The last of five complete lessons on linear sequences. Looks at patterns of squares or lines that each form a linear sequence. Adapted from a resource by another TES user called flibit (who has made some excellent resources). Printable worksheets included.

Worksheet where answers to questions are used to obtain a 3-digit code (which I set as the combination to a lockable money box containing a prize). Questions on a mixture of all the GCSE-standard percentage skills.

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 generating equivalent ratios and simplifying a ratio. Activities included: Starter: A set of questions to remind pupils how to find equivalent fractions and simplify fractions. I always use fraction equivalence to introduce ratio, so reminding pupils of these methods now helps them see the connections between the two topics. Main: A matching activity where pupils pair up diagrams showing objects in the same ratio. Examples and quick questions on finding equivalent ratios (eg 2:5 = 8:?) A matching activity on the same theme. Examples and a set of questions on simplifying ratios. A challenging extension task, using equivalent fractions in a problem-solving scenario. Plenary: A final odd-one-out question to reinforce the key ideas of the lesson. Printable 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 inverse operations. Includes questions with decimals, with the intention that pupils are using calculators. Activities included: Starter: Four simple questions where pupils fill a bank in a sum, to facilitate a discussion about possible ways of doing this. Slides to formalise the idea of an inverse operation, followed by a set of questions to check pupils can correctly correctly identify the inverse of a given operation and a worksheet of straight-forward fill the blank questions (albeit with decimals, to force pupils to use inverse operations). I have thrown in a few things that could stimulate further discussion here - see cover image. Main: The core of the lesson centres around an adaptation of an excellent puzzle I saw on the Brilliant.org website. I have created a series of similar puzzles and adapted them for a classroom setting. Essentially, it is a diagram showing boxes for an input and an output, but with multiple routes to get from one to the other, each with a different combination of operations. Pupils are tasked with exploring a set of related questions: the largest and smallest outputs for a given input. the possible inputs for a given output. the possible inputs for a given output, if the input was an integer. The second and third questions use inverse operations, and the third in particular gives pupils something a lot more interesting to think about. The second question could be skipped to make the third even more challenging. I’ve also thrown in a blank template for pupils to create their own puzzles. Plenary: Your standard ‘I think of a number’ inverse operation puzzle, for old time’s sake. Printable worksheets and answers included. Please do 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 connected ratios, with the 9-1 GCSE in mind. The lesson is focused on problems where, for example, the ratios a:b and b:c are given, and pupils have to find the ratio a:b:c in its simplest form. Assumes pupils have already learned how to generate equivalent ratios and share in a ratio- see my other resources for lessons on these topics. Activities included: Starter: A set of questions to recap equivalent ratios. Main: A brief look at ratios in baking, to give context to the topic. Examples and quick questions for pupils to try. Questions are in the style shown in the cover image. A set of questions for pupils to consolidate. A challenging extension task where pupils combine the techniques learned with sharing in a ratio to solve more complex word problems in context. Plenary: A final puzzle in a different context (area), that could be solved using connected ratios and should stimulate some discussion. Printable worksheets and answers included. Please review 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 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 on the theme of star polygons. An excellent way to enrich the topic of polygons, with opportunities for pupils to explore patterns, use notation systems, and make predictions & generalisations. No knowledge of interior or exterior angles needed. The investigation is quite structured and I have included answers, so you can see exactly what outcomes you can hope for, and pre-empt any misconceptions. Pupils investigate what happens when you connect every pth dot on a circle with n equally spaced dots on their circumference. For p>1 this generates star polygons, defined by the notation {n,p}. For example, {5,2} would mean connect every 2nd dot on a circle with 5 equally spaced dots, leading to a pentagram (see cover image). Pupils are initially given worksheets with pre-drawn circles to explore the cases {n,2} and {n,3}, for n between 3 and 10. After a chance to feedback on this, pupils are then prompted to make a prediction and test it. After this, there is a set of deeper questions, for pupils to try to answer. If pupils successfully answer those questions, they could make some nice display work! To finish the lesson, I’ve included a few examples of star polygons in popular culture and a link to an excellent short video about star polygons, that references all the ideas pupils have considered in the investigation. I’ve included key questions and other suggestions in the notes boxes. 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 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 prime factors. 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: Questions to test pupils can list all factors of a number using factor pairs. Main: Pupils find all factors of a number using a different method - by starting with the prime factor form of a number and considering how these can be combined into factor pairs. Links well to the skill of testing combinations that is in the new GCSE specification. Possible extension of pupils investigating what determines how many factors a number has. Plenary: A look at why numbers that are products of three different primes must have 8 factors. No worksheets required and answers included throughout. Please review it if you buy as any feedback is appreciated!

A complete lesson for first teaching how to compare fractions using common denominators. Intended as a precursor to both ordering fractions and adding or subtracting fractions, as it requires the same skills. Activities included: Starter: Some quick questions to test if pupils can find the lowest common multiple of two numbers. Main: A prompt to generate discussion about different methods of comparing the size of two fractions. Example question pairs on comparing using equivalent fractions, to quickly assess if pupils understand the method. A set of straightforward questions with a progression in difficulty. A challenging extension where pupils find fractions halfway between two given fractions. Plenary: A question in context to reinforce the key skill and also give some purpose to the skill taught in the lesson. Optional worksheets (ie no printing is really required, but the option is there if you want) and answers included. 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 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!

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 increasing or decreasing by a percentage. Activities included: Starter: A template for pupils to work out lots of different percentages of £30 Main: Examples and a set of straight-forward questions making percentage changes. A connect 4 game for pupils to play in pairs, taking it in turns to work out percentage changes and win squares on a grid. A few questions to discuss about the game. A puzzle where pupils arrange numbers and percentage change statements to make a loop. Plenary: Some examples looking at making a percentage decrease a different way - eg decreasing by 25% by directly working out 75% Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for introducing the trapezium area rule. Activities included: Starter: Non-calculator BIDMAS questions relating to the calculations needed to area of a trapezium. A good chance to discuss misconceptions about multiplying by a half. Main: Reminder of shape properties of a trapezium Example-question pairs, giving pupils a quick opportunity to try and receive feedback. A worksheet of straight forward questions with a progression in difficulty, although I have also built in a few things for more able students to think about. (eg what happens if all the measurement double?) A challenging extension task where pupils work in reverse, finding measurements given areas. Plenary: Nice visual proof of rule by relating to the rule for the area of a parallelogram. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!