A collection of five nicely presented powerpoints each with 5-10 logic puzzles, taken from the books of Raymond Smullyan. For example: Knights always tell the truth and Knaves always lie. You meet two people. The first says “At least one of us is telling the truth.” What can you say about the two people? All provided with answers, and references from which Raymond Smullyan book they are taken from.

Three examples of how matrices can be used to solve real problems. Requires knowledge of matrix multiplication matrix inverses simple probability Aimed at Advanced Higher Maths but useful for anyone who wants to answer the question ‘what are matrices used for’.

A fun challenge to try and work out the maths behind the fact that a dog will take the optimal path into a river to get a ball. Needs knowledge of visualising 2D motion distance speed time finding the minimum of a quadratic Provided with solutions

Some condensed notes for Advanced Higher Mechanics which include all the key formulas that pupils need to memorise.

A variety of resources for pupils to master Excel. Starts with a simple introduction then moves on to using it to run statistical tests. Although this isn’t part of the syllabus it’s useful for pupils to be able to check their answers, and learn some useful skills. AH Statistics - Simple Activities to learn Excel AH Statistics - How to draw a graph in Excel AH Statistics - Excel AH Statistics - Excel (solutions) AH Statistics - More Excel

Three worksheets for pupils to become familiar with using a TI82 (or similar) Graphics Calculator. Calculator Guide. Explains how to do Basic Navigation, Basic Maths, Statistical Distributions and Statistical Tests. Calculator Practice. Some practice questions to be solved by Graphic Calculator. Solutions at the end. TI82 Stats Calculator Questions. A Powerpoint with some more practice

Three probability resources: Conditional Probability with tree diagrams, Conditional Probability with Venn diagrams, and Conditional Probability with Set Notation. A short video explaining how to solve a conditional probability problem using tree diagrams. A video using a Venn Diagram to determine if the events are independent, mutually exclusive, and calculate some conditional probabilities. This is done alongside calculating with a table. Practice questions with solutions using Set Notation

Two worksheets of questions, one written just before the 2016 US Election and one just before the 2020 US Election. The questions cover sampling, mean and variance, outliers, confidence intervals as well as some more thoughtful questions on the errors in sampling.

A series of statistics questions that cover everything that might be needed for an Advanced Higher Geography project. Largely overlaps with Advanced Higher Statistics. Topics included are: Descriptive statistics (mean, median, mode, range, interquartile range, standard deviation, standard error, coefficient of variation) Inferential statistics (chi-squared) Linear regression Nearest Neighbour analysis Full solutions at the end.

Bridge is a great card game that is played in pairs. It is similar to whist (with tricks and trumps) and requires four to a table. The attached booklets start with the very basics (e.g. dealing the cards) then teach the main concepts. Each booklet has a page of learning, then a short quiz, and so on. I have used these successfully at a school bridge club. Answer booklet included too.

An example of using Venn Diagrams to categorise the numbers from 1 to 20 as either even or prime. Included is Powerpoint Video explanation

Two resources about the Poisson Distribution A Powerpoint that contains everything you need for the Poisson distribution recap of the properties of the Normal and Binomial distributions (to avoid getting them mixed up) examples of situations with Poisson distributions solving small problems using the Poisson formula solving medium problems using a data booklet solving large problems using a normal approximation analysis of the assumptions involved in a Poisson distribution summary of the properties of the Poisson distribution An extra page of questions with solutions at the end

Some resources to help understand the normal approximation to a binomial distribution. A Powerpoint investigating when a Binomial distribution is close to a normal distribution, and also a video commentary of the Powerpoint. We find that if the sample size is too small (or too skewed) then the normal approximation is good. Specifically, we want np>5 and nq>5. A couple of worked solutions to example problems, in video form

A Powerpoint with questions and answers, alongside video solutions. The following questions are solved for a normally distributed population: probability of being above a certain value probability of being below a certain value probability of being between two values Final answers are found using a data booklet (specifically the one for Advanced Higher Statistics in Scotland) Also included ‘AH Statistics Normal Distributions with Phi Notation’ which shows how the number of standard deviations above or below the mean leads to a probability. Normal distribution short questions

Three resources: A Powerpoint with questions and answers, alongside video solutions. The following questions are solved: finding the mean of a sample finding the variance of a sample estimating population mean from a sample estimating population variance from a sample Mean and Varirance questions by P Benson for which I’ve written out solutions Expectation Algebra questions

A Powerpoint with questions and answers, alongside video solutions. The following binomial questions are solved: finding exact probabilities using the formula finding more than or equal probabilities using hte data booklet solving large problems using the normal approximation

A series of worksheets on the following topics. The first three are easier (age 11/12 or S1 in Scotland), the second three harder (age 12/13 or S2 in Scotland) #1 - algebra, percentage, area, perimeter, indices, primes #2 - fractions, substitution, negatives, percentages, Pythagoras, rounding, area #3 - simplifying, polygons, substitution, percentages, rounding #4 - algebra, sequences, volume, percentages, ratio, DST, standard form #5 - angles, area, percentages #6 - fractions, angles, polygons, Pythagoras, area, volume, circles Included with solutions

A series of practice questions on the following converting between improper fractions and mixed numbers adding, subtracting, dividing and multiplying fractions converting between fractions, decimals and percentages Included with answers Edit 2022 -added More Fractions Powerpoint and PDF

Building up and using the skills for Pythagoras: squaring square rooting short side long side mix of short and long side some word problems. Answers included at the end.

A chance for pupils to learn what mathematicians really do: they pick a mathematician from the list and are then guided through a very simplified version of their work. The aim is that pupils learn about a mathematician but also do some real maths! The file Modern Mathematicians.pdf lists all the options, then there are 25 separate tasks to look at. Suggested answers also included.