Knowledge Organisers – Update

Another update to the post on Knowledge Organisers, a post which includes comments on their use as well as some great resources for Key Stage 3 through to A Level.

This great (and growing collection from Becky Reed is for GCSE Mathematics.

B Reed Indices KO

Indices GCSE Knowledge Organiser extract – Becky Reed

We have here a collection of very clear and also attractive resources. Like other resources in the post I think these are useful in class and for students to use at home also. There are several  examples given which is really helpful.

PhET Simulations – Mathematics


PhET Simulations – Math HTML5

A reminder of all the wonderful PhET simulations available for Mathematics which work on PCs, tablets and phones – Math-HTML5.

Teachers can register for an account which is highly recommended as this offers access to a wealth of further resources including clear instructions for the use of each simulation and activities for students.

If you have not checked these for a while note the latest addition on Vectors, Vector Addition offers choices of  a 1D Screen, a 2-D Screen, and a Lab Screen where students can play with two sets of vectors and compare their sums and add up to 10 vectors of the same type. Using Vector Addition: Equations students can experiment with vector equations and compare vector sums and differences. It is possible to customize the base vectors or explore scalar multiplication by adjusting the coefficients in equation.
PhET vectors

See also Tips for Using PhET.

I have mentioned the excellent PhET Simulations many times on this blog, some reminders below:


Algebra - Area model

Try Area Model Algebra, this is very simple to use. Rectangles of various sizes can be built showing the relationship between multiplication and area.

See also Area Model Decimals and Equality Explorer.

Area Model - Decimals - PhET Simulations

Equality Explorer - PhET SIMS

The ability to display or hide the variable and to take snapshots means working can be clearly shown.

Equality Explorer 2 - PhET SIMS

To help students understand the links between algebraic and graphical representations technology can be so helpful. Try Graphing Quadratics. Using this you can generate definitions for vertex, roots, axis of symmetry and compare different forms of a quadratic function. For your older students, you can define a curve by its focus and directrix!

PhET Quadratics Explorer

PhET Quadratics Explorer focus directrix


Try Graphing Slope-Intercept which allows you to easily demonstrate the equation of a straight line.
PhET slope intercept

We can demonstrate correlation coefficients and lines of best fit with this PhET simulation on Least Squares Regression.

Correlation & Line of best fit

Choose from a range of examples or choose Custom to add your own points and guess then check the correlation coefficient. You can also draw your own line of best fit and compare it to the theoretical line of best fit. Note the option to include residuals for both your own attempt and the line of best fit.

Trig Tour

Trig Tour is another personal favourite, use degrees or radians. Students can look for patterns in the values and on the graph when you change the value of theta. This simulation shows how trig functions are defined for negative angles and angles greater than 90 degrees.

For an excellent introduction to Functions the PhET Simulation, Function Builder provides a very visually appealing resource. Using the pattern option even very young students could explore important concepts. This is very intuitive to use, the slides in the following slideshow demonstrate examples of its use. 

PhET Balancing Act working nicely on my phone!

Staying with Mechanics, one of my favourites now available in HTML5 collection: Projectile Motion.


PhET Projectiles

The simulations are all free to use online, and/or you can download all the HTML5 sims so they are available offline in an app. Available at a very low price ($0.99) for iOS and Android this supports HTML5 sims.

Summer 2020

AMSP Transition

AMSP Transition to A level Mathematics

For Year 11 students, AMSP (Advanced Mathematics Support Programme have announced that their Transition to A level Mathematics free online course has now launched.

(See also Maths At Home which includes further links to transition resources, including AMSP’s resources for Year 10 (no registration or log in required for Year 10 resources), also note Colin Hegarty’s collection of online lessons.

Arithmagons posterFrom Nrich for Primary and Secondary, a challenge each weekday from 20 July to 28 August.

Noted in Mathematical Miscellany #42, remember we have from Wayne Chadburn Keeping Year 10 going over the summer

Mr Chadburn Summer Boost Calendars

Wayne Chadburn has produced calendars for July and August which can be given to Year 10 students for daily practice of key mathematical skills over the summer break.

July 2020

Transum Starters

On Transum, the starters for every day include of course, July and August.

Every day, is just that, including the weekends, it’s worth checking the weekends! Have a look at Saturday 25th and Sunday 26th July for example.

For Saturday we have Middle of Centres:

Middle of Centres
Whilst on the subject of calendars and dates, we can of course consult MacTutor’s Mathematicians of the Day. Not only can we see Mathematicians of the Day, but also a quote and a theorem. Theorem of the day offers a gallery of theorems, note the helpful listings, we can search for theorems by subject for example.

Mathematical Miscellany #43

Primary booklets

White Rose Maths – Primary Booklets

From White Rose Maths, a range of colourful and very attractively presented booklets is available free on Amazon. The booklets can be found on Amazon for the Kindle or downloaded as pdf files from the White Rose Maths Parent Workbooks page. There is one booklet for each of the White Rose Maths blocks for Year 1 to Year 6. The booklets could be used alongside the Primary Assessments.

Primary Assessments

White Rose Maths – Primary Assessments

Maths Overview 1-6Staying with primary resources, Miss A has shared her (free) Maths overview 1-6 on TES Resources. This curriculum overview for years 1-6 includes the main parts of the National Curriculum, White Rose guidance links and a link to the NCETM maths mastery assessment document.

Miss A has also created overviews for English and Science.

So, to the other end of the school, for Year 13 Further Mathematics, an update to my post on Further Calculus (for Further Mathematics). We can use WolframAlpha or Desmos for Improper Integrals.

Improper Integrals University of Pennsylvania

The image shows this resource on Improper Integrals from the University of Pennsylvania, a clear presentation with worked examples.

Such integrals could be shown using WolframAlpha or Desmos. In Desmos, simply type b=infinity for the upper limit. For more on Integration with Desmos, see Learn Desmos: Integrals.
Improper Integral

Improper Integral

Desmos – Integration

Knowledge Organisers is a very popular post, I see Nicola Whiston has been very busy with her Year 10 collection.
Nicola Whiston KO

There has been a great deal of interest in my post on HELM notes, note that in Section 48 we have Engineering Case Studies, which provides a compendium of Engineering Case Studies illustrating many applications of Mathematics. I like the way each case study starts by stating the Mathematical Skills involved.

HELM Case Studies

HELM Notes (48)

The example above seems like a good excuse to show some holiday pictures! (Photograph by David Young).
cosh x Desmos image

Mathematical Miscellany #42

Mr Chadburn Summer Boost Calendars

Summer GCSE Calendars – Mr Chadburn

Keeping Year 10 going over the summer…from Mr Chadburn who has produced calendars for July and August which can be given to Year 10 students for daily practice of key mathematical skills over the summer break.

For A complete set of A Level Statistics and Mechanics Knowledge Organisers – see these resources from Lucyjc.  These resources are available free on TES Resources: Statistics and Mechanics. All include Key Words and Definitions and What Do I Need to Know sections.
Knowledge Organisers - Lucy
And for Pure Mathematics, we have from @misschakera a set for the first year of A Level.
Pure KO

I have added all these very attractively presented resources to this post on Knowledge Organisers which includes links to resources and very importantly the use of knowledge organisers.

OCR Support Highlights

OCR Planning – Support highlights

Staying with A Level, from OCR – see the new resources for A Level to help planning for 20-21 Schemes of Work. New resources are available: new Curriculum Planners, Support Highlights & Resource Plus Mapping resources. Look under ‘Planning’ for: and .

Dan Pearcy

Dan Pearcy

From Seneca’s Virtual Conference, I learned of a new site to most definitely keep an eye from Dan Pearcy.

New content will be added and I am very much looking forward to exploring this site. There is already much food for thought here.





Note the very useful summary of Seneca’s free Distance Learning & Home Study Program in Flavia Belham’s blog post.

And finally…
An excellent read from Blake Harvard, Desiring Difficulties asking how do we get students to desire the difficulties produced by more effective learning strategies? Note the poster available at the end of the post. Try demonstrating what works to the students – let them see the effectiveness of the strategies discussed.

Talking to students about effective learning strategies I have always found the resources from the The Learning Scientists so useful.

For valuable resources to support the techniques described here see the excellent downloadable materials on study strategies. Note how each strategy is backed up by research.