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Broad Topics > Mathematics Tools > Interlocking cubes

Triple Cubes

Stage: 1 and 2 Challenge Level:

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

How Many?

Stage: 1 Challenge Level:

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Even and Odd

Stage: 1 Challenge Level:

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Holes

Stage: 1 and 2 Challenge Level:

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

Making Longer, Making Shorter

Stage: 1 Challenge Level:

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Stage: 2 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Chairs and Tables

Stage: 1 Challenge Level:

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Building Blocks

Stage: 2 Challenge Level:

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

Cubes Within Cubes

Stage: 2 and 3 Challenge Level:

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

The Third Dimension

Stage: 1 and 2 Challenge Level:

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Nine Colours

Stage: 3 Challenge Level:

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Making Sticks

Stage: 1 Challenge Level:

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Cubes

Stage: 1 and 2 Challenge Level:

This feature brings together tasks which make use of interlocking cubes.

Many Ideas with a Few Cubes

Stage: 1 and 2

This short article outlines a few activities which make use of interlocking cubes.

Four Layers

Stage: 1 and 2 Challenge Level:

Can you create more models that follow these rules?

Three Sets of Cubes, Two Surfaces

Stage: 2 Challenge Level:

How many models can you find which obey these rules?

Cubes Here and There

Stage: 2 Challenge Level:

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

More Building with Cubes

Stage: 2 Challenge Level:

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Building with Cubes

Stage: 1 Challenge Level:

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

Numbers as Shapes

Stage: 1 Challenge Level:

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Path of Discovery Series: 2. First Steps

Stage: 1

This article takes a closer look at some of the toys and games that can enhance a child's mathematical learning.

Two on Five

Stage: 1 and 2 Challenge Level:

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Cubist Cuts

Stage: 3 Challenge Level:

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

Four Colours

Stage: 1 and 2 Challenge Level:

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Creating Cubes

Stage: 2 and 3 Challenge Level:

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Wag Worms

Stage: 2 Challenge Level:

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

Green Cube, Yellow Cube

Stage: 2 Challenge Level:

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

Soma - So Good

Stage: 3 Challenge Level:

Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?

Snakes

Stage: 1 Challenge Level:

Explore the different snakes that can be made using 5 cubes.

3 Blocks Towers

Stage: 1 Challenge Level:

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

Penta Place

Stage: 2 Challenge Level:

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

The Big Cheese

Stage: 2 Challenge Level:

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

Train Carriages

Stage: 1 and 2 Challenge Level:

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Fencing

Stage: 2 Challenge Level:

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Fencing Lambs

Stage: 2 Challenge Level:

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

New House

Stage: 2 Challenge Level:

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

Christmas Presents

Stage: 2 Challenge Level:

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

Stairs

Stage: 1 and 2 Challenge Level:

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Prompt Cards

Stage: 2 Challenge Level:

These two group activities use mathematical reasoning - one is numerical, one geometric.