Hit it (3-digit numbers)
Stage 1 and 2 – A thinking mathematically context for practise providing opportunities to deepened understanding in estimating, rounding and place value knowledge
From Mike Askew, A practical guide to transforming primary mathematics, 2016
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-RWN-01
- MA1-RWN-02
- MAO-WM-01
- MA2-RWN-01
Collect resources
2 markers
some paper
a 0-9 dice (you can also use playing cards A-9 or numeral cards).
Hit it!
Watch Hit it (3-digit numbers) video (9:11).
Michelle
Alright there mathematicians, welcome back and welcome back Barbara!
Barbara
Hello Michelle, lovely to see you.
Michelle
And you. Umm, and maths! Hello maths! I hope you're having a great day maths! Oh, I really am!
[There are 2 A4 pieces of paper on the screen. Both of them are in portrait orientation. There is also 2 dice. One is green and one is blue.]
Barbara
Yeah, I'm everywhere!
Michelle
Imagine if maths was personified, right, like what character would it be?
Barbara
It would just be me. [Laughter]
Michelle
I feel like it would be the Hulk.
Barbara
The Hulk, yeah!
Michelle
Cuz it can be like...
Barbara
But more easy going...
Michelle
Really big and powerful, but really clever as well.
Barbara
But more fun than the Hulk.
Michelle
The Hulk is fun.
Barbara
Oh, he's fun?
Michelle
Yeah, super fun. I love the Hulk. Who do you think is more fun than the Hulk?
Umm.
No one?
Barbara
Iron man.
Michelle
Oh yeah that's true, Iron man is pretty good.
Barbara
I got; I got your weakness!
Michelle
Alright, let’s play. So, we, we're gonna play a game called Hit it! that I learned from Mike
Askew.
Barbara
Okay, how do you play?
Michelle
So, we need a target number, which is what you're gonna try to hit.
Barbara
Okay.
Michelle
And we need a target number that's a multiple of 100.
Barbara
Okay.
Michelle
So, and we'll play between 100 and 900 to start with.
Barbara
Okay.
Michelle
So, what's the target number you'd like?
Barbara
Ahh, 500.
Michelle
Okay, so that's our target number. And we also need a game board, and it looks like this.
[Michelle writes the number 500 on a sticky note in between the 2 A4 sheets of paper. At the top of the page she draws 3 lines to represent the hundreds, tens and ones place value in a 3-digit number. Barbara draws the same on her page.]
Barbara
That looks nice and easy.
Michelle
You can create yours.
Barbara
Okay.
Michelle
And then we roll the dice, and we have to use the digits that we roll to try to form a number
that's as close as possible to 500.
Barbara
Okay.
Michelle
So, we're trying to hit the target. Ummm. And who should go first?
Barbara
Well, I think me.
Michelle
We need like a mathematical way of deciding.
Barbara
Okay.
So, what about number of letters in your last name?
Michelle
Okay, well I have 9.
Barbara
[Sigh] I've got 8... I thought I had it with 8.
Okay.
Michelle
You know what you could also play?
You know how last time we said the person with the largest number of letters in their first name?
Barbara
Yeah.
Michelle
And I still won that round. This is really advantageous because usually you get cranky about having so many letters.
Barbara
Oh, that's true actually.
Michelle
In your name but you could also do total letters in your whole name.
Barbara
I don't have a middle name.
Michelle
Oh well, I have 2, so I still get to go first. This may not do me any favours, but let's play.
All right, oh 3. So.
[Michelle rolls a 3.]
Barbara
Oh, that's a hard choice!
Michelle
It's a hard choice, and I can't decide whether to err on the side of caution or to be quite crazy. So, I'm gonna go for a crazy idea.
[Michelle writes 3 in the ones column of her 3-digit number.]
Barbara
Okay.
Michelle
Your go.
Barbara
7. Okay, well that's...
[Barbara rolls a 7.]
Michelle
It's, this is sort of a similar choice.
Barbara
Similar choice.
Michelle
Cause it's still 2 away from the 5.
Michelle
Like the 3 was.
Barbara
Yeah, but I was thinking that the, because I was thinking that 4 would be a really good number to get.
Michelle
Four, would be a good number.
Barbara
Because you could get 495 or 6, right?
So yeah, that's true so it's about the same, isn't it?
Michelle
Yeah.
Barbara
So, 7 and then get a really low number.
But I'm not ready to do that, so I'm just gonna put this, 7 tens.
[Barbara writes 7 in the tens place of her 3-digit number.]
Michelle
Okay.
I, well, I'm gonna say 7 tens also.
[Michelle rolls a 7. She writes the number in the tens place of her 3-digit number.]
Barbara
So now you really want a 4!
Michelle
Yeah.
Barbara
Because a 4 would better than a 5, wouldn't it?
Michelle
That's true!
Yes.
Barbara
Okay, well now 77.
[Barbara rolls a 7. She writes it in the ones place of her 3-digit number. Michelle points to the empty hundreds place.]
Michelle
This digit determines everything.
Barbara
It does.
Okay.
Michelle
Cuz neither, you know sometimes...
Barbara
And even though 4 is the best for both of us. Oh, uh....
[Laughter] I think I've got it.
Michelle
It couldn't have been worse!
907. Actually, you haven't won yet! Because if you get a 9, I win.
[Michelle rolls a 9. She writes the number 9 in the hundreds place of her 3-digit number, making the number 973.]
Barbara
So, I need an 8?
Michelle
You need...
Barbara
8, 7, 6, 5, 4, 3.
Michelle
Yeah.
Barbara
And then but 2. Oh, I wonder who would win if I have 2?
Ah who cares because I have 477!
[Barbara rolls a 4. She writes it in the hundreds place of her 3-digit number, making the number 477.]
Michelle
So, you have to be on it, we have to be able to explain how far away we are from the target.
Barbara
Okay.
Michelle
Before you get your point.
So how far away are you from 500?
Barbara
Okay so, if I, if I had 480.
Michelle
Uh-huh.
Barbara
I would be 20 away.
Michelle
Yeah.
Barbara
So that's 3 more. So, so 3, 3 further away than that. So, I'm 23 away from...
Michelle
The target.
Okay and I am way more than 23 away!
In fact, I'm 473 away.
Barbara
Okay so, I think...
Michelle
You do win. You get a point.
Barbara
Sometimes a little 8 letter... [Laughter] I try to think that made a difference. I just got a bit lucky with my 4.
[On the right of her board, Barbara draws a single tally mark to indicate that she has won the game. They create a new game board and draw 3 lines that represent the hundreds, tens and ones place of a 3-digit number.]
Michelle
Okay. You score yourself a tally mark and let's play again.
Barbara
Okay.
Michelle
Let's do best out of 3.
Barbara
Okay, let's do it.
Are we keeping the same target number?
Michelle
We can, or we can change it. What would you like to do?
Barbara
Ummm, I think keep it it. Maybe for the third game.
Michelle
We might change it.
Michelle
Yeah. Alright.
Barbara
Sometimes it’s nice to use the same numbers because you might develop some strategies.
Michelle
You can roll first because you won.
Barbara
Yes! 2. Oh, similar choice.
[Barbara rolls a 2. She writes it in the tens place of her 3-digit number.]
Michelle
Do you know what I should have done, is actually made the 300?
Barbara
Yeah. That actually would have been much better.
Michelle
But I still wouldn't have won though.
Barbara
No but it wouldn't have been as sad as your result!
Michelle
Well, I feel like if you're gonna lose, lose big!
Barbara
So, I'm gonna choose 2 tens, so I've got 20 something.
Michelle
Okay. Come on! Good numbers Ooh. Oh, okay.
Barbara
Now it's your time! You get a do-over Michelle would you do things differently?
Michelle
I still don't know that I would, but I'm gonna give it a go, and see what happens.
[Michelle rolls a 3. She writes it in the hundreds place of her 3-digit number.]
Barbara
Okay.
[Laughter]
400.
[Barbara rolls a 4. She writes it in the hundreds place of her 3-digit number.]
Michelle
Rats! So, so, actually we already know you've got the point, right?
Barbara
Yep.
Michelle
Anyway.
Barbara
And we already know who won best out of 3 too!
Michelle
I'm gonna go a 1 here. Your go.
[Michelle rolls a 1. She writes it in the ones place of her 3-digit number.]
Barbara
Cuz you still want to get as close as possible right?
Michelle
You do.
Barbara
Ohhh, see I wish I'd put my 2 in the end there, because I would have been so close.
[Barbara rolls an 8. She writes it in the ones place of her 3-digit number and makes the number 428.]
Michelle
You would have been really close.
Okay. Look the good news is I couldn't have formed any bigger a number.
[Michelle rolls a 3. She writes it in the tens place of her 3-digit number and makes the number 331.]
Barbara
No.
Michelle
So, there were.
Barbara
No bad choices.
Michelle
No bad choices!
So how far away are you with this one?
Barbara
Okay, so I am 70 something. So, 72.
Michelle
Yes, I agree with you, because 2 more would make it 430.
Barbara
That's right.
Michelle
And then another 70...
Barbara
Yeah. I thought about it the other way. I thought, I've just pretended I had 30 and then I added the 2 later.
Michelle
Oh, that's a good idea.
Barbara
So, we just, we worked it out the the same way, but we changed the order around.
Michelle
Yeah.
So, what I'm gonna think about, this idea, if that was a zero.
Barbara
Okay.
Michelle
So, I would need 70 more to get to the next 400.
Barbara
Okay.
Michelle
The hundred, so that's actually 69.
Barbara
Yes.
Michelle
And then I need 169.
So not as bad as 973 but still not as good. Not as close as 73.
So, a puck mark for you.
[Barbara writes a tally mark next to her game board to show that she has won the game.]
And this ones with a clean sweep.
Would you like to keep the target or change it?
Barbara
You know what, I think you should choose.
Michelle
Oh no... Let's choose.
Barbara
Because if I'm gonna beat you at least it could be your own architecture that brings you down.
Michelle
I'm gonna choose 700, just to see how that changes the game.
Because 500 is sort of in the middle right?
[Michelle writes 700 on a sticky note and places it between the 2 A4 sheets of paper. Both the presenters draw a game board with 3 lines representing and hundreds, tens and ones place value of a 3-digit number.]
Barbara
Yeah.
Michelle
So, let's see what happens.
Okay.
Barbara
That's a, I'm thinking about this in a really different way now.
Michelle
Okay. You roll.
Oh...
Barbara
Six hundred.
[Barbara rolls a 6. She writes the number in the hundreds place of her 3-digit number.]
Michelle
Okay. Ohhhh, 900.
Well, I'm not gonna put it in the hundreds.
Barbara
No.
Michelle
But I might put it in the tens.
[Michelle rolls a 9. She writes it in the tens place of her 3-digit number.]
Barbara
Okay, I mean if you get a 6, 690 something would be fantastic.
[Barbara rolls a 9. She writes it in the tens place of her 3-digit number.]
Michelle
So good.
Oh...
Barbara
690 something would be fantastic!
Michelle
I feel like you've got rigged dice!
Ok, your go.
[Michelle rolls a 1. She writes it in the ones place of her 3-digit number.]
Barbara
Let's swap them. [Laughter]
[Michelle and Barbara swap dice.]
Doesn't matter now. 3.
[Barbara rolls a 3. She writes it in the ones place of her 3-digit number to make the number 693.]
Michelle
Oh, rats!
Barbara
693.
Michelle
So even if I got a 6 now, you still get the clean sweep.
Barbara
Yep, and you chose the target number and we swapped dice.
Michelle
Oh my gosh and I got a 1. Okay, so how far away are you?
[Michelle rolls a 1. She writes it in the hundreds place of her 3-digit number to make 191.]
Barbara
7.
Michelle
Mm hmm and I’m.
Barbara
That's my best one yet.
Michelle
That is your best one, and I'm like...
Barbara
Is that your worst one yet?
Michelle
It could be my worst. I think it is. So, I would need another 9 to get to 200.
Barbara
Humm.
Michelle
And then another 500.
So, I'm 509 away! So, it is my worst one yet. Look if you're gonna lose, lose big.
Barbara
Go big or go home as they say!
Michelle
Have fun playing Hit it! mathematicians.
You could play, umm, actually with 4-digit numbers.
Barbara
Oh yeah.
Michelle
And you can even try with decimals.
Barbara
And I guess you could do it, so that if you, you know, you can't go over, so you can only go...
Michelle
Under?
Barbara
Yeah.
Uh huh. There's a lot of variations. There's heaps of cool things you could do. Have fun playing!
So, what's some of the mathematics with this game?
This task gives us an opportunity to practice and deepen our skills and understanding in things like estimating, rounding, using our place value knowledge, reasoning, and explaining how we know which number is closest to the target number using flexible strategies.
So over to you mathematicians
You can play this game in lots of different ways, you could use 2, 4, 5-digit numbers and beyond. You could also play using decimal fractions.
Have fun!
[End of transcript]
Instructions
- Draw up your game board (in this game, we were working with 3-digit numbers but you can use larger or smaller numbers if you like).
- Select a multiple of hundred between 100 and 900 to be your target number.
- The person with the most letters in their surname goes first.
- Take it in turns to roll the dice and use the digit somewhere in your number.
- Once the digits are full, players read their number and determine how far they are away from the target number. The player who is closest to the target number wins a point.
- The winner with the most points after 3 rounds is declared the winner.