# Geometric Sparks

I really enjoyed attending a London Maths session yesterday morning – led by Dietmar Kücheman, we had several very enthusiastic Maths teachers working on his lovely Geometric Sparks tasks.

I created the illustration here with Autograph (web version) and was reminded how much I like the features of Autograph web including that lovely colour palette for styling objects! I created a very simple Autograph web file which allows you to move point C along the line (y = -2x + 16), you can also move points B and D to create a rectangle, the Area will be shown for any rectangle. For a more sophisticated version, try this, created by Robert Smith (@RJS2212) (on his phone!)

You can see these tasks on Dietmar Küchemann’s blog Geometric Sparks, but note that Dietmar has now updated these tasks and they have been published by ATM, see Geometric Sparks – Generating links with shapes in space, book and slides, by Dietmar Küchemann.

As you can see from the Introduction to the tasks on his blog, Dietmar Küchemann has based the tasks on NCETM’s Secondary Mastery Professional Development Materials, Theme 6 is on Geometry.

See also, published by the DfE, new guidance -written by the NCETM’s Secondary Team to support the teaching of maths at Key Stage 3. This guidance offers a detailed ordering of the maths that students need to learn from the beginning of Year 7 until the end of Year 9. (See more on KS3 on my KS3 page).

You can look inside the Geometric Sparks publication to see the format for each task. Each task is clearly presented with a commentary and possible methods of solution, including the answer/s.

Perhaps an approach many students might use…

We looked at several tasks in the session, Week 3 Monday provides a lovely illustration of how useful it can be to add lines to a diagram. From Robert Smith, on Autograph again, see his Autograph file for this task.

I took Rob’s file and added some lines and displayed the angles….

It’s a small world sometimes – in October I included Enigma Maths hub in my post on solving linear equations, so I was delighted to meet Jayne Webster at the Geometry Sparks event. Do keep an eye on that site for future developments too.

We can check the Geometry resources on Enigma Maths hub.

# Plans and Elevations

Needing some resources for Plans and Elevations this week – some great resources are…

Diagnostic Questions
A go-to site where I know I can find a quiz on any topic. Looking at the AQA Quiz Collection, we find – 2D Representations of 3D Shapes.

A lovely (free) interactive 3d modelling tool to demonstrate plans and elevations is available in the Geometry collection on on the excellent MathsPad. MathsPad is a subscription site (a very reasonable subscription providing value for money in my personal opinion), you can search for Free resources and you will discover an excellent collection.

TES Resources

This search returns many excellent (free) resources on TES on Plans and Elevations, note that these are TES Picks. The slide shown here is from a very clear PowerPoint, Plans and Elevations,  author, Fintan Douglas.

Dr Frost

Another go-to site, from Dr Frost we have his Plans and Elevations resources. Dr Frost’s consistently high-quality resources include full solutions; you will also find plenty of challenges for students aiming at the highest grades.

SSDD Problems

SSDD Problems tagged Plans and Elevations are currently Triangular Prisms 2 and Triangular Prisms 3.

Don Steward

Many excellent challenges from Don Steward on Plans and Elevations.

# Coordinate Geometry – Underground Maths

Exploring Algebra Review Questions from Underground Mathematics I came across some Coordinate Geometry questions I really like and yesterday spending a day with the very talented writing team and my fellow Underground Mathematics Champions we explored Straight Line Pairs, a question with much scope for exploration and possible methods of solution.

The image above has been created from the Printable/supporting materials.

My Year 11s will be looking at Coordinate Geometry this week and I have some other questions I would like them to try. It is possible to create pdf files for a collection of questions, see Saving Favourite Resources, one of Underground Mathematics’ How To Videos. (See the tutorials page I have in the Underground Maths series of pages – a work in progress).

You will find a whole collection of such questions if you look at Geometry of Equations. This includes many resources including Review questions. Note the Building Blocks resources. I think I’ll be using Underground Mathematics resources with ever younger students – Year 9 can try Lots of Lines! You will see from the the supporting materials that this has come from the brilliant Standards Unit (A10) collection. Students must sort the lines into six pairs, each pair matching one of the given descriptions.

Staying with the Building Blocks I do like Straight Lines where students must decide which of 17 equations are equations of a straight line.
Look at the list – a wonderful lesson in not jumping to conclusions here! Both my Year 9 and my Year 11 are going to be trying these this week!

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Straight Lines reminded me of Line Pairs, I feel an extension for Year 11 coming on!

By Colleen Young

# Review Questions – Underground Mathematics

I wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications  I believe this site will provide us with rich resources for these new specifications.

Each section includes Review Questions, look at Thinking about Algebra for example; scroll down the different resource types for the Review questions for this station.

Alternatively you can browse all the Review questions.

An excellent feature of Underground Mathematics is the excellent search facility; we could look at the Review questions by type. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.

See the example question below, for each review question you will find the question, a suggestion, the solution and sometimes suggestions for taking it further with for example GeoGebra resources.

Note the star by the title – if you choose to log on to the site (you don’t have to but it’s a very good idea!) you can save any favourite resources to your collection.

I can never resist a quick illustration on Desmos! I think I’ll start an Underground Maths Desmos collection! Note the use of the hyperlink on Desmos to link to the question.
Select the image for the Desmos page.

I think we have a wonderful supply of excellent questions here to challenge our students and help them see connections between the various areas of the subject. These are ideal to use with A Level students; some are also useful for higher level GCSE students aiming at those top grades or Level 2 Further Maths students. Any student who wants to study Mathematics at university should certainly be using this site.

By Colleen Young

# Looking for Resources

Pondering a question on Twitter I realised that I always have a few sites I rely on where I know I can always find something. So I thought I’d pick a random example to illustrate.

So – constructions, for demonstrations I always use John Page’s Math Open Reference, his demonstrations are so clear and can be shown step by step; students can also be given the website so they can access them themselves. I found this many years ago when I wanted some demonstrations for constructions – a Google search returned it as the first entry!

Math Open Ref – Bisecting an Angle

So obviously we need some questions / activities. Where to look – our textbooks are fine – plenty of questions there, but what else is available?

On Nrich, try a search by topic facility to find all the resources for a particular topic; searching on constructions there are several resources returned.

Nrich – triangle construction

CIMT – I don’t think CIMT have ever failed me! One can actually do a Google search such as CIMT constructions to very quickly find resources. It is worth being familiar with the site so you know what is where; I would always check the Year 7, 8 and 9 material and also the GCSE course. In this case, the Year 9 resources include Unit 12 on Constructions and loci. As well as the text we have all the supplementary teacher resources. Note that for some Teacher Resources you will need the CIMT password.

I often find Nrich and CIMT more than sufficient and

### And how will I know what they know?

So of course quality resources are key but I don’t want to spend too much time looking for them if it stops me spending sufficient time on the above. I believe it is very worthwhile to have a few key sources so you can find something efficiently and quickly.

Having said that, since this post is on finding resources I’ll mention a few more!

The old Exemplification examples for Key Stage 3 have some very useful example. In this case use the Geometry and Measures document and do a search for constructions.

Teachit Maths though a subscription site offers its entire collection of activities as pdfs free. A search on constructions returns a small number of resources including a good card sort.

I’ll finish with Craig Barton’s and Simon Woodhead’s wonderful Diagnostic questions site. (Select this link for all posts on Diagnostic Questions, these include some instructions for use and other resources for rich questions.) Start typing construction into the search box and various choices will be returned.