# Looking at Lego

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

## Problem

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Have a look at the three pictures above, each showing a pair of rectangles.

What do you see?

What mathematical relationships could these six arrangements show?

## Getting Started

It may be helpful to create the rectangles using Lego, or something similar, yourself.

What are you counting?

What are you counting?

## Student Solutions

We had just a few solutions sent in for this activity, but they were excellent, thank you.

Lauren and Violet from Westridge Private School in the USA wrote: ”¨

First, we counted the legos and the rows added up to 12 and 12 on the first picture, 24 and 24 on the second, and 72 on the third.

12 + 12 = 24. 24 + 24 = 48. 48 + 24 = 216. 216 $\div$ 3 = 72!

Melanie from St Adrians RC Primary School sent in the following:”¨

I started off by colour-coding the squares so it is much easier to know which one I'm talking about. The first thing I noticed was that the two rectangles in each picture had the same perimeter and area. Then I realised that in each picture the squares high was ascending by four studs vertically. Then I saw that to get from the first picture to the second one you had to do the equation 12 Ã— 2 to both of the rectangles but to get from the second one to the third one you had to do the equation 24 Ã— 3. Then for the division to get from the third picture to the second picture you had to do the calculation 72 Ã· 3 and to get from the second one to the first one you had to do 24 Ã· 2.

Children from St Monans Primary School in Scotland wrote the following (a larger version of their poster can be see by clicking on the picture:

As a class we did some maths talk around what we could see and our teacher jotted down some of our observations. We then worked in pairs to come up with as many different number sentences to describe some of the relationships we could see in the pictures. We decided to call the bumps on the lego "connectors".

We also labelled the pictures A, B and C so that we could even describe the relationships between the different pictures.

Finally we brought all our results together and explained our ideas to each other. We created a large display of all our results too with speech bubbles for our initial observations.

Maybe you could create another set of three pictures made from Lego rectangles of different sizes and explore further?

Lauren and Violet from Westridge Private School in the USA wrote: ”¨

First, we counted the legos and the rows added up to 12 and 12 on the first picture, 24 and 24 on the second, and 72 on the third.

12 + 12 = 24. 24 + 24 = 48. 48 + 24 = 216. 216 $\div$ 3 = 72!

Melanie from St Adrians RC Primary School sent in the following:”¨

I started off by colour-coding the squares so it is much easier to know which one I'm talking about. The first thing I noticed was that the two rectangles in each picture had the same perimeter and area. Then I realised that in each picture the squares high was ascending by four studs vertically. Then I saw that to get from the first picture to the second one you had to do the equation 12 Ã— 2 to both of the rectangles but to get from the second one to the third one you had to do the equation 24 Ã— 3. Then for the division to get from the third picture to the second picture you had to do the calculation 72 Ã· 3 and to get from the second one to the first one you had to do 24 Ã· 2.

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Children from St Monans Primary School in Scotland wrote the following (a larger version of their poster can be see by clicking on the picture:

As a class we did some maths talk around what we could see and our teacher jotted down some of our observations. We then worked in pairs to come up with as many different number sentences to describe some of the relationships we could see in the pictures. We decided to call the bumps on the lego "connectors".

We also labelled the pictures A, B and C so that we could even describe the relationships between the different pictures.

Finally we brought all our results together and explained our ideas to each other. We created a large display of all our results too with speech bubbles for our initial observations.

Image

Maybe you could create another set of three pictures made from Lego rectangles of different sizes and explore further?

## Teachers' Resources

### Why do this problem?

The array structure of Lego offers a visual representation of multiplication and this activity encourages learners to make the connection between repeated addition and multiplication. The use of Lego as a stimulus for mathematical activity will provide a hook for some children and make them curious to explore further.### Possible approach

Ideally, it would be good to create the rectangles yourself from Lego and display them on the table or floor with everyone sitting around. Ask children what they see and allow time for them to talk in pairs before coming together to share their thoughts. Try to welcome all contributions without placing value on some more than others. At this stage, pupils will comment on all sorts of things, not necessarily only the mathematical!Begin to steer conversations towards mathematics, using relevant responses if possible. Ask children what mathematical relationships they can see represented by the Lego. Give time for them to talk in pairs again before taking some responses all together. Once you feel that everyone has grasped the task, give them time to work in pairs.

As you move around the room, listen in on conversations. Some pupils may focus initially on the colours and find relationships to link them. It may be necessary to talk with different pairs about what they are counting, whether it is rods (single width) or bricks (wider than 1) or the individual raised 'bumps' (you may find that the class agrees on a word to describe these).

If children record each number sentence on a separate strip of paper, you could create an engaging classroom display, with a photo of the Lego rectangles in the middle and examples of relationships around them. You could also jot down pupils' noticings and record them in speech bubbles along with the number sentences.

### Key questions

Tell me how you've done this.What have you noticed about these two rectangles that you are using?

How do you work out the relationship?

What calculations have you done?

### Possible extension

Pupils may use manipulatives to create their own rectangles and show the relationships that are represented. Some learners may like to go further by considering cuboids instead of rectangles:Image