Maze consists of squares containing questions (on addition, subtraction, multiplication and division of fractions) with answers, some of which are wrong. Pupils are only allowed to pass through squares containing correct answers. Extension - pupils design their own maze (I like to discuss how they can make their maze harder by including classic misconceptions). Extra worksheet included to help pupils think about misconceptions (warning - this may well confuse weaker pupils!)

A collection of 5 activities involving square numbers that I’ve accumulated over the years from various sources: a puzzle I saw on Twitter involving recognising square numbers. a harder puzzle using some larger square numbers and a bit of logic. a sequences problem that links to square numbers a mini investigation that could lead to some basic algebraic proof work a trick involving mentally calculating squares of large numbers, plus a proof of why it works Please review if you like it or even if you don’t!

A complete lesson on finding percentages of an amount using non-calculator methods. Looks at finding 50%, 25%, 75%, 10%, 5%, 20% and 1%. Activities included: Starter: A set of questions where pupils convert the percentages above into their simplified, fraction form. Main: Some examples and quick questions on finding percentages of an amount for pupils to try. A set of questions with a progression in difficulty, from finding simple percentages, to going in reverse and identifying the percentage. The ‘spider diagrams’ are my take on TES user alutwyche’s spiders. An extension task where pupils arrange digits (with some thought) in order to make statements true. Plenary: A nice visual flow chart to reinforce how the calculations required are connected. Printable worksheets and answers included. Please review if you use as any feedback is appreciated!

A complete lesson for first teaching how to find a fraction of an amount. Activities included: Starter: A matching activity, where pupils pair up shapes with the same fraction shaded. Main: Some highly visual examples of finding a fraction of an amount, using bar modelling. Some examples and quick questions for pupils to try (these don’t use bar modelling, but I guess weaker pupils could draw diagrams to help). A set of questions with a progression in difficulty, from integer answers to decimal answers to some sneaky questions where the pupils need to spot that the fraction can be simplified. An extension task where pupils arrange digits (with some thought) in order to make statements true. Plenary: A nice visual odd-one-out puzzle to finish, that may well expose a few misconceptions too. Optional, printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on identifying the y-intercept of a linear function. Intended as a precursor to using gradient and y-intercept to plot a linear function, but after pupils have plotted graphs with a table of values (ie they have seen equations of lines already). A good way of getting pupils to consider gradient without formally being ‘taught’ it. Activities included: Starter: A puzzle about whether two boats (represented on a grid) will collide. Main: Examples and three worksheets on the theme of identifying y-intercept. The first could just be projected and discussed - pupils simply have to read the number off the y-axis. The second is trickier, with two points marked on a grid, and pupils extend this (by counting squares up and across) until they reach the y-axis. The third is a lot more challenging, with the coordinates of 2 points given on a line, but no grid this time (see cover image). Could be extended by giving coordinates of two points, but one either side of the y-axis (although I’m going to do a whole lesson on this as a context for similarity, when I have time!) Plenary: A look at how knowing the equation of a line makes finding the y-intercept very easy. Examples, printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on using a table of values to plot a linear function. Nothing fancy, but provides clear examples, printable worksheets and answers. Please review it if you buy as any feedback is appreciated!

A complete lesson on using knowledge of gradient to find the equation of a line parallel to a given line. Examples, activities, printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on interior angles of polygons. Activities included: Starter: A slide showing examples and non-examples of interior angles, for pupils to think about a definition, followed by a set of images where pupils must identify any interior angles (sounds easy and dull, but isn’t!) Main: A recap of visual proofs of why the interior angles of a triangle sum to 180 degrees and those of a quadrilateral sum to 360 degrees, leading to the obvious question of “what next?” Prompts for the usual “investigation” into the sum of interior angles for polygons, by splitting into triangles. A set of questions designed to be done with mini whiteboards, starting with basic sums of interior angles, interior angles of regular polygons and finally a few variations (see cover image). A four-part worksheet (one page if printed two-a-side and two-sided) with a similar progression in difficulty. Plenary: A slide summarising the rules encountered, together with some key questions to check for any misconceptions. Printable worksheets and answers included. I’ve also included suggested questions and extensions in the notes boxes at the bottom of each slide. Please review if you buy as any feedback is appreciated!

A complete lesson looking at slightly trickier questions requiring Pythagoras’ theorem. For example, calculating areas and perimeters of triangles, given two of the sides. Activities included: Starter: A nice picture puzzle where pupils do basic Pythagoras calculations, to remind them of the methods. Main: Examples of the different scenarios pupils will consider later in the lesson, to remind them of a few area and perimeter basics. Four themed worksheets, one on diagonals of rectangles two on area and perimeter of triangles, and one on area and perimeter of trapeziums. Each worksheet has four questions with a progression in difficulty. Could be used as a carousel or group task. Plenary: A prompt to get pupils discussing what they know about Pythagoras’ theorem. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson of more interesting problems involving perimeter. I guess they’re the kind of problems you might see in the Junior Maths Challenge. Includes opportunities for pupils to be creative and make their own questions. Activities included: Starter: A perimeter puzzle to get pupils thinking, where they make changes to shapes without effecting the perimeter. Main: A set of four perimeter problems (on one page) for pupils to work on in pairs, plus some related extension tasks that will keep the most able busy. A matching activity, where pupils match shapes with different shapes but the same perimeter, using logic. I would extend this task further by getting them to put each matching set in size order according to their areas, to address the misconception of confusing area and perimeter. Pupils are then prompted to design their own shapes where the perimeters are the same. Plenary: You could showcase some pupil designs but much better, use all of their answers to create a new matching puzzle. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on solving two step equations of the form ax+b=c using the balancing method. Designed to come after pupils have solved using a flowchart/inverse operations. Activities included: Starter: A set of questions to check that pupils can solve one step equations using the balancing method. Main: A prompt for pupils to consider a two step equation. An animated solution to this equation, showing physical scales to help reinforce the balancing idea. An example-problem pair, to model the method and allow pupils to try. A set of questions with a variation element built in. Pupils could be extended by asking them to predict answers, or to explain the connections between answers after finishing them. A related, more challenging task of solving equations by comparing them to a given equation, plus a suggested extension task for pupils to think more mathematically and creatively. Plenary: A closer look at a question, looking at the two different balancing approaches that could be taken (see cover slide). Depending on time, pupils could go back and attempt the previous questions using the second approach. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson of more challenging problems involving the sine rule. Designed to come after pupils have spent time on basic questions. Mistake on previous version now corrected - please contact me for an updated copy if you have already purchased this. Activities included: Starter: A set of six questions, each giving different combinations of angles and sides. Pupils have to decide which questions can be done with the sine rule. In fact they all can, the point being that questions aren’t always presented in the basic ‘opposite pairs’ format. Pupils can then answer these questions, to check they can correctly apply the sine rule. Main: A set of eight more challenging questions that pupils could work on in pairs. Each one is unique, with no examples offered, and therefore I’d class this as a problem solving lesson - pupils may need to adopt a general approach of working out what they can at first, and seeing where this takes them. Questions also require knowledge from other topics including angle rules, shape properties, bearings, and the sine graph. I’ve provided full worked answers FYI, but I would get pupils discussing answers and presenting to the class. Plenary: A prompt for pupils to reflect on possible rounding errors. Most of the questions have several steps, so it is worth getting pupils to think about how to avoid rounding errors. I’ve left each question as a full slide, but I’d print them 4-on-1 and 2-sided, so that you’d only need to print one worksheet per pair. Please review if you buy as any feedback is appreciated!

A complete lesson on the scenario of using the sine rule to find an obtuse angle in a triangle. Given the connection this has with triangle congruence and the graph of sine, these ideas are also explored in the lesson. Designed to come after pupils have spent time doing basic sine rule questions and have also encountered the graph of sine beyond 90 degrees. Activities included: Starter: A goal-free question to get pupils thinking, that should help recap the sine rule and set the scene for the rest of the lesson. Main: A prompt for pupils to construct a triangle given SSA, then a closer look at both possible answers. Depending on the class, this could be a good chance to talk about SSA being an insufficient condition for congruence. A related question on finding an unknown angle using the sine rule. Pupils know there are two answers (having seen the construction), but can they work out both answers? This leads into a closer look at the symmetry property of the sine graph, and some quick questions on this theme for pupils to try. Then back to the previous question, to find the second answer. This is followed by four similar questions for pupils to practice (finding an obtuse angle using the sine rule) Two extension questions. Plenary: A slide to summarise the lesson as simply as possible. Answers and printable worksheets included. 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 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 set of questions in real-life scenarios, where pupils use SOHCAHTOA to find angles an distances. Activities included: Starter: Some basic SOHCAHTOA questions to test whether pupils can use the rules. Main: A set of eight questions in context. Includes a mix of angle of elevation and angle of depression questions, in a range of contexts. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first introducing how to find angles in a right-angled triangle using a trig ratio, but as a pupil-led investigation. Intended to come after pupils have practiced identifying hypotenuse/opposite/adjacent and calculating sin/cos/tan. Activities included: Starter: A set of questions to check pupils can correctly calculate sin, cos and tan from a triangle’s dimensions. Main: A structured investigation where pupils: Investigate sin, cos and tan for triangles of different size but the same angles (i.e. similar triangles), by measuring dimensions of triangles and calculating ratios Investigate what happens as the angle varies by measuring dimensions of triangles, calculating ratios, and plotting separate graphs of sin, cos and tan. Using their graphs to estimate angles for conventional SOHCAHTOA questions (i.e. finding an angle given two sides) Plenary: A prompt to get pupils to discuss/reflect on their understanding of the use of trig ratios. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete revision lesson for pupils to practice SOHCAHTOA, both finding sides and angles. Activities included: Starter: A set of questions to test whether pupils can find sides and angles, and give a chance to clear up any misconceptions. Main: A treasure hunt of SOHCAHTOA questions. Straight forward questions, but should still generate enthusiasm. Could also be used as a a more scaffolded task, with pupils sorting the questions into sin, cos or tan questions before starting. Activity has been condensed to two pages, so less printing than your average treasure hunt! Bonus: Another set of straight-forward questions, that could be given for homework or at a later date to provide extra practice. Printable worksheets and answers included. Please review 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!