In this post I have pulled together lots of different ways of studying 3D shapes, with my new favourite ‘Pull-Up’ shapes. For each activity I have linked it to my favourite nRich tasks, check out their collection here.

**Fold-Up for the Notebook**

This great idea from Pinterest, means pupils can have this 3D shape in their class books but it still folds flat! I believe this idea originally came from Hooty’s Homeroom blog, check out their website here for full instructions.

__n-Rich Pyramid N-gon__

The base of a pyramid has n edges. In terms of n, what is the difference between the number of edges of the pyramid and the number of faces? Check out this nRich task here.

**Construct and Hang-Up**

Using toothpicks or wooden skewers as edges and midget gems or marshmallows as vertices most 3D shapes can be built. These make great 3D shapes for display but also useful for when exploring trigonometry and Pythagoras’ Theorem in 3D. Midget gems will go hard and therefore will withstand the test of time on the classroom windowsill. Check out our blog post ‘Sweets, cocktails sticks and 3D shapes’ here.

NRich Cube Paths Puzzle

Use tooth picks and midget gems to construct** **a skeletal view of a 2 by 2 by 2 cube with one route ‘down’ the cube.

How many routes are there on the surface of the cube from A to B?

(No `backtracking’ allowed, *i.e.* each move must be away from A towards B.)

**Pull-Up**

Often the building of 3D solids leads to some not so pretty and poorly constructed shapes, partly due to ‘accidentally’ cutting tabs off and mostly due to poor fine motor skills. I recently read Liz Meenan’s article for the Association of Teachers of Mathematics, who had experienced the same and in her article she talks about pull-up nets.

The nets are constructed pretty much as usual, however there are no tabs but instead small holes in strategically

placed corners. A thread is then looped through these holes in order, pull on the thread to pull-up your 3D shape.

Check out the full ATM article by Liz Meenan here.

Net Profit- add some challenge to the pull-up cube activity with this nRich task.

The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube? More questions and solutions here.

**Pop-Up**

I absolutely love making the pop-up Spider for a Halloween activity. The pop-up spider is a dodecahedron painted black. Check out our blog post here for this and other Halloween maths ideas.

Alternatively, get pupils to construct equilateral triangles using a compass, therefore create the net for this pop-up octahedron. Check out our post ‘A lesson off-never’ here for further details.

n-Rich Dodecamagic

Here you see the front and back views of a dodecahedron which is a solid made up of pentagonal faces. Using twenty of the numbers from 1 to 25, each vertex has been numbered so that the numbers around each pentagonal face add up to 65. The number F is the number of faces of the solid. Can you find all the missing numbers?

You might like to make a dodecahedron (pop up or not) and write the numbers at the vertices.

Check out the n-Rich task here.

n-Rich Magic Octahedron

In a Magic Octahedron, the four numbers on the faces that meet at a vertex add up to make the same total for every vertex. If the letters F,G,H,J and K are replaced with the numbers 2,4,6,7 and 8, in some order, to make a Magic octahedron, what is the value of G+J? Click here for the website and access to solutions.

**Build-Up (Virtually**)** with Building Houses**

This can be used on the interactive whiteboard to build with ‘virtual’ cubic cubes by pupils or teacher. The shape can be rotated to consider different views (side/front elevation etc). Check out the website here. Colleen Young has a great blog on the use of this app, check it out here.

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