Tag Archives: math

3-D Shapes in more than 3-ways

3 Nov

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

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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’ here.

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.)

Pull-Up

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.

Pop-Up

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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

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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Mathematical Shapes Calendar, Origami

3 Jan

2013New 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.

cal2009small

Another great website with a wide variety of 3D shape Origami calendars are available from this website CDO. The site is in Italian but also has printable 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.

dodecaflexCheck 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 from Sharon and Laura! Get in touch @numberloving and check out our free and premium resources in our TES NumberLoving Store.

Pushing the Sudoku Boundaries!

16 Dec

Try these numberloving favourites!

I was first introduced to Sudoku as a NQT ten years ago and found this puzzle right up my street. I am sure many of you know how to complete a Sudoku puzzle, this article concentrates on puzzles beyond the basic Sudoku. For beginners click here for hints and tips on the classic puzzle.

So what happens when you breeze through [most] sudoku challenges found in newspapers and magazines alike? Or you maybe simply looking for a new logic challenge! Well I recommend the samurai Sudoku. As you can see this joins five classic sudoku to get your brains really working.

Click here for a daily samurai Sudoku, or tap into its archives and puzzles can be printed (myself I prefer to print as a break from the computer). Or there are many books like The Times Samurai Su Doku available through online bookstores.

Way beyond the classic Sudoku is Kuboku a 3D Sudoku cube game created by Creaceed this app, available for £1.49 (at time of publishing). The video below gives a demonstration of Kuboku, don’t forget you get extra Kuboku points if you can complete it faster. You will be interested to know there is no sound in the game, unlike the video!

For a 3D Sudoku in 2D try this flip pad, also known as Tredoku. Tredoku keeps to the same rules as classic Sudoku with the added dimensions or corners which need to be considered whilst completing. Some printable Tredoku available here.

Also don’t forget killer Sudoku, in this game not only do the digits 1-9 have to be placed in the same way as classic Sudoku but you are only given guidance on the total of groups of numbers. Therefore knowing combinations of digits for a given total is helpful. This is an example of one online playing site, there are many available. I use that particular site as its archives are easy to navigate.

New to myself, and frustratingly yet to fully master is the greater than and less than Sudoku, as shown on the right. Again the ultimate goal of placing digits 1 to 9 are the same, however the only hints you are given are the inequalities < or >. I found A day in the Life‘s blog helpful and need to dedicate time to completing one of these over the Christmas break. Play online here, or some print and play here.

The Bermuda Triangle Sudoku game, is a nice twist, with triangle placement of the digits 1-9 as well as colour coordination. Luckily the sound can be muted once the game has begun by clicking on the word sound in the top left corner.

Many of these variations named above are available online, or as a downloadable app for those with a smartphone and on the move. Here is a list of recommended websites for Sudoku. If you have an favourites to add to the list please your comment, authors of Numberloving are always looking for a new puzzle challenge!

Merry Christmas!

Numberloving does not endorse any product or site, we merely blogging about our favourites. There are of course other sites/books/sellers to get these services.

Your Christmas Reading List!

15 Dec

I can’t think of anything better than cuddling up in the holidays with a good book (about Maths of course). Here are Number Loving’s top holiday reads:

1. If the world were a village by David J. Smith is a fascinating account of what the world’s population would be like if it were scaled down to a village of 100 people. You are told so many facts about their ethnic origin, education, standard of living and more, making this a brilliant book to bring out when doing statistics or proportion. It also brings in global issues, for example 17 people in the village can not read and write, what is this as a fraction? or a percentage? if there are 7 billion people in the world how many can not read and write? You can generate endless questions with a sense of importance about them.

2. Addition by Toni Jordan is a fictional comedy about a fellow Maths obsessive, it is really funny and has some nice Maths references

3. Origami Fun Kit for Beginners by Dover is a great introduction to origami, students absolutely adore to do this and it brings in so much Maths in terms of shapes, fractions, angles, estimating, … the list goes on. It is well worth learning a few simple ones to bring out as a fun starter.

4. Conned Again Watson: Cautionary Tales of Logic, Math and Probability by Colin Bruce is a brilliant account of twelve Sherlock Holmes mysteries which all bring in elements of statistics and game theory, I have taken much inspiration from the stories in this book.

5. Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart is a fabulous collection of interesting Mathematical happenings, you can dip in and out of the book and I must have got at least 20 starters and plenaries from ideas in here, there are a few in the series and all are worth a good read. There are quite a lot of books like this on the market but this is definitely one of the best.

6. Secrets and Mince Pies by Craig Barton is a very funny fictional book, written by the ever popular Mr Barton it charts the run up to Christmas of a typical family making it seasonal too, recommended to all but especially number lovers. And what is even better is that it’s available on the Kindle for less than £2!

7. Alex’s Adventures in Numberland by Alex Bellos is a brilliant book charting the travels of Alex Bellos as he jaunts around the globe, there are some real gems in here which will inspire lots of engaging starters for your lessons

8. A brief Guide to the Great Equations by Robert Crease is a stunning book, it describes the ten most beautiful equations and the story behind their conception. Of course it includes Euler’s equation but the other nine are equally brilliant. This is an absolute must read for any A-level Maths teachers to help put some history and beauty into your lessons. Or for any Maths lovers for some self-indulgence!

Happy reading and Merry Christmas from Number Loving!

Carpet Constructions

26 Oct

Bringing ‘Old School’ into new school

So every store cupboard has them, the yellow ‘old school’ construction equipment.

Bring this old school equipment back to life by allowing pupils to graffiti the carpet with maths! I couldn’t think of more beautiful art work.

Pupils can construct bisectors, triangles, regular polygons, angles, using the equipment and some chalk (easily brushes off). Alternatively this can be done in the playground.

Not only do pupils enjoy this but it actually helps pupils who struggle with their fine motor skills.

The uses of chalk are endless; completing a venn diagram on the floor, drawing 2D shapes and labelling as much as they can (equal lengths, parallel sides). Write the answer 5, ask the pupils to come up with as many questions as they can that equal 5. Basically using chalk will hook pupils into doing anything you would do with pen and paper!

If you try it I would love to hear how it goes. Good luck! Get in touch @numberloving

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