Averages and Spread

The Core Maths resources, now available on STEM Learning include many excellent Statistics resources. The resources are designed to enable students to use and apply statistics in unfamiliar contexts. There are several resources with large data sets available, very useful for students to get used to working with such data sets

Many of these resources could also be adapted for younger students, with my Year 10 students (UK age 14-15) I will use the data and parts of the questions from Averages and Spread: two which explores how to calculate and interpret different measures of location and dispersion.

If we look at the first question, for example, we have the data shown here. Students are required to calculate the mean, median, mode, interquartile range, range, variance and standard deviation (these last two we can save until Year 12).

Averages and Spread 2 qn 1

I particularly like this interpretation question which we can use to give some context to the use of the upper quartile as here we have the upper quartile of 21.2 above the safe limit, suggesting that a quarter of scientists exceeded the safe limit.

The safe level for one year’s exposure is 20.0 mSv. Explain if the following statement is correct, using the data you have just calculated.

‘The scientists at CERN are working within the safe levels of radioactive exposure.’

Full solutions are given in the Teachers’ notes. The activity also includes questions on frequency distributions, one with grouped data.

Averages and Spread 2 CMSP

Core Maths Support Program

We will also be able to review some charts and diagrams using these examples, drawing a box plot for the first example and a cumulative frequency chart for the grouped data example.

For some further useful resources, on TES we have a simple but effective exercise for students to practise drawing box plots byjhofmannmaths, a good example of a time-saving resource for teachers with ready drawn grids for students.

Looking at other resources by jhofmannmaths, I see many well-received resources; I like his simple but useful Expanding simple brackets mistakes which could be a useful Starter / Plenary (or anytime!).  Silly Suzie has made some errors! I appreciate resources like this with several copies to a page – very useful if you want to get a lesson started very promptly and have just changed room – it can be that the paper beats the technology!

Erica - IntegrationTalking of silly Suzie reminds me of Erica and her errors by Andy Lutwyche. I used his  Erica’s Errors on Integration very successfully with Year 12 this week, many of whom made the same mistakes as Erica. We had some great discussions on how easy it is to make such errors and they seem to believe me more than ever that having a look at the graph is a really good idea!

Integration – Desmos & WolframAlpha

With my year 12 students (UK age 16-17) we have been looking at definite Integration. Desmos and WolframAlpha are both excellent for checking work and by using the technology we have a very clear visual representation adding to our understanding.

One of the homework questions for my students involves finding the total shaded area bounded by f(x) = x4−3x3−4x2+12x, the x-axis, the line x=−1 and the line x=3.

We could use WolframAlpha for a quick check. I like the visual representation showing students clearly that they are dealing with areas above and below the x-axis.
Definite Integral
Scrolling down the page we see that this query also returns the indefinite integral.
Indefinite Integral
For the total shaded area, students could change the limits of the query to evaluate each section.

Or we could turn to the excellent Desmos where we can very simply change the limits.

Definite Integration Definite Integration 2

If you are unfamiliar with Integration with Desmos, turn to Learn Desmos: Integrals.
Note you can explore the graph shown in the video.

We could also show students this introduction to Integration on GeoGebra.

A version of this post for students which also includes links to some useful notes and examples can be found on Mathematics for Students.
Integration notes University of Plymouth

Math is fun!


A favourite site – Mathisfun! is a treasure trove of resources.
There are clear indices; the Index from the Home page takes you to the very useful Index by Year and Subject. Explanations and examples are very clear and each section has additional questions to try with solutions. Look for example at the Algebra Index and choose any topic to see the very clearly presented information and activities.

Polynomial Long Division
Polynomial Long Division


You can also use the following pages to search :

I often refer to this site and know that students like the clear presentation. I have used everything from Balance when Adding and Subtracting with younger students to working out the inverse of a 3×3 Matrix with the Sixth Form and lots in between! The Dictionary too is very helpful.
Algebra Balance

3x3 Matrices - Inverses

Thinking about my current teaching, with Year 12 we are looking at the Binomial Expansion, we can see some clear illustrations here including a rather nice illustration for (a+b)3.

With Year 10, having met Surds for the first time this year, some additional examples will be helpful; as mentioned above – each section has a quiz
Surds Quiz

My Further Mathematicians are studying Complex Numbers, some rather nice illustrations can be found here for them.
Complex Numbers
..and on the subject of Complex Numbers, John and Betty can provide an introduction!
John & Betty

Spot the Mistake

…and other updates.

Edexcel Model Answers example
Updating the page on Edexcel’s Teaching and Learning materials (part of the A Level (16+) Resources series) I have included their now complete set of GCSE to A Level Transition worksheets and also exemplar answers with examiner comments, a particularly valuable resource. These booklets look at questions from the AS and A level Sample Assessment Materials, which was used in the trial undertaken in summer 2017. Real student responses are shown together with commentary showing how the examining team apply the mark schemes. The commentary includes always useful notes on common errors. Noting that these could be used in class and students asked to find errors reminded me of some more excellent resources – time for an update of the Spot the Mistake collection.

Erica's Errors - A Lutwyche

Particularly excellent resources come from Andy Lutwyche, look at his excellent Erica’s Errors series for Spot the Mistake activities.

For more resources – see the Spot the Mistake collection.

MEI Making Sense of Information
Another updated page in the A Level series is on Statistics; this includes links to all the large data sets used by the examination boards as well as suggestions and resources for teaching. Note the September/October 2017 edition of MEI’s very helpful M4 magazine which has a focus on the teaching of Statistics and includes information and examples of updates on the large data sets for all the examination boards. The PowerPoint resource could also be used with younger students to get them thinking about the presentation and interpretation of data.

Other checked and updated posts include



Open Middle

Open Middle

I was happily distracted this morning by this lovely problem, Create a System of Two Equations by Daniel Luevanos on Open Middle, accessible for students yet such a great task for mathematical thinking. We could discuss inequalities here as well as simultaneous equations.

Noting the link to a Desmos page as a suggested answer I couldn’t resist creating a more general Desmos page.
Open Middle Problem

Graspable Math created a canvas for this problem, in class we could have this available as well as Desmos. Note the scrub feature.
Sim Eq Opn Middle Problem 1
Sim Eq Opn Middle Problem

Now we could systematically change one variable at a time and start talking about inequalities….

If you are not familiar with Open Middle do explore these excellent problems; you can read more about the type of problems you will find on the site on the About page.

About Open Middle

Open Middle

Note the various ways you can search; note the drop-down menus for each grade.