10 or bust (additive strategies)
This is a thinking mathematically context for practise focussed on developing additive thinking and reasoning strategies.
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, 2021
You will need:
a game board (for example use a number track, a ten-frame, a drawing of 10 fingers, a drawing of a known number combination to 10)
counters or dried beans or pasta
a dice, spinner or numeral cards from 1 - 6
pencils or markers.
Watch 10 or bust video (6:23).
Alright, welcome back mathematicians!
[Screen shows a white piece of paper with 10 coloured blocks in a row on the paper. The name Michelle is written on a sticky note which is on the white paper. The name Ayesha is on another sticky note to the right of the white paper. Above the white paper is one pile of yellow counters and another pile of green counters.]
How are you today?
I'm good and you?
Very well thank you. So today Ayesh and I are playing our game together but remotely so I'm gonna keep a track of your game as well as my game at the same time so I could see what was happening as if we were together so well, because we're going to play ten frame or bust or sorry, 10 or bust.
What structure did you want to use today for, for your, to keep track of 10? You could use like a number line. Or you could use a drawing of your hands.
Or you could use your favourite dice patterns or something?
I'm thinking because it's around the number 10. I would like to use a ten frame.
Oh, so I think I have one from something I was doing before, so I've got your ten frame here and Ayesha, I thought I might like to use a number line today.
So, I, so I just made it out of blocks. I have 10, I'll just check. I've got 2, 4, 6, 8, 9 and I need one more, so that I've got 10 and I can use that to measure my number line on and I'll draw my number line and then I can draw the numbers on there.
And then I can label them 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. OK. Have you got dice over there, Ayesha?
[Michelle places a blank ten frame next to the paper with the coloured blocks. The ten frame is 5 rows of 2 squares. She puts the sticky note with the name Ayesha above the ten frame. Michelle then counts the row of coloured blocks two at a time, 2, 4, 6, 8, 9, and adds one more coloured block to make 10. Michelle draws a number line beneath the coloured blocks and labels the number line with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.]
And I've got some counters. I've decided that you're going to be green and I'm going to be yellow.
[Michelle moves the yellow counters onto the piece of paper with the number line and the name Michelle displayed and the green counters onto the ten frame with the name Ayesha displayed.]
And then do you want to roll the dice first, or will I?
Here, I'll have to go.
Right, I got 4.
OK, so are you putting that on your ten frame?
[Michelle points to the ten frame.]
I've decided to add that to my ten frame.
And did you make it 4 so it looks like a square, Ayesha? Or did you make it four so it's in one line and you see one less than 5?
[Michelle points to the first two rows of the ten frame, which is four squares. She then points to the top 4 squares in the first column of 5 squares.]
I did it so I see one less than 5.
Ok, so 1, 2, 3, 4.
[Michelle puts one green counter on each of the 4 squares in the first column of the ten frame, beginning from the top of the column.
OK, now remember when we play, we only get 3 rolls of the dice and you can only choose not to use one, but it has to be in your first move or your second move.
OK, so I've got a decision to make for the next go.
Yeah, I'm rolling my dice and I got a three.
[Michelle rolls the dice and she rolls 3.]
So, I'm going to put down 3 on my number line 1. 2. 3. OK, Ayesha, your turn again.
[Michelle adds 3 yellow counters to the number line, on the numbers 1, 2, and 3.]
Alright... This time, I got a 6.
Oh, what are you gonna do?
Well. I know that next turn I have to use it so whatever I roll is going to take me over 10, so
I think I'll skip this one and sit this one out. So, I'm not going to add 6 to my ten frame.
Yeah, because I'm just going to show everybody what that would look like if you had six more. It would mean your ten frame is full and no matter what number you rolled; you would be busted.
[Michelle adds 6 yellow counters to the 10 frame, and outlines the full 10 frame with her finger. She picks up the dice and displays the different numbers on the dice.]
OK, that's, that's a good strategy. I feel disappointed you chose it, 'cause you know I like to win, but I think it's good thinking Ayesha.
[Michelle removes the 6 yellow counters and puts them back into the pile.]
OK, and now we're only one number apart too, you're on 4 and I'm on 3.
[Michelle points to the 3 counters on the number line and the 4 counters on the ten frame.]
OK, guess what, Ayesha? I rolled a 6 too. And I'm so tempted to play it because that would get me to 9.
[Michelle points from the number 4 to the number 9 on the number line.]
I'm going to try it and see what happens.
So, I've got three and I need to add 6 more so I'll just get six counters first. And 3, 4, 5, 6, 7, 8, 9. I hope I get a one.
[Michelle picks up 6 yellow counters. She points to the number 3 and then adds the counters to the numbers 4, 5, 6, 7, 8 and 9 on the number line.]
Yes, so I see here. I really need to get a 9 or more for us to even tie or for me to win so that means to get a 9 that means I need to at least roll a 5 and to get 10 I'll have to roll a 6.
Yeah, but I also have one more roll that I can't cancel out, so I could bust. Your go Ayesha, roll your dice!
Hey. I got a 4.
OK. So, Ayesha, where do you want me to put your 4?
[Michelle picks up 4 green counters from the pile.]
Do you want to continue down the line?
Right underneath on the bottom row. So, that I have 4 on the top row and 4 on the bottom row.
[Michelle rotates the ten frame so it is now 2 rows of 5 squares. She moves the 4 green counters on the ten frame to the first 4 squares on the top row.]
Oh yeah, I had my ten frame turned the other way so I just turned it so that I could do what you were saying.
[Michelle adds another 4 green counters to the first 4 squares on the bottom row, so they are beneath the 4 counters on the top row.]
So, so now it looks like each one on the top row has a partner down the bottom?
And there's 2 empty boxes. So that means you're on 8.
[Michelle rotates ten frame back to original position of 5 rows of 2 squares. The top row is empty. Each of the other 8 squares has a green counter.]
OK, I hope I get lucky and get a one. Let's see what happens.
[Michelle rolls the dice and she rolls 4.]
Oh, oh Ayesh. I got a 4 so I am definitely busted 'cause I get 10 and then I actually would need three more.
[Michelle adds one yellow counter to the number 10 on the number line and shows the extra counters she still needs to place.]
So, congratulations, Ayesha, you won that round.
Do you want to play again?
Of course! Let's have another go.
Alright. Have fun out there you mathematicians.
[End of transcript]
Have 3 turns each to roll the dice and place the matching number of counters on your game board.
You can choose to miss one turn, but it cannot be your last roll.
If you go over 10, you have ‘busted’ and are out of the game.
The player closest to 10 after 3 rolls each is the winner.
Players can play best out of 3, playing by making up to 10 as well as backwards to zero.
How could we change the game to make it more/less challenging?
Did you work out a way to play this game so that you didn’t lose?
What was your strategy?
Did it work?