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!

Non-calculator sums with standard form is a boring topic, so what better than a rubbish joke to go with it? Pupils answer questions and use the code to reveal a feeble gag.

A complete lesson on prime factors, but not the usual questions. Intended as a challenging task to come after pupils are familiar with the process of expressing a number as a product of prime factors (see my other resources for a lesson on this). Activities included: Starter: A nice ‘puzzle’ where pupils work out three seemingly unrelated multiplication sums (a good chance to practice another non-calculator skill), only to find they give the same answer. Intended to stimulate some discussion about prime factors. Main: Four mini-activities, where pupils use one number’s prime factor form to obtain the prime factor form of some related numbers. An opportunity for pupils to be creative and come up with their own puzzles. Plenary: A final puzzle to check pupils’ understanding of the key idea of the lesson. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson for first teaching pupils how to find the nth term rule of a linear sequence. Activities included: Starter: Questions on one-step linear equations (which pupils will need to solve later). Main: Examples and quick questions for pupils to try and receive feedback. A set of questions with a progression in difficulty, from increasing to decreasing sequences, for pupils to practice independently. Plenary: A proof of why the method for finding the nth term rule works. Answers provided throughout. Please review it if you buy as any feedback is appreciated!

A complete lesson on gradient of curves. Examples and questions on calculating average gradient between 2 points on a curve and estimating instantaneous gradient at a point. Printable worksheets and answers included. Please review it if you buy 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 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 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 on how to use a protractor properly. Includes lots of large, clear, animated examples that make this fiddly topic a lot easier to teach. Designed to come after pupils have been introduced to acute, obtuse and reflex angles and they can already estimate angles. Activities included: Starter: A nice set of problems where pupils have to judge whether given angles on a grid are acute, 90 degrees or obtuse. The angles are all very close or equal to 90 degrees, so pupils have to come up with a way (using the gridlines) to decide. Main: An extended set of examples, intended to be used as mini whiteboard questions, where an angle is shown and then a large protractor is animated, leaving pupils to read off the scale and write down the angle. The range of examples includes measuring all angle types using either the outer or inner scale. It also includes examples of subtle ‘problem’ questions like the answer being between two dashes on the protractor’s scale or the lines of the angle being too short to accurately read off the protractor’s scale. These are all animated to a high standard and should help pupils avoid developing any misconceptions about how to use a protractor. Three short worksheets of questions for pupils to consolidate. The first is simple angle measuring, with accurate answers provided. The second and third offer more practice but also offer a deeper purpose - see the cover image. Instructions for a game for pupils to play in pairs, basically drawing random lines to make an angle, both estimating the angle, then measuring to see who was closer. Plenary: A spot the mistake animated question to address misconceptions. As always, printable worksheets and answers included. Please do review if you buy, the 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 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.

The second of two lessons on Fibonacci sequences with the 9-1 GCSE specification in mind. Please see my other resources for the first lesson, although this also works as a stand-alone lesson. Inspired by a sample exam paper question where pupils had to work out the first two terms of a Fibonacci sequence, given the 3rd and 6th terms. Activities included: Starter: A set of simultaneous linear equation questions, to check pupils can apply the basic method. Main: A nice puzzle to get pupils thinking about Fibonacci sequences. Examples and a set of questions with a progression in difficulty, on the main theme of finding the first terms using simultaneous linear equations. A lovely extension puzzle where pupils investigate a set of Fibonacci sequences with a special property. Plenary: A brief look at some other curious properties of the 1, 1, 2, 3, 5, … Fibonacci sequence, ending with a few iconic images of spirals in nature. Slides could be printed as worksheets, although lesson has been designed to be projected. Answers included throughout. Please review if you buy as any feedback is appreciated!

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 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!