Go fish (collecting and solving doubles)
A thinking mathematically context for practise resource focussed on using and solving doubles facts
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-CSQ-01
Collect resources
You will need:
playing cards 1-10
someone to play with.
Watch
Watch Go fish (collecting and solving doubles) video (6:47).
[Text over a navy-blue background: Go fish – collecting and solving doubles. 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 white waratah of the NSW Government logo.]
Speaker
Go fish, collecting and solving doubles.
[A title on a white background reads: You will need…
Bullet points below read:
- playing cards 1–10
- somebody to play with.
On the right-hand side of the text is an image of a pair of hands holding a deck of cards.]
Speaker
You'll need some playing cards, one to 10, with all the picture cards removed, and somebody to play with.
[Text over a navy-blue background: Let’s investigate!]
Speaker
Let's play.
[A large white sheet of paper on a blue background.]
Speaker
Hello there, mathematicians. Welcome back. I have one of my favourite mathematicians here with me today. Hi, Holly.
Holly
Hi.
Speaker
We are going to share with everybody today a game called Go Fish, collecting and solving doubles. Now, Holly, when I've played Go Fish before, you try and match your numbers, which we know is actually a double. So, if I get two threes, that's double three. But what about the solving part? What does that mean?
Holly
That means if I actually get a double three, then I need to solve it. So, I would solve it by going, three plus three equals 6. Cause I know that 'cause I did math in my head.
Speaker
Oh, OK. So, you're saying that double three is a known fact for you. So, for me to be able to match and keep the double, to keep the match, I have to solve it as well. OK, that sounds like a really fun game. Alright, Holly.
[The speaker holds out a deck of cards.]
Speaker
So, to play this game, we need a deck of cards.
[She turns the deck over to show the card values.]
Speaker
And all of our picture cards have been removed. Now our picture cards are our ace, king, jack and queen.
[She hands out 7 cards on top of the sheet and another 7 on the bottom of the sheet.]
Speaker
We need 7 cards each.
[She places the rest of the deck in the middle of the sheet.]
Speaker
And then we put the remaining cards in the middle as our draw pile.
[The speaker and Holly collect their cards.]
Speaker
OK, Holly, now I'm going to show everybody at home my cards, so everybody can see. But you can keep yours hidden if you like. It creates a little bit of mystery.
[The speaker holds up her card. From left to right, she has a 3, 1, 6, 8, 7, 10 and 6.]
Speaker
So, already I look at this, and I can see that I have double 6.
[She collects the two 6s and puts them down on the bottom left-hand corner of the sheet.]
Speaker
So, Holly, for me to be able to keep that, double 6, Holly, is 12. Now, for me to remember double 6, I actually think of double 5 being 10.
[She points to both 6 cards.]
Speaker
So, then double 6 must be 12.
[She points to the 6 card on the left.]
Speaker
Because 6 is one more than 5.
[She points to the 6 card on the right.]
Speaker
6 is one more than 5. That's my strategy of remembering what double 6 is. Do you have any doubles there, Holly?
[Holly puts down two 3 cards.]
Holly
Yes, I have double three, which we just explained that it is 6.
Speaker
OK, so, that's a known fact for you. OK, alright, Holly, let's start. OK, you can do the honours.
[The speaker holds out her cards.]
Holly
Do you have a 10?
Speaker
Yes, I do have a 10.
[The speaker hands her card to Holly. Holly puts down a 10.]
Holly
So, 10 plus 10 is easy. It's 20.
Speaker
Two 10s is 20. Yeah. Nice. OK.
Holly
Do you have a...
Speaker
Oh, so, Holly, you're going again because you got a match. So, in this game, if you are successful in getting a match, you get another go, is that right?
Holly
Mm-hmm.
Speaker
OK.
Holly
Do you have a 7?
Speaker
I do have a 7.
[The speaker hands her card to Holly. Holly puts her cards down.]
Holly
That was quite funny 'cause I just saw one, I'll say, that's definitely a 7.
Speaker
Oh, you're doing a little bit of sneaky, and Holly, double 7 is?
[The speaker lifts the card on top.]
Holly
14
Speaker
And how do you know what double 7 is?
[Holly points to the pair of 6s.]
Holly
Because that is 12, and then it's one more than that. And then we have another one. And we know that 12 + 2 = 14 like in two, four, 6, eight, 10, 12, 14.
Speaker
Right, Holly. So, you're using what you knew or what you noticed about two 6es being 12 to solve two 7s being 14?
Holly
Mm-hm.
Speaker
That's really nice thinking.
[Text over a navy-blue background: A little while later…
On top of the sheet is a row of pairs of cards. From left to right, there is a pair of 10, 9, 7, 3 and 3. In the centre of the sheet is a deck of cards. On the bottom of the sheet is another row of pairs of cards. From left to right, there is a pair of 6, 1, 5, and 4. The speaker is holding her cards, obscuring the pair between 5s and 4s.]
Speaker
Holly, do you have a 9?
[Holly hands a card to the speaker.]
Holly
I just picked that up.
Speaker
Wow. Double 9. Now, I remembered what you said about double 9 being two less than double 10.
[The speaker points to the pair of 9s. Then to the pair of 10s.]
Speaker
So, double 9 is 18.
[The speaker collects the 9s and puts them down next to her 4s.]
Speaker
And I can see now that I have 6 pairs. And, Holly, you have 5 pairs. Holly, do you have an eight?
Holly
Go fish.
[The speaker picks up a card from the deck. Then Holly picks up a card. Holly puts a pair down. She picks another card from the deck. The speaker gets a 7 from Holly. She puts the 7s over the 6s. She picks up a card from the deck. She gets a 4. Holly takes the 8 from the speaker and puts it down. She takes the 4 from the speaker and puts the 4s down.]
Speaker
So, Holly, now we have to see who collected and solved the most doubles.
[The speaker moves Holly’s row of cards up the sheet.]
Speaker
Now, I'd like to put mine in the structure of a 10-frame, so I can see. Can we just move yours just out of the way for a moment, so everybody can see?
[The speaker moves her row of cards up the sheet.]
Speaker
OK. 5 and two more I know is 7. So, I collected and solved 7 doubles.
[The speaker moves her cards down. Holly pushes her cards down.]
Speaker
Holly, let's move yours onto the board so everybody can see. I'll move them up here for you. Oh, I can see the 5.
Holly
One, two. (GASPS) Uh-oh, I still have one more.
[Holly puts down a pair of 8s.]
Speaker
Oh. Yes, and you have one more than what I have. You had eight. So, Holly, you are the winner of collecting and solving doubles.
Holly
Woohoo.
Speaker
Over to you, mathematicians. Have fun.
[Text over a navy-blue background: What's (some of) the mathematics?]
Speaker
What's some of the mathematics?
[A title on a white background reads: What's (some of) the mathematics?
Bullet points below read:
- Games provide us with the opportunity to practice our mathematical skills and understanding.
- When we were playing Go Fish, we used our knowledge of 'same' and 'different' to find and make matches.
Below the points is an image of a deck of cards in the middle of a white sheet. A pair of cards in the top right corner and bottom left corner. 5 cards are being held.]
Speaker
Games provide us with the opportunity to practice our mathematical skills and understanding. When we were playing Go Fish, we used our knowledge of 'same' and 'different' to find and make matches.
[A title on a white background reads: What's (some of) the mathematics?
Bullet points below read:
· We also used different strategies to solve double facts.
o Sometimes we used known facts.
o Sometimes we used known facts to solve ones that we don't know just yet. For example, Holly used what she knew about double 6 being 12 and her knowledge that 6 is one less than 7 to solve double 7.
o We also used knowledge of spatial patterns and structures like a 10-frame to work out who had the most or least number of pairs.
On the right-hand side of the points are two images. The one at the top is an image of an open palm over a pair of 6s. The image below is a 10-frame with two rows of 5 pairs of cards, and another row below of 2 pairs of cards.]
Speaker
We also used different strategies to solve double facts. Sometimes we used known facts. Sometimes we used known facts to solve ones that we don't know just yet. For example, Holly used what she knew about double 6 being 12 and her knowledge that 6 is one less than 7 to solve double 7. We also used knowledge of spatial patterns and structures like a 10-frame to work out who had the most or least number of pairs.
[ 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
- Each player gets 7 cards. The rest of the cards are placed in a pile in the middle as the draw pile.
- Players try to make matches, that is, pairs of cards that are the same
- Once players can't make any more matches using their own cards, they can take turns to ask their opponent for a card.
- If their opponent has a card of that number they must give it to the asking player.
- If they don't, they say 'go fish' and the player gets a card from the central pile of cards.
- For the player to keep the match they must solve the doubles fact. For example, if a player collected a double 9, they must solve and say ‘double 9 is 18’ to their opponent.
- If at any point a player has no cards left, they can pick up another 7 cards from the draw pile.
- Play continues until all there are no cards left in the draw pile and/or all matches have been made.
- The player with the most matches at the end is the winner!
Discuss/reflect
- How many pairs did you collect?
- Is this more than, less than or the same as your opponent?
- What’s the difference between how many pairs you collected and how many pairs your opponent collected?
- What strategies did you use to solve the doubles?
- If you played the game again tomorrow, what’s an adaptation we could make.