# Building towers

This is a thinking mathematically targeted teaching opportunity, focussed on relationships for adding and subtracting with benchmarks and part-part-whole concepts.

## 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
• MAE-RWN-01
• MAE-RWN-02
• MAE-CSQ-01
• MAE-CSQ-02

• MAO-WM-01
• MA1-RWN-01
• MA1-RWN-02
• MA1-CSQ-01
• MA1-FG-01

## Collect resources

You will need:

• some building blocks

• a dice, numeral cards 1-6 or spinner

• pencils or markers

## Watch

Watch Building towers video (7:22).

### Michelle

Welcome back little mathematicians and I'm here with Barbara this afternoon. Hi Barbara.

Hi Michelle.

### Michelle

How are you going?

I'm good, keen to play.

### Michelle

I know! This game is really fun, it's called build your towers basically and so we each have...

This is your board game, and this is mine and we have to roll the dice and take turns to fill our tower. So, would you like to go first?

[There are 2 groups of 4 sticky notes with numbers written on them. The group of sticky notes on the left is pink and is arranged as a square game board. The group of sticky notes on the right is blue and is arranged as a square game board. The numbers on each game board are the same. From the top left, in a clockwise direction, the numbers are 5, 7, 3 and 11.

There is a dice in the middle of the 2 game boards and a plastic container of assorted tower blocks is below the game boards.

Michelle points to the pink game board showing it is for Barbara and points to the blue game board showing it is for Michelle.

Michelle passes the dice to Barbara. Barbara rolls the dice and rolls 5.]

So, 5.

### Michelle

Five so you get to build 5 and you can put it on your tower here, here, here, or here.

[Michelle points to each of the numbers on the pink game board.]

Ok.

### Michelle

Or where it fits.

### Barbara

Oh, picked up an extra one. There we go. So, I'm going to put it here because that's 5.

[Barbara picks up 5 tower blocks, joins them together and places them on the number 5 on the pink game board.]

### Michelle

Yes, so that tower now is already filled for you. Alright, my go. I got a 5 too. Say I'm going to go 1, 2, 3, 4, 5 and I'm going to put that on my tower of 5 here too.

I could put it on 7 if I wanted, so I knew that I would need 2 more bricks, but I'm going to put it here for 5 because that's one tower that I have completed.

[Michelle rolls the dice and rolls 5. Michelle picks up 5 tower blocks, joins them together and places them on the number 5 on the blue game board. Michelle then demonstrates placing this tower on the number 7 and then returns it to the number 5.]

### Barbara

So, at the moment we are the same.

[Barbara rolls the dice and rolls 4.]

### Michelle

The same. Oh, actually and we could check that too, because we could pick up our towers and if we compared them.

### Barbara

Exactly the same.

### Michelle

See, even though they're different colours and different sized bricks, they're the exact same height.

[Michelle picks up both towers and puts them side-by-side to show they are the same height. Michelle then returns each tower to the number 5 on each game board.]

Ok, great.

Sorry.

### Barbara

So, 4. Well, it can't go here but I can put it in either one of these is that correct?

[Barbara first points to the number 3 to show that 4 tower blocks can’t go on the number 3 on the pink game board. Barbara then points to the numbers 7 and 11 to show that 4 tower blocks will fit on either of those numbers.]

### Michelle

Yeah. And you could put some here and some here and some here if you wanted.

[Michelle points to the numbers 7, 11 and 3 on the pink game board.]

### Barbara

Oh, really! OK. I think I'll just stick to putting my 4 with my 7.

[Barbara picks up 4 tower blocks, joins them together and places them on the number 7 on the pink game board.]

### Michelle

And how many more would you need?

### Barbara

I'll need 3 more.

### Michelle

Did you go 4, 5, 6, 7 to count that?

### Barbara

I knew that I needed one more to get to 5, so I did that one straight away and then I knew that I needed 2 more.

### Michelle

Nice strategy. Ok, I got another 5.

So, I think I might fill my 3 here and then I'm going to put 2 bricks into my tower that's going to become 11.

[Michelle rolls the dice and rolls 5. Michelle picks up 3 tower blocks, joins them together and places them on the number 3 on the blue game board. Michelle then picks up 2 tower blocks, joins them together and puts them on the number 11.]

### Barbara

So, how many more will you need to make it 11?

### Michelle

Oh well, if I have one here that's the one because 11 is made up of 10 and one more.

So that would be the one more part and I would need 10, but I have one here so that means I have 9 left.

[Michelle splits the 2 tower blocks on the number 11 on the blue game board into single blocks. Michelle points to each block to show how they help make the number 11. Michelle joins the 2 blocks together and puts them back on the number 11.]

### Barbara

Ok. Ok, 2. I might put these ones on here, oh actually, I might leave them here with my 3.

[Barbara rolls dice and rolls 3. Barbara picks up 2 tower blocks, joins them together and places them on the number 3 on the pink game board.]

### Michelle

Hmm, ok. I got a 4 and I am going to... I don't know because I feel like it, put 2 here so and 2 here.

[Michelle rolls the dice and rolls 4. Michelle picks up 2 tower blocks and adds them to the existing tower on number 11 on the blue game board. Michelle puts the other 2 tower blocks on the number 7.]

Oh, ok.

### Michelle

Because 4 is 2 and 2, see you can see it there on the dice.

[Michelle points to the 4 dots on the face of the dice.]

### Barbara

OK 5. So, I might... I need 3 more to get to 7, so I might put those 3 there and then the other 2 I might put towards, I might put one here to complete this tower of 3.

And then put one with the 11, so now I know I only need 10 more for that one.

[Barbara rolls the dice and rolls 5. Barbara picks up 3 tower blocks and adds them to the existing tower of 4 blocks on number 7 on the pink game board. Barbara adds one tower block to the existing tower of 2 blocks on number 3. Barbara puts one tower block on the number 11.]

### Michelle

So, we both have 5 and 3, our towers are both built for 5 and 3. Maybe we could lay them down like that?

[Michelle points to the numbers 5 and 3 on the blue game board.]

Oh, it rolls?

So, if you get stuck remembering which ones are ready.

### Barbara

Oh, that's a good idea.

### Michelle

Like that.

[Michelle lays down the towers on the numbers 3 and 5 on the blue game board to show which towers are complete. Barbara lays down the towers on the numbers 3, 5, and 7 to show which towers are complete on the pink game board.]

Yes.

### Michelle

Oops, sorry 7. Five, so, oh well, I've got 2 here, so I think if I had 5 more, that might make 7.

So, I'm going to check I've got 2, 3, 4, 5, 6, 7 and I think I counted on 5 number words so I had 2 - 1, 2 3, 4, 5, and that is 7, so I can lay that down too.

[As Michelle rolls the dice it falls on the tower on the number 7. Michelle rolls number 5. Michelle shows the existing tower of 2 which is on the number 7 on the blue game board. Michelle adds 5 tower blocks to the 2 tower blocks. Michelle separates 2 blocks from this tower and then counts the remaining 5 blocks. Michelle joins them together and lays the complete tower of 7 blocks on the number 7.]

It looks like a king in a castle.

Having a nap.

### Michelle

Ah, ok, so just another one towards my tower of 11.

[Barbara rolls the dice and rolls one. Barbara picks up one tower block and adds it to the existing tower of one block on number 11 on the pink game board.]

### Michelle

Three more for me. I smell victory coming but I often speak too soon. So, I now have 3. Three and 3 is 6 and one more is 7. So, I need 4 more.

[Michelle rolls the dice and rolls 3. Michelle picks up 3 tower blocks and adds them to the existing tower of 4 blocks on number 11 on the blue game board. Michelle counts the 7 blocks once they are joined together, then puts the tower block on the number 11. Michelle passes the dice to Barbara.]

I need 9 more.

### Michelle

Whoa, you got 5.

[Barbara rolls the dice and rolls 5.]

### Barbara

Ok, well that will help.

So, once I have this 5 in my hand, I can count on the 2 that are already there, so 5, 6, 7, so now I've got 7 in that part too.

[Barbara picks up 5 tower blocks and adds them to the existing tower of 2 blocks on number 11 on the pink game board.]

### Michelle

So, it's the same. We both have 7 and we both need 4.

Aww, 3. I don't know if 3 is good or not because now I'm, I'm hoping for a one.

[Michelle rolls the dice and rolls 3. Michelle picks up 3 tower blocks and adds them to the existing tower of 7 blocks on number 11 on the blue game board.]

Yeah.

### Michelle

Ok, I've got 10 now. I need one more.

### Barbara

Ok and I need 4 more.

### Michelle

Look, it looks like a totem pole.

[Michelle shows Barbara the tower block on number 11 on the blue game board.]

### Barbara

It does.

Oh, my goodness, so I think we're the same now. I've got 3. I had 7 and 3 more gets me to 10.

[Barbara rolls the dice and rolls 3. Barbara picks up 3 tower blocks and adds them to the existing tower of 7 blocks on number 11 on the pink game board.]

Oh my gosh.

### Barbara

So, I just need one more.

### Michelle

And look, yeah, we can check they're exactly the same height, look.

### Barbara

It actually looks similar.

[Michelle and Barbara compare the towers which are on number 11 on the pink and blue game boards. They lie the towers side-by-side and see that each tower has 10 blocks and are the same height. They return the towers to the number 11 on each game board.]

### Michelle

Ok, they both have 10. We both need one. Come on one! That's my lucky dice roll.

It wasn't that lucky.

Come on lucky.

Oooh, I got closer.

[Michelle and Barbara take turns rolling the dice as they each try to roll one.]

Oops. I feel like our dice is not friendly.

### Barbara

Ok, I'll see if my luck works.

### Michelle

We could ask the question how many more rolls do you think it will take? Here you go.

[Michelle and Barbara continue to take turns to roll the dice.]

Yay! So that, no that’s mine.

[Michelle rolls dice and rolls number one.]

### Barbara

Oh, it's your turn... Oh well, I am happy for you.

### Michelle

Thank you. So now look I can prove I'm the winner because I have one more on my tower of 11.

[Michelle adds one tower block to the existing tower of 10 blocks on number 11 on the blue game board to make 11. Michelle then compares this tower to the existing tower on number 11 on the pink game board. Michelle lays the towers side-by-side to show that the tower from Michelle’s blue game board has 11 blocks and is longer than the tower from Barbara’s pink game board which has only 10 blocks. Michelle returns the towers to the number 11 on each game board. All of the towers on Michelle’s blue game board are complete so she is the winner.]

Congratulations.

### Michelle

Thank you very much.

I hope everyone else has fun.

Good game.

### Michelle

It's good isn't it. Have fun playing mathematicians.

[End of transcript]

## Instructions

• Choose 4 numbers to build as your towers (for example, 5, 7, 11 and 3).
• Take turns to roll a dice and use the number of bricks to build up your towers.
• Towers can be built up in any way you choose.
• Take turns to build up your towers until one player gets the exact roll to complete the last tower.
• You can also play this in reverse.
• Talk about how many you have, how many more you need, what strategies you used, etc.

## Other ways to play

• Build the towers and play in reverse. Taking away blocks each time until there are no blocks left.
• Change the number of towers you build.
• Change the number of blocks needed for each tower.

## Reflection

• If you were to play the game again tomorrow, what is one thing you would do differently? Why?
• Draw a picture in your mathematics workbook that shows the towers you built in order of shortest to tallest.