A complete lesson on the theme of the formula for 1+2+3+…+n, looking at how the rule emerges in different scenarios. Activities included: Starter: A classic related puzzle - counting how many lines in a complete graph. After the initial prompt showing a decagon, two differing approaches to a solution are shown. These will help pupils make connections later in the lesson. This is followed by a prompt relating to the handshaking lemma, which is the same thing in a different guise. Pupils could investigate this in small groups. Main: A prompt for pupils to consider the question supposedly put to Gauss as a child - to work out 1+2+3+…+100. Gauss’s method is then shown, at which point pupils could try the same method to sum to a different total. The method is then generalised to obtain Gauss’s rule of n(n+1)/2, followed by a worksheet of related questions. These include some challenging questions requiring pupils to adapt Gauss’s method (eg to work out 2+4+6+…+100). Plenary: A final look at the sequence Gauss’s rule generates (the triangle numbers). Please review if you buy as any feedback is appreciated!

A complete lesson for introducing quadratic sequences. Rather than go straight into using or finding nth term rules, the focus is on looking at differences between terms to identify and extend given sequences. Activities included: Starter: A related number puzzle Main: Slides/examples to define quadratic sequences A set of sequences, some quadratic, for pupils to determine whether they are quadratic or not. A more challenging, open-ended task, where, given the first, second and fourth terms of a quadratic sequence, pupils form and solve an equation to find the third term. Having solved once for given numbers, pupils can create their own examples. Plenary: A comparison between linear and quadratic sequences. No printing required, please review if you buy as any feedback is appreciated!

A complete lesson on areas of composite shapes involving circles and/or sectors. Activities included: Starter: A matching activity using logic more than area rules. Main: Two sets of challenging questions. Opportunity for pupils to be creative/artistic and design their own puzzles. Plenary: Discussion of solutions, or pupils could attempt each other’s puzzles. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A hyperlinked list of geogebra interactives I’ve found on a range of maths topics. Not made by me, I’m just sharing in case people find them useful.

A complete lesson on sharing an amount in a ratio. Assumes pupils have already learned how to use ratio notation and can interpret ratios as fractions - see my other resources for lessons on these topics. Activities included: Starter: A set of questions to recap ratio notation, equivalent ratios, simplifying ratios and interpreting ratios as fractions. Main: A quick activity where pupils shade grids in a given ratio( eg shading a 3 x 4 grid in the ratio shaded:unshaded of 1:2). The intention is that they are repeatedly shading the ratio at this stage, rather than directly dividing the 12 squares in the ratio 1:2. By the last question, with an intentionally large grid, hopefully pupils are thinking of a more efficient way to do this… Examples and quick questions using a bar modelling approach to sharing an amount in a a given ratio. A set of questions on sharing in a ratio, with a progression in difficulty. Includes the trickier variations of this topic that sometimes appear on exams (eg Jo and Bob share some money in the ratio 1:2, Jo gets £30 more than Bob, how much did they share?) A nice puzzle where pupils move matchsticks(well, paper images of them) to divide a grid in different ratios. Plenary: A final spot-the-mistake question, again on the theme of the trickier variations of this topic that pupils often fail to spot. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson designed to be used to consolidate pupils’ ability to add and subtract a negative number. Activities included: Starter: Some straight forward questions to test if they can remember the basic methods and help identify misconceptions. Main: A set of differentiated questions to give pupils a bit more practice. A game adapted from the nrich website. A closer look at the design of the game, with pupils making a sample space diagram. Plenary: Some final questions to prompt discussion and reflection on how to remember the rules used. Printable worksheets and answers included. Please review if you use this!

A complete lesson on the 1/2 absinC area rule. Doesn’t include ‘reverse’ problems (I’ve made a separate resource on this). Activities included: Starter: A set of questions on area of triangles using bh/2. Main: An area question for pupils to attempt, given two sides and the angle between them. If they spot that they can use SOH to get the perpendicular height, they have effectively ‘discovered’ the 1/2absinC rule. If they don’t spot it, then the rule can be easily explained at this point. A set of questions designed to be done as a class using mini whiteboards, progressing from identifying the correct information needed to calculate area, to standard questions, to trickier questions (see cover slide for an example). A two-page worksheet (I’d shrink and print as one page) with a similar progression in difficulty, for pupils to consolidate. Includes a suggested extension task in the comments box of the powerpoint. Plenary: A closer look at question one from the worksheet, which links to the graph of sine.

A complete lesson on solving equations of the form sinx = a, asinx = b and asinx+b=0 (or with cos or tan) in the range 0 to 360 degrees. Designed to come after pupils have spent time looking at the functions of sine, cosine and tangent, so that they are familiar with the symmetry properties of these functions. See my other resources for lessons on these precursors. I made this to use with my further maths gcse group, but could be used with A-level classes too. Activities included: Starter: A set of four questions, effectively equations but presented as visual graph problems, to remind pupils of the symmetry properties of sine and cosine and the fact that tangent repeats every 180 degrees. Main: An example to transition from a visual problem to a formal, worded problem, and a reminder of the symmetry properties of sine and cosine. Five examples of solving trigonometric equations of increasing difficulty, including graphical representations to help pupils understand. A set of similar questions for pupils to do independently. I’ve made this into a worksheet where the graphs are included, to scaffold the work. Includes an extension task where pupils create equations with a required number of solutions. Plenary: A “spot the mistake” that addresses a few common misconceptions. Printable worksheets and answers provided. Please review f you buy as any feedback is appreciated!

A set of challenging activities using Pythagoras’ theorem. Activities included: Starter: Given two isosceles triangles, pupils work out which one has the larger area. Main: Examples/practice questions, followed by two sets of questions on the theme of comparing area and perimeter of triangles. Both sets start with relatively straight forward use of Pythagoras’ theorem, but end with an area=perimeter question, where pupils ideally use algebra to arrive at an exact, surd answer. Plenary: Not really a plenary, but a very beautiful puzzle (my take on the spiral of Theodorus) with an elegant answer.

A complete lesson on finding the nth term rule of a quadratic sequence. This primarily focuses on one method (see cover slide), although I’ve thrown in a different method as an extension. I always cover linear sequences in a similar way and incorporate a recap on this within the lesson. Starter: To prepare for the main part of the lesson, pupils try to solve a system of three equations with three unknowns. Main: A recap on finding the nth term rule of a linear sequence, to prepare pupils for a similar method with quadratic sequences. Examples on the core method, followed by a worksheet with a progression in difficulty for pupils to practice. I’ve included two versions of the worksheet - a simple list of questions that could be projected, or a much more structured worksheet that could be printed. Worked solutions are included. A worked example of an alternative method, that could be given as a handout for pupils who finish early to try on the questions they’ve already done. Plenary: A proof of why the method works. I’d much rather show this at the start of the lesson, but in my experience this usually overloads students and puts them off if used too soon! Please review if you buy as any feedback is appreciated!

A complete lesson on using an nth term rule of a quadratic sequence. Starter: A quick quiz on linear sequences, to set the scene for doing similar techniques with quadratic sequences. Main: A recap on using an nth term rule to generate terms in a linear sequence, by substituting. An example of doing the same for a quadratic sequence, followed by a short worksheet for pupils to practice and an extension task for quick finishers. A slide showing how pupils can check their answers by looking at the differences between terms. A mini-competition to check understanding so far. A set of open questions for pupils to explore, where they try to find nth term rules that fit simple criteria. The intention is that this will develop their sense of how the coefficients of the rule affect the sequence. Plenary: A final question with a slightly different perspective on generating sequences - given an initial sequence and its rule, pupils state the sequences given by related rules. No printing needed, although I’ve included something that could be printed off as a worksheet. Please review if you buy, as any feedback is appreciated!

A complete lesson on using an nth term rule of a linear sequence to generate the first 5 terms in the sequence. Activities included: Starter: Questions to check pupils can evaluate simple algebraic expressions. Main: Introduction to the idea of an nth term rule. Example-question pairs, giving pupils a quick opportunity to try to generate sequences and receive feedback. A set of questions on generating the first 5 terms of increasing sequences, with a progression in difficulty and an extension task. A similar task for decreasing sequences. Plenary: A ‘spot the mistake’ question. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on finding percentages of an amount using non-calculator methods, by relating them to the key percentages of 10%, 25% and 1%. See the cover image to get an idea of the intention of the lesson. Activities included: Starter: A set of questions to recap on finding 50%, 25%, 75%, 10%, 5%, 20% and 1% of an amount. Main: Some slides to introduce the idea of using the key percentages to find other percentages. A worksheet to consolidate these ideas, followed by three flowcharts in the style of the cover image, where pupils are given a starting number and work out all the percentages. The starting numbers get progressively more difficult. I use this as a non-calculator task, but it could be used with calculators too. An extension task where pupils work out some percentages not included in the flowcharts, by combining percentages. Plenary: A great discussion question, looking at four possible ways to calculate 75% of a number. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A presentation to get pupils thinking a about the origins of the metric system. There’s quite a lot of information in there, but I think its interesting so I’m going to make my pupils look at it! There are no worksheets or ‘usual’ metric questions, but I’ve put some follow up questions and possible activities in the comments boxes on each slide. Please let me know if you have any better ideas as mine are a bit lame. Most of the information is taken from Wikipedia so please let me know if you see any innacuracies!

A complete lesson for introducing mean, median and mode for a list of data. Activities included: Mini whiteboard questions to check pupil understanding of the basic methods. A worksheet of straight forward questions. Mini whiteboard questions with a progression in difficulty, to build up the skills required to do some problem solving... A worksheet of more challenging questions, where pupils are given some of the averages of a set of data, and they have to work out what the raw data is. Some final questions to stimulate discussion about the relative merits of each average. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on the equation of a circle with centre the origin. The intention is to get pupils familiar with not only the format of the equation of a circle, and a derivation of the equation, but also problems involving coordinates on a circle. Activities included: Starter: A related question where pupils try to identify which of three given points are closer to the origin, before considering what must be true if points are a given distance from the origin. Main: The starter leads directly into a clear definition of the equation of a circle, followed by a set of quick diagnostic whole-class questions to check for understanding. Example-question pairs of increasingly difficult problems involving coordinates on circles, followed by a set of three worksheets. The last one is more of a mini-investigation, with opportunities for pupils to conjecture and generalise. Plenary: Three final puzzles to check for understanding. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

Hard to describe! Shows how the functions sin and cos effect the trajectory of a cricket ball. A nice real-life example of SOHCAHTOA and the trigonometric functions. Includes some challenging questions at the end. Could be used to revise/demonstrate the curves of sin and cos at GCSE or introduce component form in A-Level Mechanics.

A powerpoint with worksheets on the profit parabola model. A nice rich task to use with high-ability GCSE students, to deepen their understanding of quadratic functions/maximum points and also to see a real-life application of maths.

A few activities on the theme of proving Pythagoras’ theorem, including a version of Perigal’s dissection I took from another TES user. The intention is to encourage discussion about what proof is, and to move pupils from nice-looking but hard to prove dissections to a proof they can make using relatively simple algebra (expanding and simplifying a double bracket). Please review if you use it, like it or even hate it!

An always, sometimes, never activity looking at various properties of triangles (angles, sides, perimeter, area, symmetry and a few more). Includes a wonderfully sneaky (but potentially confusing!) example of triangle area sometimes being the product of the lengths of all three sides. A good way of stimulating discussion, revising a range of topics and exposing misconceptions. Please review and give feedback, whether you like the activity or whether you don’t!