# Squares bingo!

Stage 2 and 3 – a thinking mathematically context for practise focused on using known multiplication facts to solve problems with square numbers.

## Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus (2022) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2024.

## Outcomes

- MAO-WM-01
- MA2-MR-01
- MA2-MR-02

- MAO-WM-01
- MA3-MR-01
- MA3-MR-02

## Collect resources

- 4 x 4 grid or draw your own grid with blank paper
- playing cards (Kings, Jacks and Jokers removed)
- two different coloured markers.

## Squares bingo!

Watch Squares bingo! video (6:51).

This video was developed with Alishia from Sylvania Heights PS, Kristy from Minchinbury PS and Stephanie from Parramatta PS.

### Speaker

Squares bingo from Bay-Williams and Kling.

[Text over a blue background: Squares bingo. Small text beneath the title reads: From Bay-Williams and Kling. In the lower right-hand corner of the screen is the waratah of the NSW Government logo.

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

Bullet points below read:

· Gameboard template or blank paper.

· A deck of playing cards (remove the Kings, Jacks and Joker cards)

· A few different coloured markers or highlighters.

A green highlighter, a pink highlighter and a black marker sit beside a blank sheet of paper. Above the highlighters and marker there is a hand of cards faced down. Small text above and to the right of this image reads: NSW Department of Education. Text below this in bold font reads: Squares Bingo gameboard.

Beneath this text there are two blank 4 x 4 grids, one above the other.

Small text beneath these grids reads: education.nsw.gov.au]

### Speaker

When playing the game today, you're going to need the Squares Bingo Gameboard template or a blank piece of paper. You're also going to need a marker to draw your own grid on, one deck of playing cards with the King, Jack, and Joker cards removed. And finally, a few different coloured markers or highlighters.

[White text in the centre of a blue background: Let’s play! Small text on the top left reads: NSW Department of Education.

A 4 x 4 grid filled with numbers drawn on a piece of paper sits on a wooden table. The numbers in the top row of the grid from left to right, are: 0, 49, 4, 4, 4. In the second row: 64,16,81,9. In the third row: 36, 1, 100, 25. In the fourth row: 0, 16, 36, 25. To the top right of the grid is a Robin figurine, to the top left, a Batman figurine. There is an open pink highlighter to the left of the sheet of paper and a face down deck of cards beside a green highlighter to the right of the sheet of paper. Above the grid there are two rows of numbers. The numbers on the top row are: 0, 1, 4, 9, 16, 25. The numbers on the bottom row are 36, 49, 64, 81, 100. ]

### Speaker

Playing the game today are two superhero mathematicians. We've got Batman and Robin.

[The speaker picks up the pink highlighter and places it back down again.]

### Speaker

Batman is player one, and he's going to be using the colour pink.

[The speaker picks up the green highlighter and places it back down again.]

### Speaker

His trusty sidekick Robin, is player two, and is going to be using the colour green. Let's get started. I wonder who will win.

[The speaker flips the card at the top of the deck, revealing an Ace of Clubs. She then picks up the pink highlighter]

### Speaker

Batman has drawn an ace, this represents a one. In the game, he uses the Same-As strategy for one.

[The speaker puts up one finger on her hand and moves it up and down twice. ]

### Speaker

This means one-one is the same as one.

[The speaker moves her hand with one finger raised up and down once.]

### Speaker

He finds one on the gameboard and marks it off.

[The speaker uses the pink highlighter to mark off the number 1 in the second column of the third row.]

### Speaker

Next is Robin's first go.

[The speaker flips the card at the top of the deck, revealing a 5 of Diamonds.]

### Speaker

He turns over a five. He knows the product of five fives is 25.

[The speaker picks up the green highlighter. She gestures to the two 25s in the fourth column of rows 3 and 4 in the grid.]

### Speaker

Hey, look! There are two 25s on the gameboard. He needs to be strategic in his thinking about which 25 to mark off. He knows that to win the game he needs four square products in one line.

[The speaker gestures with her finger at 4 numbers making a horizontal line on the grid. She then gestures to 4 numbers making a vertical line on the grid. She then gestures to 4 numbers in a row making a diagonal line on the grid.]

### Speaker

This line can be horizontal, vertical or diagonal. He can either block Batman's row, or start his own diagonal line.

[The speaker gestures to the third row of the grid. She then marks the number 25 in the fourth column with the green highlighter. She then removes the 5 of diamonds from view.]

### Speaker

Robin chooses to play defensively, and decides to block Batman's row, by marking off this 25. Back to Batman.

[The speaker flips the card at the top of the deck, revealing a 9 of hearts.]

### Speaker

He has flipped a nine and is unsure of the square product. He imagines an array of nine tens.

[90 pink dots arranged in a 9 x 10 grid appear on a white background.]

### Speaker

He knows it is one nine less, so one nine disappears.

[The top row of pink dots turn blue and then disappear.]

### Speaker

He's left with nine nines, which he knows is 81.

[The grid of dots disappears.]

### Speaker

Great thinking, Batman! You're using what you know to work out what you don't know.

[The speaker picks up the pink highlighter and marks off the number 81 in the third column of the second row. She then removes the 9 of hearts from view.]

### Speaker

OK. Now, it's Robin's turn.

[The speaker flips the card at the top of the deck, revealing a Queen of hearts.]

### Speaker

He flips a queen, this is a zero in the game. He knows the Same-As strategy that he used for ones, should also be used for zeros. He has zero zeros, this is the same as zero groups of zero.

[The speaker points to the two zeros in the first and fourth row of the first column of the grid.]

### Speaker

He notices that there are two zeros on the game board. Which zero should he pick? Hmm, I can see that too.

[The speaker points to the 0 in the fourth row of the first column.]

### Speaker

Robin should pick this zero because he can now block Batman from marking his diagonal line.

[The speaker gestures to the diagonal line going from the fourth row of the first column to the first row of the fourth column and then marks off the 0 with the green highlighter. She then removes the queen of hearts from view.]

### Speaker

Batman is going to try and bounce back.

[The speaker flips the card at the top of the deck, revealing a 6 of hearts.]

### Speaker

He's drawn a six and will use what he knows about fives.

[ 30 pink dots arranged in a 6 x 5 grid appear on a white background.]

### Speaker

He knows the product of five and six is 30, so he imagines adding one more six to the array, which is 36.

[A row of 6 blue dots appear on top of 6 x 5 formation of pink dots, creating a 6 x 6 grid of 36 dots.

The speaker points to the two 36s in the grid, one in the first column of the third row, the other in the third column of the third row.]

### Speaker

As you can see, it doesn't matter which 36 Batman chooses, both will block a path for Robin. He chooses this 36.

[The speaker points to the 36 in the third column of the fourth row and then marks it off with the pink highlighter. She removes the 6 of hearts from view and flips the card on top of the deck, revealing an ace of hearts.]

### Speaker

Oh, no! Robin has turned over an ace.

[The speaker puts up one finger on her hand and moves it up and down twice.]

### Speaker

Even though he knows one squared is one, there are no more ones on the game board. He misses a turn.

[The speaker flips the card on top of the deck, revealing a 2 of spades. She picks up the pink highlighter.]

### Speaker

Back to Batman. Who draws a two. He knows that the square product of two is four and is choosing this one.

[The speaker points to the number four in the third column of the first row and then marks it off with the pink highlighter.]

### Speaker

He now has three out of four square products in one column.

[The speaker points to the highlighted numbers 4, 81 and 36 in the first, second and fourth row of the third column. She picks up the green highlighter.]

### Speaker

Could this help him to win the game?

[The speaker removes the 2 of spades from view and flips the card on top of the deck, revealing an 8 of clubs.]

### Speaker

Robin's turn again. He has pulled an eight. He knows that when you multiply a number by eight, you can use repeated doubling.

[8 pink dots in a row line the bottom of a white box. A second row of 8 pink dots appear immediately above the first row, doubling the number of pink dots. Two more rows appear, doubling the number of pink dots again. The 4 rows of pink dots double once more, filling the white box with an 8 x 8 grid of pink dots.]

### Speaker

Double eight is 16. Double 16 is 32, and double 32 is 64. There is only one 64 on the gameboard.

[The speaker points to the number 64 in the first column of the second row of the grid.]

### Speaker

Robin does not have a choice. He can only mark off this one.

[The speaker marks off the number 64 with the green highlighter. She then removes the 8 of clubs from view.]

### Speaker

Batman can now see that he only needs to mark off 100 in this column to win.

[The speaker points at the number 100 in the third column of the second row of the grid.]

### Speaker

Can you think of which card he needs to turn over to win?

He needs to turn over a ten. As he knows, ten tens are 100.

[The speaker flips the card on top of the deck, revealing a 10 of diamonds.]

### Speaker

Oh, what a flip! Batman has drawn a ten! Bingo!

[The speaker marks off the number 100 with the pink highlighter. She picks up the batman figurine and moves him around in the air.]

### Speaker

(SINGS BATMAN THEME SONG) Batman! Batman is the winner of Squares Bingo. Well done, Batman.

[She puts batman back in his place. Text on a blue background reads: What’s (some of) the mathematics?]

### Speaker

What is some of the mathematics that we've explored today?

[Black text on a white background reads: Games can help us practise using what we know to solve what we don’t know yet, including with multiplication and division number facts.

· For example, Batman flipped 9 and he had to square it, meaning he had to work out 9 nines. This isn’t a number fact he knows so he thought about what else he knows that could help him. He knows he can use 9 tens to help him solve 9 nines so he imagined an array of 9 tens which he knows is 90. Then he took away 1 nine to find 81.

### Speaker

Games can help us practise using what we know to solve what we don't know yet, including with multiplication and division number facts. For example, Batman flipped nine. He had to square it, meaning he had to work out nine nines. This isn't a number fact he knows. So, he thought about what else he knows that could help him. He knows he can use nine tens to help himself, nine nines. So he imagined an array of nine tens, which he knows is 90. Then he took one nine away to find 81.

[To the bottom right of the text appears a 9 x 9 grid of pink dots. They then disappear.]

### Speaker

Robin flipped an eight, which he had to square, meaning he had to work out eight eights.

[Beneath the text, a row of 8 pink dots appears. A second row of 8 pink dots appear immediately above the first row, doubling the number of pink dots. Two more rows appear, doubling the number of pink dots again. The 4 rows of pink dots double once more, creating an 8 x 8 grid of pink dots]

### Speaker

He used what he knows about doubling. He doubled eight, then doubled 16, then doubled 32. To find a total for eight eights, which is 64.

[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

- Print a copy of the game board to play or watch the video to learn how to draw your own game board.
- Place the square products randomly inside the grid, making sure each square product is used at least once and there are no empty spaces.
- The player who gets four in a row (horizontally, diagonally or vertically) is the winner. If there are two of the same square products on your bingo card you are only allowed to cover up one for each card that you flip.
- Player 1 flips one card and determines its square product, using your marker, highlight or colour in the square product on the bingo board.
- Player 2 has their turn, flipping over their card and selecting their square product on the bingo board.
- If a player selects a card and the square product has already been taken they miss a turn.
- Remember to think about your strategy, you can block the other player from completing their row.