A complete lesson for first teaching pupils how to express a number as a product of its prime factors using a factor tree. Activities included: Starter: Three puzzles relating to prime numbers, intended to increase pupils’ familiarity with them. Main: Examples and questions (with a progression of difficulty and some intrigue). Plenary A ‘spot the mistake’ question. No worksheets required and answers included throughout. Please review it if you buy as any feedback is appreciated!

A complete lesson on the theorem that a perpendicular bisector of a chord passes through the centre of a circle. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees A tangent is perpendicular to a radius Angles in alternate segments are equal Tangents from a point are equal so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: An animation reminding pupils about perpendicular bisectors, with the intention being that they would then practice this a few times with ruler and compass. Main: Instructions for pupils to investigate the theorem, by drawing a circle, chord and then bisecting the chord. Slides to clarify the ‘two-directional’ nature of the theorem. Examples of missing angle or length problems using the theorem (plus another theorem, usually) A similar set of eight questions for pupils to consolidate. An extension prompt for pupils to use the theorem to locate the exact centre of a given circle. Plenary: An animation of the proof without words, the intention being that pupils try to describe the steps. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated!

A complete lesson for first teaching how to simplify a fraction. Activities included: Starter: Some quick questions to test if pupils can find the highest common factor of two numbers. Main: A short activity where pupils sort a selection of fractions into two groups, based on whether they are simplified or not. Example question pairs to quickly assess if pupils understand how to simplify. A set of straightforward questions with a progression in difficulty. A challenging extension where pupils must arrange four digits to create fractions that simplify to given fractions. Plenary: Some questions in context to reinforce the key skill and also give some purpose to the process of simplifying fractions. Optional worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson (or maybe two) for introducing the area rule of a circle. Activities included: Starter: A mini-investigation where pupils estimate the area of circles on a grid. Main: Quickfire questions to use with mini whiteboards. A worksheet of standard questions with a progression in difficulty. A set of three challenging problems in context, possibly to work on in pairs. Plenary: Link to a short video that ‘proves’ the area rule very nicely. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

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 complete lesson on finding the area of a sector. Activities included: Starter: Collect-a-joke starter on areas of circles to check pupils can use the rule. Main: Example-question pairs, giving pupils a quick opportunity to try and receive feedback. A straight-forward worksheet with a progression in difficulty. A challenging, more open-ended extension task where pupils try to find a sector with a given area. Plenary: A brief look at Florence Nightingale’s use of sectors in her coxcomb diagrams, to give a real-life aspect. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

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 on gradient between two points, that assumes pupils have already spent time calculating gradients of lines, and is intended to give pupils an opportunity to use their knowledge of gradient in a slightly more challenging way. The examples and activities involve using knowledge of coordinates and gradient to find missing points on a grid. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on using knowledge of gradient and y-intercept to find the equation of a line. Progresses from positive integer gradients to fractional and/or negative gradients. Examples, printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on finding the gradient of a line that is perpendicular to another. Intended as a precursor to finding equations of lines perpendicular to another. Examples, a range of challenging activities and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson for first teaching how to divide fractions by whole numbers. Activities included: Starter: A simple question in context to help pupils visualise division of fractions by whole numbers. Main: Some example and questions for pupils to try. A set of straightforward questions. A challenging extension where pupils must think a lot more carefully about what steps to take. Plenary: A final example designed to challenge the misconception of division leading to an equivalent fraction, and give a chance to reinforce the key method. Worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching the concept of equivalent fractions. Activities included: Starter: Some ‘fill the blank’ multiplication and division questions (basic, but a prerequisite for finding equivalent fractions with a required denominator or numerator). Main: Visual examples using shapes to introduce concept of equivalent fractions. A worksheet where pupils use equivalent fractions to describe the fraction of a shape. Examples and quick-fire questions on finding an equivalent fraction. A worksheet with a progression in difficulty on finding an equivalent fraction. A challenging extension task where pupils look at some equivalent fractions with a special property. Plenary: A statement with a deliberate misconception to stimulate discussion and check pupils have understood the key concepts. Worksheets and answers included. 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 on solving one step equations using inverse operations. Does include some decimals, as I wanted to give a more complete example set and make it hard for pupils to just use trial and error to find solutions. As such, I would let pupils use calculators. Activities included: Starter: A short task where pupils match up simple one step ‘flll the blank’ statements, flow charts and equations. Then a prompt for them to discuss the solutions to these equations. I would expect them to at least know that to solve means finding numbers that make the equation true, and even if they have no prior knowledge of solving methods, they could verify that a given number was a solution to an equation. See my other resources for a lesson on introducing equations. Main: Some diagnostic questions to be used as mini whiteboard questions, where pupils turn one step equations into flow charts. Examples and a set of questions on using inverse operations to reverse a flowchart and solve its corresponding equation. A more open ended task of pupils creating their own questions, plus an extension task of creating equations with the largest possible answer, given certain criteria. Plenary: A prompt to discuss an example of an equation that can’t be solved using inverse operations. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on the theorem that opposite angles in a cyclic quadrilateral sum to 180 degrees. Assumes that pupils have already met the theorems that the angle at the centre is twice the angle at the circumference, the angle in a semicircle is 90, and angles in the same segment are equal. See my other resources for lessons on these theorems. Activities included: Starter: Some basics recap questions on the theorems already covered. Main: An animation to define a cyclic quadrilateral, followed by a quick question for pupils, where they decide whether or not diagrams contain cyclic quadrilaterals. An example where the angle at the centre theorem is used to find an opposite angle in a cyclic quadrilateral, followed by a set of three similar questions for pupils to do. They are then guided to observe that the opposite angles sum to 180 degrees. A quick proof using a very similar method to the one pupils have just used. A set of 8 examples that could be used as questions for pupils to try and discuss. These have a progression in difficulty, with the later ones incorporating other angle rules. I’ve also thrown in a few non-examples. A worksheet of similar questions for pupils to consolidate, followed by a second worksheet with a slightly different style of question, where pupils work out if given quadrilaterals are cyclic. A related extension task, where pupils try to decide if certain shapes are always, sometimes or never cyclic. Plenary: A slide showing all four theorems so far, and a chance for pupils to reflect on these and see how the angle at the centre theorem can be used to prove all of the rest. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on adding a negative number. Activities included: Starter: Some questions on number bonds. Main: A slide showing a number pattern to demonstrate the logic of adding a negative. Example question pairs with number lines, for pupils to practice and give a chance to provide instant feedback. A set of differentiated questions. A more challenging task for pupils to discuss in pairs, where they try to find examples or counterexamples for different scenarios. Plenary: A final question to prompt discussion about misconceptions pupils may already have. Printable worksheets and answers included. Please review it 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 expressing a change as a percentage. Activities included: Starter: A puzzle to remind pupils of how to make a percentage change. Main: Examples and quick questions for pupils to try, on working out the percentage change. A worksheet with a progression in difficulty and a mix of question types. An extension task involving a combination of percentage changes. Plenary: A ‘spot the mistake’ question. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on finding a term given its a position and vice-versa. Activities included: Starter: Recap questions on using an nth term rule to generate the first few terms in a linear sequence. Main: Short, simple task of using an nth term rule to find a term given its position. Harder task where pupils find the position of a given term, by solving a linear equation. Plenary: A question to get pupils thinking about how they could prove if a number was a term in a sequence. No worksheets required, and answers are included. Please review it if you buy as any feedback is appreciated!

A complete lesson on the alternate segment theorem. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees A tangent is perpendicular to a radius so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: Some basic questions to check pupils know what the word subtend means. Main: Animated slides to define what an alternate segment is. An example where the angle in the alternate segment is found without reference to the theorem (see cover image), followed by three similar questions for pupils to try. I’ve done this because if pupils can follow these steps, they can prove the theorem. However this element of the lesson could be bypassed or used later, depending on the class. Multiple choice questions where pupils simply have to identify which angles match as a result of the theorem. In my experience, they always struggle to identify the correct angle, so these questions really help. Seven examples of finding missing angles using the theorem (plus a second theorem for most of them). A set of eight similar problems for pupils to consolidate. An extension with two variations -an angle chase of sorts. Plenary: An animation of the proof without words, the intention being that pupils try to describe the steps. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated.