May 28 2015

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.

A3 Constructions
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!

$bisect angle Math Open Ref$

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

I want to spend time planning my lesson and thinking about my students’ learning and how I’m going to help them understand and make it stick.

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.

GCSE New Content – Iterative Methods for Numerical Solution of Equations

(Updated May 2017 with Transum resources in the Further Resources section, March 2017 with Edexcel’s New Content Resources and further TES resources and November 2016 – Diagnostic Questions added to Further Resources /Questions section.)

Looking at the new content for UK GCSE Mathematics a completely new entry on the specification is “find approximate solutions to equations numerically using iteration”.

For some more information on this AQA have some very useful resources, including their Bridging the Gap resources which look very useful for students who have studied the 2007 Key Stage 3 Programme of Study and will be studying a new Mathematics GCSE specification. The resources include examples on iterative methods for solving equations numerically.

AQA Bridging the Gap resources

Students can be reminded to use the ANS key on their calculators; it seems to me that this will be a good opportunity to show students how useful Excel can be for such techniques and will enable teachers to quickly generate results with different starting values.
Excel - iterative solution of equations

From an AQA specimen paper, we see how this may be examined:

AQA Specimen Paper 2 Higher

AQA specimen exam question a

AQA specimen exam question b

In case you are wondering about that flowchart, Newton-Raphson is the method being used.

a little algebra and we see what AQA are up to in their flowchart.
Iteration NR 2

I do love my graphics tablet!
(See Writing Maths Online)

Looking at Edexcel’s Content Support you will find very helpful resources for teaching new content. For new content, information, examples and exercises (with answers) are given. This includes Iteration. Scroll down the list for a zipped file.

Further Resources / Questions

In this post I have included fully worked examples and related graphs; this includes an example (note the pdf file) where an equation has been solved using trial and error and then rather more efficiently using an iterative technique.

Nuffield National Curriculum Mathematics

Diagnostic Questions

On the brillant Diagnostic Questions site you will find excellent coverage of topics new to the GCSE specification. You can also search all questions for a topic of your choice, for example a search on iteration will lead you to the whole collection of Trial and Improvement and Iterative Methods questions. (You will need to be logged in to the site to follow the link. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free. If you scroll down the page you’ll see that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”

From piximaths – see Iterations.

Also on TES Resources dannytheref has a very clear PowerPoint and accompanying worksheet on how to answer iteration questions.

This search on TES returns some further free GCSE Iteration resources including a very clear introduction, Iteration and Square Roots from Owen134866 and a Tarsia puzzle from Jill Hillitt which provides several examples.

On Just Maths we have so many wonderful resources including 9-1 questions by topic, looking at the Higher Tier questions, note that under Algebra (scroll down) Iteration – questions and solutions are available. Questions from Edexcel, AQA and OCR are included.

Maths Genie

The Maths Genie website includes numerous questions and solutions; on this page, scroll down to the last section for Higher and note that under Algebra we have for Solving Equations Using Iteration, revision examples, examination questions and solutions. Looking at the examination questions, the first three questions use Trial and improvement, questions 4 to 7 are on iterative techniques.

For more questions Transum Mathematics offers the exercises shown below on Iteration:
Level 1 – Generating sequences using next term rule.
Level 2 – Rearranging equations.
Level 3 – Using flowcharts to define iterations.
Level 4 – Solving Equations to 1dp.

Level 1 will be useful for KS3, students can find the notation very unfamiliar for sequences.

May 16 2015

Mobile Puzzles – Algebra

Mobile Puzzles

The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC) includes a wonderful collection of Mobile Puzzles. Visit solveme.edc.org to play SolveMe Mobiles (also available for the iPad.)

Looking at the menu, you will see categories with different levels of difficulty available from very simple puzzles to rather more complex puzzles which promote good mathematical thinking.

Students must determine the weight of each object shown which makes a good introduction to the skills required to solve equations, linear and simultaneous.

Looking at some of the Master level puzzles, you will find rather more complex puzzles:

Note the menu in the corner of each puzzle page:

Selecting ‘Information’ provides extensive help; note that various tools are available so you can annotate puzzles and / or add symbols and equations.

create equation
Note that you can then drag a heart to subtract a heart from both sides:
puzzle demo
Note that under settings you can choose to show numbers in the mobile as in the illustration. If the solution is correct, the mobile will balance.

On the other hand….
puzzle demo wrong answer

May 10 2015

GCSE New Content

Note that GCSE New Content has now been given a dedicated page which will be regularly updated. (One of the GCSE series of pages.)

Having read various documents on the new GCSE specifications I thought it would be useful to create a simple summary of new content and add links to relevant resources. On GCSE New Content major changes are indicated by red text, there are also links to relevant resources in each section.

Resources are also listed separately on the GCSE New Content – Resources page.
GCSE