3D Shapes in more than 3-ways

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

mobileUsing 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.  CIMG0057Midget 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

imageNRich 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.)


image imageOften 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.

imageNet 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.



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.IMG00133-20111104-1331

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

imageIn 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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Volume with Mario and Luigi

angry2One of our most popular blog posts to date has been “Nets to catch Angry Birds” (view here) in which these computer game characters are constructed into 3D shapes using nets. Leading to investigations about area, volume, surface area and scale factors and some great display work.

In our pursuit to continue to “Pimp Our Displays” as described in an earlier post here, I wanted to do something different to Angry Birds. I’ll admit I am not an avid game player at all but even I know Minecraft is big and very ‘blocky’ in its nature, so I went searching and it really didn’t take long, here is what I found. First I came across this TES resource, which includes the net of a Minecraft zombie and creeper, this was uploaded by Daniohara.

minecraft_steveSome further research and I found FPS-X-Games.com blog by Steven Bear and his printable resources on his post “Minecraft Mob” here. His post includes nets to build Steve the Minecraft character, shown on the left. Nets to make the Creeper, the Pig, the Zombie and the Spider.

Barking Dog also provides printable nets for the Minecraft materials such as sand, dirt, stone and grass, check it out here. And check out a Minecraft Fan Club page here with more printable nets.

I was still not satisfied, I continued to think about how I could bring the classwork into a great display and bingo I thought Mario! Mario is timeless, everyone knows Mario, Luigi, those blocks and that tune!

Wow check out this site Deviant Art and Taringa.net from here I downloaded the resources ready for the Mario class and display work. So the plan is to print these in full colour, pupils can then construct, consolidating their learning about surface area. I will then make a Mario 3D display, by having at least two separate rows of 3D mystery blocks and 3D versions of Mario, Luigi and the other characters. I will then get the pupils to do the calculations of volume or surface area alongside the display!

Check these out nets;

mario_bros___cubeecraft___papercraft_by_marcokobashigawa-d6z2mps cube mariomushroom









So what if Mario is not your thing, just image search “Cubecraft Cartoons” and if there is a cartoon character you can think of I bet it is there!

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Mathematical Shapes Calendar, Origami

New Year, New calendar

Inspired by David Mitchell’s Mathematical Origami book , I started to think what about using an origami dodecahedron as a calendar! A quick search revealed it had been done!

Todd’s place will produce rhombic calendars in different languages, with or without guidelines, you can also change the font and colours too. However you will need to save as a PS file and then use the online converter detailed on the site.

Another great website with a wide variety of 3D shape Origami calendars are available from this website CDO.

The site is in Italian but this can be changed at the top, it also has printable worksheets in English and other languages. I found the guidelines on the printouts very useful.

This video below shows how to make one of my favourites and not just because it looks great but I also think it would be interesting to ask pupils work out the surface area of the completed shape.

To increase the difficulty pupils could use pencil and compass techniques to construct each of the faces and then construct! Great for extra curricular maths club!

Inspired by my colleague Sister Mary-Anne I have been thinking how else to use flexagons, and have found these on the Origami Resource Centre with a calendar based on a pentahexaflexagon by Ralph Jones.

Check out their website for templates like this (to the right ). Scroll down to Flexagon Calendars to download the 2013 printable worksheets to make your own and there are also links to video instructions.

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Halloween Pop-Up Spiders and 3D Shapes

Our next idea for a mathematical Halloween activity involves 3D shapes. Using a pop-up dodecahedron pupils can review the properties of 3D shapes such as vertices, faces and edges and have a great pop-up spider to take home.

Where’s the maths

  • Nets of 3D shapes
  • Properties of shapes; faces, edges and vertices
  • Planes of symmetry
  • Angle properties of each face of the dodecahedron

You will need

  • Template of a dodecahedron, download one from Sen teacher website from here.
  • Some black card
  • Elastic bands
  • Black pipe cleaners for the legs
  • Elastic bands for pop-up ability
  • Stick on eyes


Download a template of a dodecahedron from here the SEN website and use as a template.

Cut out the dodecahedron on black card but separate into two pieces like this;

Now test the pop-up ability of your spider by following this quick video;

Then decorate your spiders with eyes and legs made from pipe cleaners! Alternatively make a normal 3D Dodecahedron to make a spider that does not pop-up!

We like to hear how the ideas worked for you and would love to see a picture of any spiders made by your class!

Check this out made by @jonsmcest!

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Skeletons, Ghouls and Rotational Symmetry

Amazing Skeleton snowflake by She Walks Softly Author and a great demonstration of rotational symmetry.

This Ghouls and bats template can be downloaded from here, courtesy of Extreme Cards Blog Spot showing rotational symmetry of order four.

halloween kirigami

A wide variety of creepy snowflake templates can be downloaded from PaperPumpkins

A rotational spider template can be downloaded from New Halloween Games here.

These snowflakes are great and look amazing when done but they require a steady hand. Instead you could ask pupils to create their own spooky snowflake with a given order of symmetry.

Check out Matters of Grey and Anthony Herrera’s star wars snowflakes which are fabulous and should be kept in mind for Christmas.

Join this activity with the hama bead activity described in Hama Bead & Symmetry blog here for another rotational symmetry activity, you may want to buy extra orange and black beads for Halloween!

Happy Halloween from Number Loving! Get in touch @numberloving and check out our free and premium resources in our NumberLoving Store.

Hama beads & Symmetry

When I was younger I loved hama beads, for those who haven’t used them they are little cylindrical beads which you arrange on a grid, when you are happy with your creation you iron over the beads and they bond together. When studying lines of symmetry what better way to test student understanding than by asking them to create their own pattern. I did this with my low ability year 7’s, I differentiated by letting them pick the number of lines of symmetry which they had in their pattern. I had also drawn lines of symmetry on some of the grids for the weakest students. They loved it and even stayed at break to make another one!

You can buy hama beads and the grids off ebay or amazon but most toy stores sell them too, for a class you only need a small amount but I would buy a medium pack so you don’t run out of any colours.  If your class do this we would love to see their work, tweets us @laurareeshughes and @numberloving and check out our free and premium resources in our TES NumberLoving Store.