Interlocking cubes

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Path of discovery series: 2. First steps

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

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Many ideas with a few cubes

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

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Take some ... cubes

In this article we outline how cubes can support children in working mathematically and draw attention to tasks which exemplify this.

problem

Triple cubes

Age

5 to 11

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.

problem

Stairs

Age

5 to 11

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.

problem

Chairs and tables

Age

5 to 7

Challenge level

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

project

How many?

5 to 7

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

problem

Holes

Age

5 to 11

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?

problem

Even and odd

Age

5 to 7

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?

problem

Train carriages

Age

5 to 11

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?

problem

Three block towers

Age

5 to 7

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?

problem

Snakes

Age

5 to 7

Challenge level

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

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Making sticks

Age

5 to 7

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?

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Four colours

Age

5 to 11

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.

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Two on five

Age

5 to 11

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?

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Numbers as shapes

Age

5 to 7

Challenge level

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

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Making longer, making shorter

Age

5 to 7

Challenge level

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

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Building with cubes

Age

5 to 7

Challenge level

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

problem

Four layers

Age

5 to 11

Challenge level

Can you create more models that follow these rules?

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The third dimension

Age

5 to 11

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?

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Prompt cards

Age

7 to 11

Challenge level

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

problem

New house

Age

7 to 11

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?

problem

Fencing lambs

Age

7 to 11

Challenge level

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

problem

Fencing

Age

7 to 11

Challenge level

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

problem

The big cheese

Age

7 to 11

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?

problem

Building blocks

Age

7 to 11

Challenge level

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

problem

Brush loads

Age

7 to 11

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.

problem

More building with cubes

Age

7 to 11

Challenge level

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

problem

Cubes here and there

Age

7 to 11

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?

problem

Multilink cubes

Age

7 to 11

Challenge level

If you had 36 cubes, what different cuboids could you make?

problem

Presents

Age

7 to 11

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?

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Green cube, yellow cube

Age

7 to 11

Challenge level

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

Coloured wooden blocks arranged to make a two-by-two cube.

problem

Creating cubes

Age

7 to 11

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.

problem

Three sets of cubes, two surfaces

Age

7 to 11

Challenge level

How many models can you find which obey these rules?

problem

Penta place

Age

7 to 11

Challenge level

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

problem

Wag worms

Age

7 to 11

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.

problem

Cubes within cubes

Age

7 to 14

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?

problem

Soma - so good

Age

11 to 14

Challenge level

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

problem

Nine colours

Age

11 to 16

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?

problem

Cubist cuts

Age

11 to 14

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?

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Interlocking cubes