Resources are not always so easy to find for Advanced Level Further Mathematics – so a project started and which I will work on in the next few weeks – a new series of Further Math pages to have the Further Mathematics information and resources in one place.
You will find content on each of the pages here. With compulsory Pure Content for Further Mathematics for all the awarding organisations, it is useful to look at material from all the examination boards for that content – specimen materials and topic tests for example.
Desmos now provides several functions for computing statistical properties from lists of data.
It is also possible to perform basic statistical tests, count combinations and permutations, and work with distributions. The supported functions can be found on page 11 of the Desmos User Guide. Part of the Learn Desmos series, you can see many functions demonstrated in this series of graphs.
Also very helpful is this Desmos article, from which we see that the Normal, Poisson and Binomial distributions are all supported.
With a requirement for Advanced Level being the use of technology to explore data, the Desmos statistical functions will provide a very valuable addition to our lesson toolbox.
In this article on Data Visualisations, we see that boxplot, dotplot and histogram functions are available.
The excellentMaths Careerssite is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?
Also from Maths Careers, see this post with instructions on how to make this wonderful pair of linked Möbius hearts.
If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….
Note the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper.
To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white space at the end – the picture here has been made using strips 10 cells long.
When factorising quadratic expressions I always encourage students to check coefficients first, if the coefficient of x2 and the constant are prime for example they clearly do not need elaborate methods.
Some students have difficulty with the splitting the middle term method; if one must have a recipe to follow – try the box method.
Mathematical Etudes are creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises.
Note the Etudes by topic at the foot of the page; Number, Algebra, Geometry, Probability & Statistics are available. Looking at Algebra for example, under Solving Equations we see Connected Quadratics which is where I found Lyszkowski’s method of factorising quadratics.
Comparing the two methods with an example:
We could have a look at the general case for the box method :