101 and you're out!

Collect resources

You will need:

  • 1cm square grid paper in student mathematics workbook
  • different coloured pencils or markers
  • two spinners (see mathematics workbook)
  • paper clip for spinner.

Watch the video to learn how to play…

(From Dianne Siemon, RMIT University)

Transcript

OK, everybody, welcome back! We're here today to have a look at the game multiplication toss, which some people also call how close to 100. To play today I'm using a spinner, and I just made it by printing out a decagon and drawing lines across the opposite angles and labeling it from 0 to 9.

And I'm going to use my paper clip that I found in the drawer, and a pen and I can flick it...

And that will give me the numbers that I'm going to use. And in fact I could start with five, and I now also have a zero which is no good for me because what I know is that 5 times 0 or 0 fives is 0.

So for my first recording of my game I can't block out anything because 5 zeros is the same as 5 x 0, which is equivalent to 0.

So fingers crossed my next go is more lucky!

Ahhh 0 and 2, so this time I could say 0 twos is equivalent to 0 times 2, which is also 0. Okay, third time lucky!

Come on, spinner!

Excellent, so this time I got an 8 and ahhh...I think that's a 5 so I can actually now get to colour in my board here and because I got an 8 and a 5, I can choose to make 8 fives or 5 eights.

So I'm just going to go with 5 eights because I like them better.

So I need 8 in my rows, so 1 2 3 4 5 6 7 8 and I need 5 down here so that's 2 3 4 5. So I get to draw a border all around this area of my game board.

And I'm going to record this as 5 eights. And I'm also going to record it over here. So 5 eights

is equivalent in value to 5 times 8, which is equivalent to 40.

Now if I wasn't sure I could use the grid here to help me work out how many squares are encased in my green section. And because mathematicians like to code and keep a record of their ideas, I might also put a green marker here to say that corresponds to this section on my game board.

Alright, let's see. I've had a disastrous start, but I could have a successful finish. I'm going to call that a 3.

And a 0. I got too excited so I could say 0 threes or 3 zeros but I know they're the same as zero, so 3 zeros

is equivalent to 3 times 0, which is zero OK.

Come on, spinner!

Four...

Fives so I could do 4 fives so that would be across here like this. Or I could do 5 fours which would...ok,...go like this. And i might actually do that. I'm going to use a different color mark at this time so I know this is 4 because, actually I can subitise that many.

And that takes me all the way down to here.

I realized I didn't actually have to count those 'cause I know my board is 10 by 10. 5 fours I am I going to record that, over here. 5 fours is equivalent in value to 5 times 4, which is 20. And I actually know that because that's the same as saying 10 twos and you just rename that as 20. Like this, you could say that's 10 twos which is the same as 2 tens. We could just keep going, but we won't.

I could write that 0 sevens or 7 zeros. 0 x 7 which equals 0. Let's try.... come on one! 6...and a 9... now I definitely know I can't go here because I've got 1, 2, 3, 4, 5, 6...1 row of six left that I could use or one row of two. So in this case I have to record 6 nines ...but I couldn't go.

So they were my 10 goes and I have eight squares remaining and I covered 92 centimeters squared. How did you go in your game?

A spinner made with a decagon divided into 10 sections from the centre and numbered 0-9. There is a pencil at the centre point keeping a paper clip in place. When you spin the paper clip, you have a spinner.

Instructions

  • Players take turns to spin the spinners. If a 3 and 6 are spun, players can enclose either a block out of 3 rows of 6 (3 sixes) or 6 rows of 3 (6 threes).
  • The game continues with no overlapping areas.
  • The winner is the player with the largest area blocked out after 10 spins.
  • Eventually the space on the grid paper gets really small.
  • Then, you have to think:
    • What if my 3 sixes won’t fit as 3 sixes or as 6 threes?
    • Players can partition to help them! So, for example, I can rename 3 sixes as 2 sixes and 1 six (if that helps me fit the block into my game board).

Watch Multiplication toss - follow up 1 to see a strategy to help you when your board starts to get full.

Transcript

Coming soon

Feeling skeptical about Michelle's thinking?

Watch this video to see how she proves 6 threes = 3 threes + 3 threes = 18. It's a strategy you can then use to prove your thinking too!

Transcript

Coming soon

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