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
Outcomes
- 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).
[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…
Bullet points below read:
- 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.]
Barbara
OK, ready everyone?
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.
Barbara
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.
Speaker
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
OK, your go.
[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.]
Barbara
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?
Bullet points below read:
- 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.