Go fish! – partially covered arrays
A thinking mathematically context for practise, focussed on developing multiplicative strategies including the composition of arrays
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
- MA2-MR-01
- MAO-WM-01
- MA3-MR-01
Collect resources
You will need:
- a set of game cards (PDF 602 KB) (with pictures of different partially covered arrays and their matching product)
someone to play with.
Watch
Watch Go fish! partially covered array video (6:55).
[Text over a navy-blue background: Partially covered arrays go fish. 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
Partially covered arrays go fish.
[A title on a white background reads: You will need…
Bullet points below read:
- A set of game cards with pictures of different partially covered arrays and their matching product and somebody to play with.
- somebody to play with.
On the right-hand side of the text are two images: on the left side is an image of a pair of hands holding cards with black dots and rectangles, on the right side is an image of a pair of hands holding cards with numbers.]
Speaker
You will need a set of game cards with pictures of different partially covered arrays and their matching product and somebody to play with.
[Text over a navy-blue background: Let’s play!]
Speaker
Let's play!
[A large white sheet of paper on a blue background.]
Speaker
Hello there, mathematicians. Welcome back. I have Sam with me today. Hi, Sam.
Sam
Hi.
Speaker
Now, Sam, are you familiar with the game Go Fish?
Sam
Mm-hm.
Speaker
Yeah, I think a lot of people probably are out there, but we're going to play a slightly different version. We're going to play partially covered array go fish.
[The speaker puts down a pack of array cards with dots and rectangles, and a pack of product cards with numbers.]
Speaker
So, to play this game, you'll need a pack of partially covered arrays and the matching product cards.
[The speaker picks up the deck of array card and flips through it. She picks up the deck of product cards and flips through it.]
Speaker
So, you can see here we've got a range of partially covered arrays and the matching product cards.
[The speaker refers to the array card on top of the deck. It has 5 black dots running down the left side, and another 5 black dots running across the top. A blue square fills the space under the dots. She points to the dots on the top right-hand corner and the bottom left-hand corner on the array card. Then she places her palm over the blue square.]
Speaker
Now, partially covered arrays are essentially arrays that have been partially covered where the dots are hidden.
[She turns her hand over, and points to the square. She traces the dots with her finger.]
Speaker
But we know that underneath that rectangle or that square are all of the remaining dots.
[She quickly points along the 5 dots across the top. Then she motions to the product card 25.]
Speaker
And I can read this array as five fives, which I know is 25. So, Sam, to play Go Fish, we're going to shuffle our cards.
[The speaker picks up both packs and shuffles them.]
Speaker
And deal seven each.
[She places 7 cards on top of the sheet. Then another 7 on the bottom of the sheet. She places the remaining pack in the centre of the sheet.]
Speaker
And these stay in the middle.
[The speaker and Sam collect their cards.]
Speaker
Go Fish is about collecting a matching array and product.
[The speaker places an array card with 5 dots running down the side and 2 dots going across, and product card 10 on the top left corner of the sheet. She places the 10 product card over the array card.]
Speaker
So, Sam, you already have matched five twos, which you know is ten. So, there's one match. OK. You can do the honours.
Sam
Do you have the matching array to 20?
[Sam holds out a 20 card.]
Speaker
OK. Let me have a look.
[The speaker holds out her cards. She looks through them.]
Speaker
OK. I don't think so. Oh, actually, so I'm looking for five fours, four fives, two tens, or ten twos.
[She picks out a card with 10 dots running down the side and 2 dots going across. She hands it to Sam.]
Speaker
And this looks like ten twos. So, yes, Sam. Well done.
Sam
Thank you.
[Sam places his matched cards next to the other cards on the sheet.]
Speaker
And because you were successful in gaining a match, you get to go again.
Sam
Do you have the matching array to 50?
Speaker
To 50, OK.
[The speaker holds out her cards. She looks through them.]
Speaker
So, I'm probably looking for an array that is five tens or ten fives. It doesn't look like I've got that one, so, no, Sam, go fish.
[Text over a navy-blue background: A little while later…
On top of the sheet is a row of 5 matched cards. On the bottom of the sheet, is a matched card on the bottom left corner.]
Sam
OK. Do you have the matching array for two threes, the matching product?
[Sam holds out an array card with 3 dots running down the side and 2 dots across.]
Speaker
For two threes, which is six. No, I do not, Sam.
Sam
You seem to have all the arrays.
Speaker
Go fish.
[Sam picks up a card from the pack.]
Sam
Oh, yes. (LAUGHS)
Speaker
Oh, that was a lucky pickup. Put it down here so everybody can see just how much you're winning by at the moment. (LAUGHS) Alright, Sam. Do you have the matching product card for one ten?
[The speakers places Sam’s matched cards on the right edge of the sheet.
She holds out a card with 10 dots going across.]
Sam
One ten product? No, I do not.
Speaker
Go fish again.
[The speaker picks up a card from the pack. She gets a 3 card.
They continue to play.]
Speaker
Do you have the matching product card for two threes?
[The speaker holds out a card with 2 dots running down the side and 3 dots running across.]
Sam
Yes, I do.
[Sam hands over a 6 card.]
Speaker
My final match! Two threes, which is six, Sam, I can see there that you have ten matches. I have seven. So, congratulations. You have won this round of partially covered arrays go fish. So, over to you, mathematicians, to have a go at playing partially covered arrays go fish, and if you want a more of a challenge and extend the number range that you're working with, you can add in the expansion pack.
[The speaker holds out a card pack and flips through it.]
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.
- We used what we knew about the structure of arrays to imagine the dots hiding in the partially covered arrays. For example, we imagined dots hiding underneath the rectangle in this partially covered array to know there were five threes.
Under the points are two images: on the left side is a partially covered array card with 5 dots running down and 3 dots across, a rectangle fills the space below the dots. On the right side is a pink thought bubble over an array card with 3 columns of 5 dots running down the card.]
Speaker
Games provide us with the opportunity to practice our mathematical skills and understanding. We used what we knew about the structure of arrays to imagine the dots hiding in the partially covered arrays. For example, we imagined dots hiding underneath the rectangle in this partially covered array to know there were five threes.
[A title on a white background reads: What's (some of) the mathematics?
Bullet points below read:
- We were practicing making connections between different forms of representations. In this game, we made connections between diagrams and numbers to make a match. For example, we made connections between an array that showed ten rows with two in each row, a diagram, and a product, 20, a number.
Under the points are two images: on the left side is an image of the sheet with Sam holding out a 20 product card and the speaker holding a set of partially covered array cards. In her set, the card on the right has 10 dots running down the side and 2 across. Both Sam’s product card and the speaker’s array card are highlighted pink. On the right side is an image of the array card next to the product card.]
Speaker
We were practicing making connections between different forms of representations. In this game, we made connections between diagrams and numbers to make a match. For example, we made connections between an array that showed ten rows with two in each row, a diagram, and a product, 20, a number.
[A title on a white background reads: What's (some of) the mathematics?
Bullet points below read:
- We used what we knew about products having different factors to make a match. For example, when we were asked for a matching array to 20, we looked for an array that had 1 twenty, twenty ones, 10 twos, 2 tens, 4 fives, or 5 fours.
Below the points is an image of the sheet with Sam holding out a 20 product card and the speaker holding a set of partially covered array cards. In her set, the card on the right has 10 dots running down the side and 2 across.]
Speaker
We also used what we knew about products having different factors to make a match. For example, when we were asked for a matching array to 20, we thought, what could 20 be?
[On the slide described before, a large pink thought bubble appears next to the bullet points and image.]
Speaker
It could be an array that had one 20—
[20 dots running across the bottom of the thought bubble appears.]
Speaker
An array that had 20 ones—
[20 dots running down the right side of the thought bubble appears.]
Speaker
One that had ten twos—
[Next to the 20 dots running down, a partially covered array of 10 dots running down with 2 dots running across appears.]
Speaker
Two tens, four fives, or five fours.
[Next to the partially covered array of 10 and 2 dots, a partially covered array of2 dots running down and 10 dots running across appears. Above this, two partially covered arrays appears: on the left, is four dots running down with 5 dots across and on the right is 5 dots running down and 4 dots running across.
A title on a white background reads: What's (some of) the mathematics?
Bullet points below read:
- We used our knowledge of spatial patterns to quantify the number of rows and the number in each row. For example, we saw that we had three rows of two or three twos.
Next to the points is an image of a partially covered array with 3 dots running down and 2 dots running across. The 3 dots have a red outline around it. The 2 dots have an arrow pointing to the right above them.]
Speaker
We also used our knowledge of spatial patterns to quantify the number of rows and the number in each row. For example, we saw that we had three rows of two or three twos.
[A title on a white background reads: What's (some of) the mathematics?
Bullet points below read:
- We used different strategies to solve multiplication and division facts.
- Sometimes we used known facts.
- Sometimes we used known facts to solve ones we don't know just yet. For example, to solve 3 fives, we used our known fact of 2 fives and added one more five to find the product 15.
Below the points is an image of a partially covered array with 3 dots running down and 5 dots running across.]
Speaker
We also used different strategies to solve multiplication and division facts. Sometimes we used known facts and sometimes we used known facts to solve ones we don't know just yet.
[On the slide described before, next to the image, 5 columns of 3 dots running down appears. The top 2 rows is highlighted pink.]
Speaker
For example, to solve three fives, we used our known fact of two fives-
[The bottom row is highlighted blue.]
Speaker
And added one more five to find the product, 15.
[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, connecting a picture card (partially covered array) with a number (a product card).
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 the card, they must give it to the asking player.
If they don't, they say 'go fish' and the player gets a card from the pile in the middle.
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!
Other ways to play
To challenge yourself and extend the number range, add the expansion pack (PDF 438.8 KB) to the gamecards.
Discuss/reflect
- What strategies did you use to determine how many dots there are in the partially covered arrays?
- Were there any arrays which were known facts for you? Which ones?
- What strategies did you use for the arrays that weren’t known facts for you?