# NRICH PROBLEM SOLVING CUBES

Path of Discovery Series: How many different towers can you make? Numbers as Shapes Age 5 to 7 Challenge Level: 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? To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. Can you do it in more than one way?

How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table? Register for our mailing list. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. What shapes can you find to use? She wants to fit them together to make a cube so that each colour shows on each face just once. The sum of the cubes of two numbers is We need to wrap up this cube-shaped present, remembering that we can have no overlaps.

You may also like Christmas Presents We need to wrap up this cube-shaped present, remembering that we can have no overlaps. I saw that the 4 pointed star was next to one of the shapes I had put down.

## Creating Cubes

How many faces can you see each time? Can you find all the ways that this can be done?

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Even and Ngich Age 5 to 7 Challenge Level: Explore the different snakes that can be made using prlblem cubes. This feature brings together tasks which make use of interlocking cubes.

Some of these models have green cubes that “hang-over” and for this challenge, we’ll decide not to use these. Fencing Age 7 to 11 Challenge Level: I put the shape down on my net:.

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. On the third picture of the cube the square was on the side and the circle on the top. Using any shape of single cube thickness, what is the highest total you can make? In the first example, I can see nine faces – there are four lots of two faces around the sides, then one face at the top. The “wall” has to be only one cube thick. Creating Cubes Age 7 to 11 Challenge Level: Are there any other ways in which I could have arranged the cubes?

# Six Numbered Cubes :

Register for our mailing list. Can you make them to check whether you had imagined them correctly? If you had 36 cubds, what different cuboids could you make? Investigate the area of ‘slices’ cut off this cube of cheese. All 5 to 11 7 to 14 cubex to 16 14 to 18 Challenge level: Have a go at using your imagination to visualise how many I can see, and try making these arrangements yourself to check your answers.

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You might do it some other way. Make a tower using one of each colour. Although there is only one cube, its net can be drawn in different ways. First I drew cuubes first three faces of the cube as a net:. Can you draw them on dotty paper?

Path of Discovery Series: Are they sticks, rectangles or squares? Kimie and Sebastian were making sticks from interlocking cubes and lining them up.

Pebbles Place four pebbles on the sand in the form of a square. Think about how we can tell whether or not two arrangements are the same. Use your three cubes every time, and see how many different ways there are to arrange them.

In the third example, I can see ten faces – there are two lots of five faces. Try with four fences, then five, then six etc. Try to find all the possible answers.