This is a series of prompts to help pupils investigate doing maths on a computer, using either Wolfram Alpha or ChatGPT. These (free) resources are very powerful and can solve word problems.

A worksheet of questions covering the different types of probability covered in the Advanced Higher Statistics Course: Conditional Probability Probability distributions With full solutions (using tree diagrams where appropriate).

For those teaching AH Statistics - I’ve gone through three textbooks finding which parts are relevant for teaching this course. The books are A-Level Statistics Study Guide (Crawshaw & Chambers) Maths in Action – Advanced Higher Statistics (Book 1 and Book 2) Statistics – Practice for Advanced Advanced Mathematics (Alan Smith)

A set of questions where pupils plot some points for a straight line, then identify the gradient and intercepts. Solutions included.

A Powerpoint introducing the basic game of Dobble, then delving deeply into how to arrange the symbols on the cards so that each pair of cards matches exactly once. Pupils will be able to make their own mini Dobble sets, with 7, 13, 21 or even up to the full 55 card set. This introduces uses the following areas of mathematics 2D geometry of lines and planes Magic squares and Latin squares

A Powerpoint with the classic Monty Hall Problem, then variations with a multiple choice questions one hundred doors ten prisoners Solutions in the notes at the bottom of the Powerpoint slides

A Powerpoint introducing the following tricky problems for pupils to think about. -99 Coins 100 Seats on a Plane Special dice Expected wait time Pascal’s Wager Solutions in the notes at the bottom on the Powerpoint See also my resource on Monty Hall Problems

Magic Squares are just the beginning! A Latin square is a grid where each symbol appears exactly once in each row a column - recognisable to most pupils as being like a Su Doku. This resources extends that idea to look at double and further Latin Squares. These are useful for many things (see e.g. my other resource on Dobble)

A colourful poweroint introducing a new idea for most pupils. In standard 2D geometry parallel lines never meet. In projective geometry we add an extra point (infinity) where the lines meet. This turns out to be useful for various problems (e.g. see my other resource on Dobble).

Duality is an important concept in understanding mathematical problems. Sometimes a problem can be ‘reveresed’ by considering it’s dual, for example swapping around lines and points in a triangle. This Powerpoint looks at how duality appears in the following contexts division and subtraction 2D shapes and 3D shapes 2D graphs including the Fano Plane

A teacher-led Powerpoint investigation into randomness to be done at the end of a topic about probability. The five short topics are Pick a random number Heads and Tails experiment Lottery Random numbers Digits of Pi What is randomness? The aim is for pupils to understand that ‘random’ isn’t truly random after all!

A set of six challenging problems where pupils must use all the digits 1-9 exactly once each, for example: Find two three-digit numbers that sum to another three-digit number Solutions provided.

A set of five harder problems about finding the mean which involve pupils using the fact that the total is the number of data points times the mean (or using algebra). Provided with solutions.

A Powerpoint with five routine questions on Integrating factor. Provided with answers.

Two pages of Powerpoints with answers on simple questions like If f(x)=3x+4, find f(5) Then tests fractions and negatives, and finally more difficult questions like If f(x)=3x+4, and f(a)=19, find a

Two extra tasks for pupils doing the Higher Statistics Module. Task 1 is using Excel to analyse some Covid infection data using regression analysis. This has example solutions inline. Task 2 is conducting a survey . Included are example model solutions…

A set of 20 questions in a loop where pupils have to convert to and from Scientific Notation. Print out all 20 in A4 and put them up around the classroom (or outdoors). Give pupils a letter A-T to start on then challenge them to complete the chain of letters by matching up numbers in normal and scientific form.

Shed Loads of Practice (SLOP) is about pupils solving a huge number of easy questions quickly to gain fluency. This is an Excel workbook that generates questions on the following topics. Some are basic numeracy some National 5 / GCSE or Higher Maths level. Negative and Positive Numbers Odd and Even Numbers Combining like terms Expanding brackets Percentages finding the multiplier Trig standard values Scale Factor Indices Print it out and give pupils just a few minutes to fill them all in.

A Powerpoint (or PDF) of algebra problems that involve ages. These are hard enough that they need the equations to be written out in full. Some need simultaneous equations to solve. Solutions given.

Practice Questions on one-sample and two-sample versions of the following tests • z-test for a difference in population means • t-test for a difference in population means (including paired) • z-test for a difference in population proportions