Have you seen…? #3

… these GCSE lesson starters from Eduqas?

Starters - Eduqas
GCSE Starters – Eduqas

A starter, with a worked solution, is available for every day of the year. Starters are also available for Foundation Upper and Foundation Lower. (Select ‘Open resource’ under Files.)

Starter - Eduqas

Eduqas have a whole collection of Mathematics resources well worth exploring. I have used their lovely Rotations, Reflections and Enlargements demonstrations for many years! Looking at the collection, a very happy discovery, these Loci resources.


Loci Teaching Tool – NGfL Cymru

Appropriately for this time of year when so many students are revising for examinations, anyone for a Mathematics Take-Away? These attractively presented resources offer very useful revision indeed. Full solutions are provided.

Mathematics Take-Away - Eduqas
Mathematics Take-Away – Eduqas


Have you seen…? #2

…the famous equation poster contest from the excellent Math Careers site?

Do you have a favourite equation? Peter Alfeld of The University of Utah has a collection he thinks are important or intriguing. My personal favourite, Euler’s identity, is his first on the list.

                    eiπ = -1

For more on beautiful equations try the 17 equations that changed the world on the World Economic Forum where for each equation we have the following information:

  • What does it mean?
  • History
  • Importance
  • Modern use

Or from BBC Earth, have a look at “What is the most beautiful equation?

For UK school age students note the famous equation poster contest from the excellent Maths Careers site. This competition closes on Friday 8th June; winners in each age group will win an Android tablet. There will also be five ‘highly commended’ certificates awarded in each group.

I have added the competition details to Mathematics for Students.

Radio 4 – Puzzle for Today

Driving to work in the mornings I often catch Radio 4’s puzzle for the day.
Answers to all the puzzles for today are provided for a limited time.
Radio 4 has provided an index to the puzzles:
Puzzles 1 to 100       Puzzles 101 to 201    Puzzles 201+

On Thursday 17th May we had one of my favourites that I have used successfully many times – Happy Numbers. Happy Numbers is accessible for a range of abilities and offers a great lesson in the value of recording results carefully so you can use previous results and save yourself work!
28 is happy
My page on Happy Numbers includes links to further resources including a Happy Number Checker on Scratch by Eulguass. Select the green flag to use the program.
Happy 19
Nrich has provided some of the puzzles, as you can see from the blog post here, Nrich has adapted selected problems to appeal to the widest possible audience. Nrich state that their ‘Puzzle for Today’ activities include edited extracts from some of the thousands of rich low-threshold high-ceiling NRICH problems, as well as adaptations of some of NRICH’s extensive collection of short problems published in collaboration with the UKMT.

Here’s another from Nrich, Puzzle 176, March 2018 can you find the number?
I see the Nrich version, one of the UKMT problems here, ‘Many Clues, One Answer‘.

A Level (16+) Teaching Resources

I have several pages on A Level 16+ resources. Valuable resources are available from all the examination boards, all of whom are continuing to add resources for planning and teaching.

I do find it useful to follow this Exams Mathematics list on Twitter, where you will see new resources by the Exam boards flagged up. (You do not need to be a Twitter user to use this list.)

This week, a further look at some OCR resources; have a look at this page on planning and teaching resources.

OCR Check In extension

OCR Check In Test – Algebra and Functions

A whole series of excellent Section Check In Tests which include fully worked solutions are available. Each test includes routine procedural questions, problem solving questions and also an extension activity.

We also have Teaching Activities which include exercises using OCR’s large data set for OCR Mathematics A (H230/H240) for teaching Statistics.
OCR Teaching Activities

Included with the Teacher Guides, notes on OCR’s large data set for OCR Mathematics A (H230/H240) are provided.

Note too the comprehensive set of Delivery Guides on planning and teaching the specification. These are available for both OCR’s specifications. Each Delivery Guide includes many further references to resources, with common content for all examination boards these are useful for everyone.
GeoGebra Alternate egment Theorem ProofLooking at the Delivery Guide on Proof, I like this GeoGebra Alternate Segment Theorem Proof by Michael Borcherds.

Also we have a proof of Pythagoras, attributed by  Americans  to President James Garfield.


GeoGebra Garfield Pythagoras Proof
This could also be a rather nice starter for younger students.

The Proof guide also includes Iff from Nrich where the Teacher Resources includes an Interactive Proof Sorter.

Nrich - Proof

It can be harder to find Mechanics resources, so the suggestions in the Mechanics Guides are welcome.
OCR Guides
See for example, Tom Button’s traffic simulations which originally featured in the DfE Standards Unit resource: Interpreting Distance-Time Graphs with a Computer. They were designed so that students could interpret linear and non-linear distance-time graphs. Tom has rewritten the original 20 simulations that featured in the Java program Traffic  in GeoGebra. (You can easily access any of the Standards unit resources from Nottingham University).

Traffic Simulations - Tom Button

Traffic Simulations – Tom Button

OCR Teaching Activities

OCR Teaching Activities

Included with the Teacher Guides and very useful for those following this specification, OCR has now provided notes on the data set for OCR Mathematics A (H230/H240).


Use of Technology

Definite Integration

Continuing with my project started last week, I have added some further resources to my Excel file showing Technology Resources by subject content. Note that I will make sure that this page always has the latest version of the file. Use of Technology is one of a series of A Level (16+) pages.

The illustration above uses Desmos to illustrate definite integration; we can also use Wolfram Alpha or GeoGebra.

Other additions include:

WolframAlphaIntegration Examples

WolframAlpha Integration Examples

I am adding links to WolframAlpha examples to both the Mathematics and Further Mathematics subject content files. The example here links to all the integration queries you ever wanted!

New on the Further Mathematics Core specification we have Differential Equations .
This post on Differential Equations on Mathematics for Students has the slideshow and also links to some very useful notes and examples. As part of this project, I plan to publish more posts like this on Mathematics for Students.

PhET Balancing Act
PhET Balancing Act

The excellent PhET HTML5 Simulations include Balancing Act, perfect for illustrating Moments. These work very well on mobile devices including phones.


PhET Balancing Act