Worksheet and worked examples with two intuitive stories of how people could need to use a reciprocal to find a whole quantity when they only know a fraction of it. Could be suitable for KS2, KS3 or advanced KS1 students. There’s versions in poster form, a problem sheet and (probably most useful for students) a version with notes and worksheet merged onto one page. (The answers are 30 minutes and 12 minutes.) To make it approachable for students in a range of countries I have versions where the money is UK pounds, the Euro or dollars-with appropriate Emoji images! Comment if you’d like a version in a different currency, I’ll add it.

Poster showing how you divide by a fraction. There’s two case studies, one simple, dividing a fraction by another fraction, and another more complicated, starting from a whole number. Suitable to be printed large on a classroom wall or at small size for students to stick into their exercise book or folder. Suitable for students around KS2 to KS3 and weaker GCSE students. As an advanced point for students doing well, it introduces the idea of reciprocals.

Here’s a one-page diagram of reverse percentages, showing and explaining the idea that you have to find the single percentage change that turns into old into new and reverse it. Both % increase and % decline are covered as examples. Suitable for students to glue into their book as an example or for putting as a poster in a classroom.

A lot of students have trouble with the idea that there’s two ways to use a divide sign: when you want to split something up between a group of known size, and when you want to split something up into units of known size but an unknown number of units. So here’s a poster covering that which explains it by telling a happy story. Could look good on a wall of a classroom or to give students to put into their books. Because people have a lot of trouble learning this, this could be useful for KS1, KS2, KS3 and weaker GCSE students who need a bit of help.

Revision notes on trigonometry: all the equations with all the rearrangements. Covers trigonometry of a right angle triangle, the sine rule and the cosine rule. Also explains when you can use the sine and cosine rule equations (e.g. that you can work out an angle using the cosine rule when you know all the sides). Suitable for all the GCSE maths specifications.

Explanation of what “per” means: that it means you need to divide. Two stories are given as examples. Suitable for primary school maths and science. Because people have a lot of trouble learning this, this could be useful across a lot of ages, KS1, KS2, KS3 or weaker GCSE students who need a bit of help.