10 and 20.

### Transcript of Turn over 3 video

[A title over a navy-blue background: Turn over 3. Small font text in the upper left-hand corner reads: NSW Department of Education. In the lower left-hand corner is the white waratah of the NSW Government logo.

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

• playing cards from Ace to 10 and the Jack (who is representing zero)
• some paper
• a marker

On 2 large sheets of paper is a table with headings: Flipped, Knew, Used, Cumulative Total. The table on the left has green headings, the one on the right has red.

A red marker is below the tables.]

### Speaker

Alright mathematicians, the battle is back. (laughter) Barbara, since you're such an amazing shuffler, can you please shuffle our cards?

[Barbara shuffles the cards.]

### Speaker

Come on, show us your amazing talent. So good. OK, so the way we play is, flip over three cards.

[The Speaker takes a card from the pile and flips it – she gets a 4. She flips 2 more cards, 9 and 10.]

### Barbara

Have we got all the cards in here?

### Speaker

We have one to ten and we have the Jack which is representing zero.

Oh, OK.

### Speaker

And what you're looking for are known facts that we can use when we're solving problems. So, for me, I know I can use things like doubles and near doubles and numbers that combine to make ten or 20. But you can only use two cards.

### Barbara

OK, well, ten and nine that's I know that's 19.

Yes.

### Barbara

It's ten and nine more, or it's nearly double nine. Is that a...

### Speaker

Yeah, so it's a near double.

### Barbara

It's a near double.

[The Speaker takes the table with the red headings and writes under Flipped: 4, 9, 10. Under Knew, she writes: Double 9 = 18; 18 + 1 = 19. Under Used, she writes: Near doubles. Under Cumulative Total, she writes: 19. She draws a line below her writing.]

### Speaker

So, you flipped four, nine and ten, and you are using... you knew that double nine is 18, and 18 and one more is 19. So, you use near doubles. And so far your cumulative total is 19 because that's the first number that you made. And we get five flips each to see who gets the biggest total at the end.

### Barbara

Oh, OK.

[The Speaker flips 3 cards – 8, 5, 2.]

### Speaker

OK. Oh yes, because eight and two is a computational pattern actually where eight and two always combine to make ten, so I used combinations to ten.

[Barbara takes the table with the green headings and writes under Flipped: 5, 2, 8. Under Knew, she writes: 10 is 8 and 2.]

### Barbara

OK, so you flipped five, two and eight. And then you knew eight and two. And would I just write 8+2?

### Speaker

Yeah, I just know ten is eight and two. So, you could do ten is eight and two. So, I used combinations to ten.

[Under Used, Barbara writes: Combinations to 10. Under Cumulative Total, she writes: 10. She draws a line below her writing.]

### Barbara

And then your cumulative total for now is ten, OK.

### Speaker

OK, and they go in there, down the bottom. Your go.

[Barbara flips 3 cards – 4, 3, 6.]

### Barbara

OK. OK, so four, three and six, but I know that six and four also make ten, so it's combinations to ten.

[The Speaker writes in the table with the red headings, under Flipped: 4, 3, 6. Under Knew, she writes: 6 + 4 = 10. Under Used, she writes: Combinations to 10.]

### Speaker

Six and four combines to make ten. And you used combinations. You could have used any double, too.

### Barbara

I could have used any double, yeah.

### Speaker

But you'd get more points because that would only be seven, whereas that's ten. And so, then what I have to do is 19 and ten more. And so, I know this is one, ten and nine. And then it would be two tens and nine, and that's 29. So, that was actually nice for my brain to figure out. OK, my go. OK, well, I have to do a near double. So, double one - actually double two is four, minus one is three.

[Under Cumulative Total, the Speaker writes: 29. She draws a line below her writing. She flips 3 cards – 4, 2, 1.]

### Barbara

OK, so four, two and one. And you knew double two is four and then take away one.

[Barbara writes in the table with the green headings, under Flipped: 4, 2, 1. Under Knew, she writes: Double 2 = 4; 4 - 1 = 3. Under Used, she writes: Near double. Under Cumulative Total, she writes: 13. She draws a line below her writing.]

### Speaker

Yeah, and so it was a near double that I used.

### Barbara

And I just write near double, that's all. OK, so your total was three and you had ten, so then, that's 13, ten and three more.

### Speaker

[Barbara flips 3 cards – Ace, 6, 10.]

### Barbara

So, can I do anything here? Because, like, I know how to add ten and six, but we're looking for patterns and we're not looking just for things that I know. So, does that mean...

### Speaker

Because numbers that combine to make ten, like six and four are a special kind of mathematical pattern. And like, double three is a special kind of pattern because it's always six.

### Barbara

And even near doubles as well.

### Speaker

Yeah, so we're actually looking for what we call known facts, but they're a special kind of pattern.

### Barbara

So, not all known facts.

### Speaker

Computational pattern, yeah. So, does that mean that I...

[The Speaker writes in the table with the green headings, under Flipped: 1, 6, 10. Under Knew, Used and she writes: X. Under Cumulative Total, she writes: 29. She draws a line below her writing.]

### Speaker

So, I think you can't go.

### Barbara

Oh, OK. Yeah, so you've got an ace, which is one, a six and a ten and you couldn't go. So, you're still on 29.

### Barbara

OK.

[The Speaker flips 3 cards – 3, 7, 5.]

### Speaker

Nice. Alright, my go. Oh and I can do, seven and three is a pattern, a computational pattern, where seven combined with three will always be ten.

[Barbara writes in the table with the green headings, and under Flipped: 3, 7, 5. Under Knew, she writes: 7 and 3 is 10. Under Used, she writes: Combinations to 10. Under Cumulative Total, she writes: 23. She draws a line below her writing.]

OK.

### Speaker

And I'm catching up.

### Barbara

You are. So, seven and three is ten. And you use combinations to ten again. OK, so, oh, that's easy. You had one ten and three more. Now, you have two tens and three more, which I can rename as 23.

### Speaker

Alright, so mathematicians, this is how you play Turn Over 3. Over to you to play, while we keep battling it out. (Laughter).

### Barbara

Go me!

[Text over a blue background: What's (some of) the mathematics?

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

• This game provides a meaningful context to find, and use, ‘known facts such as:
• doubles
• near doubles
• combinations to 10
• This game also provides an opportunity to work on recording ideas.

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

• Using playing cards Ace – 10 (representing one – 10) and the jokers (representing zero), shuffle the cards into a pile.

• Place the pile face down between 2 players.

• Take turns to turn over the top three cards.

• Players look for doubles, near doubles, combinations to 10 and 20.

• Players keep the cards of any known facts they identify and know, justifying their thinking to their partner who records it on the recording sheet.

• Any unused cards are placed into a discard pile.

• Players continue taking turns until the cards run out. When that happens,it is a reshuffle of all of the unused cards.

• Re-distribute them into 3 piles and continue playing.

• The winner is the player with the highest cumulative total at the end of 5 rounds.

## Other ways to play

• For subtraction, choose which cards to combine using known facts and then subtract the third card. Players are able to keep all 3 cards if they are able to identify a known fact and then subtract the third value, explaining your mental computation to the other player.
• Play until the whole deck of cards is used.