# 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

• 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).

## Watch

Watch Hit it (3-digit numbers) video (9:11).

Get as close to the target number using place value.

### 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.

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.

The Hulk is fun.

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?

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

### Barbara

Okay, how do you play?

### Michelle

So, we need a target number, which is what you're gonna try to hit.

Okay.

### Michelle

And we need a target number that's a multiple of 100.

Okay.

Okay.

### Michelle

So, what's the target number you'd like?

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.

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.

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.

Okay.

### 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?

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.]

Okay.

### Barbara

7. Okay, well that's...

[Barbara rolls a 7.]

### Michelle

It's, this is sort of a similar choice.

Similar choice.

### Michelle

Cause it's still 2 away from the 5.

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?

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!

Yeah.

### Barbara

Because a 4 would better than a 5, wouldn't it?

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.

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.]

So, I need an 8?

You need...

### Barbara

8, 7, 6, 5, 4, 3.

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.

Okay.

### Michelle

So how far away are you from 500?

### Barbara

Okay so, if I, if I had 480.

Uh-huh.

### Barbara

I would be 20 away.

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.

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.

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.

### 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?

Yep.

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?

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.]

No.

So, there were.

### Michelle

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.

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.

Okay.

### Michelle

So, I would need 70 more to get to the next 400.

Okay.

### Michelle

The hundred, so that's actually 69.

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.]

Yeah.

### Michelle

So, let's see what happens.

Okay.

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.

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.]

So good.

Oh...

### Barbara

690 something would be fantastic!

### Michelle

I feel like you've got rigged dice!

[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.]

Oh, rats!

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.]

7.

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.

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.

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...

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

1. 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).
2. Select a multiple of hundred between 100 and 900 to be your target number.

3. The person with the most letters in their surname goes first.

4. Take it in turns to roll the dice and use the digit somewhere in your number.

5. 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.

6. The winner with the most points after 3 rounds is declared the winner.