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
NRich Cube Paths Puzzle
Use tooth picks and midget gems to constructa 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.
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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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.
Happy New Year to all Number Loving Readers! Get in touch @numberloving and check out our free and premium resources in our NumberLoving Store.
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
How
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!
Get in touch @numberloving and check out our free and premium resources in our NumberLoving Store.
Angry birds is a popular iPhone game, which you can play online here. Big thanks and recognition to @mrprcollins for blogging about these Angry Bird nets on his blog. We like them so much that we felt we should give them a mention too, please check out Mr Collins blog for great ideas and take a look at his Angry Surds display work.
Possible uses So we have used these nets to look at surface area and volume calculator work. As you can see to the right is a picture of work completed by my colleagues’ @emmaemma53 top year 8 pupils! Many of the pupils wanted to take their’s home with them. These can also be used to look at faces, vertices and some basic 3D shape properties at key stage 3. Below is a picture of work completed
Resources These have been downloaded by Mr Collins from The Little Plastic Man an excellent site and well worth a look.
If you use these please give @numberloving @mrprcollins a mention on twitter and leave us a picture. We’d love to see the resources in action! Thanks again to Mr Collins! Get in touch @numberloving and visit our NumberLoving store for free and premium resources
Another idea for shape and space; using small jelly sweets (midget gems in the UK), cocktail sticks and almost any 3D shape can be built! Leave them for a few days and the sweets go hard.
This simple activity has a number of uses across the key stages. You can investigate the basics, such as the properties of 3D shapes (number of edges, vertices and faces), to using Pythagoras and trigonometry in 3D shapes. By constructing the 3D shapes and labeling the vertices, by writing on the sweets, pupils find it easier to extract the correct right-angled triangle which they need in order to complete the Pythagoras or trigonometry calculation.
In addition to basic shape described above they can be used to identify planes of symmetry, the shape of cross sections when calculating volumes. Or even building up 3D coordinates.
If you try it or like this idea please comment, I would love to hear how it goes! Get in touch @numberloving
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
NRich Cube Paths Puzzle
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.
Net Profit- add some challenge to the pull-up cube activity with this nRich task.
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.
New Year, New calendar
So we have used these nets to look at surface area and volume calculator work. As you can see to the right is a picture of work completed by my colleagues’ @emmaemma53 top year 8 pupils! Many of the pupils wanted to take their’s home with them. These can also be used to look at faces, vertices and some basic 3D shape properties at key stage 3. Below is a picture of work completed