A complete lesson on compound interest calculations. Activities included: Starter: A set of questions to refresh pupils on making percentage increases. Main: Examples and quick questions on interest. Examples and a worksheet on compound interest by adding on the interest each year. Examples and a worksheet on compound interest using the direct multiplier method. A challenging set of extension questions. Plenary: A prompt for pupils to think about the graph of compounded savings with time. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson (or maybe two) on finding an original amount, given a sale price or the value of something after it has been increased. Looks at both calculator and non-calculator methods. Activities included: Starter: A set of four puzzles where pupils work their way back to 100%, given another percentage. Main: Examples, quick questions for pupils to try and a worksheet on calculator methods for reversing a percentage problem. Examples, quick questions for pupils to try and a worksheet on non- calculator methods for reversing a percentage problem. Both worksheets have been scaffolded to help pupils with this tricky topic. A challenging extension task where pupils form and solve equations involving connected amounts. Plenary: A final question to address the classic misconception for this topic. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson with the 9-1 GCSE Maths specification in mind. Activities included: Starter: Some recap questions on solving two-step linear equations (needed later in the lesson). Main: An introduction to Fibonacci sequences, followed by a quick activity where pupils extend Fibonacci sequences. A challenging, rich task, inspired by one of TES user scottyknowles18’s excellent sequences rich tasks. Pupils try to come up with Fibonacci sequences that fit different criteria (eg that the 4th term is 10). Great for encouraging creativity and discussion. A related follow up activity where pupils try to find missing numbers in given Fibonacci sequences, initially by trial and error, but then following some explanation, by forming and solving linear equations. Extension - a slightly harder version of the follow up activity. Plenary: A look at an alternative algebraic method for finding missing numbers. Some slides could be printed as worksheets, although it’s not strictly necessary. Answers to most tasks included, but not the open-ended rich task. Please review if you buy as any feedback is appreciated!

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 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 introducing 3-figure bearings. Activities included: Starter: A quick set of questions to remind pupils of supplementary angles. Main: A quick puzzle to get pupils thinking about compass points. Slides to introduce compass points, the compass and 3-figure bearings. Examples and questions for pupils to try on finding bearings fro m diagrams. A set of worksheets with a progression in difficulty, from correctly measuring bearings and scale drawings to using angle rules to find bearings. Includes some challenging questions involving three points, that should promote discussion about different approaches to obtaining an answer. Plenary: A prompt to discuss how the bearings of A from B and B from A are connected. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching what mixed numbers and improper fractions are, and how to switch between the two forms. Activities included: Starter: Some quick questions to test if pupils can find remainders when dividing. Main: Some examples and a worksheet on identifying mixed numbers and improper fractions from a pictorial representation. Examples and quick questions for pupils to try, on how to convert a mixed number into an improper fraction. A set of straight forward questions for pupils to work on, with an extension task for those who finish. Examples and quick questions for pupils to try, on how to simplify an improper fraction. A set of straight forward questions for pupils to work on, with a challenging extension task for those who finish. Plenary: A final question looking at the options when simplifying improper fractions with common factors. Worksheets and answers included. Please review if you buy as any feedback is appreciated!

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 using sin, cos and tan to find an unknown side of a right-angled triangle. Designed to come after pupils have been introduced to the trig ratios, and used them to find angles in right-angled triangles. Please see my other resources for complete lessons on these topics. Activities included: Starter: A quick reminder and some questions about using formulae triangles (e.g. the speed, distance, time triangle). This is to help pupils to transfer the same idea to the SOHCAHTOA formulae triangles. Main: A few examples and questions for pupils to try, on finding a side given one side and an angle. Initially, this is done without reference to SOHCAHTOA or formulae triangles, so that pupils need to think about whether to multiply or divide. More examples, but this time using formulae triangles. A worksheet with a progression in difficulty, building up to some challenging questions on finding perimeters of right-angled triangles, given one side and an angle. A tough extension, where pupils try to find lengths for the sides of a triangle with a given angle, so that it is has a perimeter of 20cm. Plenary: A prompt to get pupils thinking about how they are going to remember the rules and methods for this topic. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated! Error on previous version now fixed. If you have bought this already and want the amended version, please message me and I will email the file directly.

A complete lesson or two on finding equations of tangents to circles with centre the origin. Aimed at the new GCSE specification, although it could also be used with an A-level group. Activities included: Starter: Two recap questions on necessary prerequisites, the first on equations of circles, the second on equations of perpendicular lines. If pupils really struggled with this I would stop and address these issues, rather than persist with the rest of the lesson. Main: A set of questions on finding the gradient of OP, given some point P on a circle, followed by a related worksheet for pupils to practice. A follow-up ‘reverse’ task where pupils find points P such that the gradient of OP takes certain values. The intention is that pupils can do this task by logic and geometric reasoning, rather than by forming and solving formal equations, although the task could be further extended to look at this. The focus then shifts to gradients of tangents, and finally equations of tangents, with examples and a related set of questions for pupils to practice. An extension task where pupils find the equation of the circle given the tangent. 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 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 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 with examples and activities on calculating gradients of lines and drawing lines with a required gradient. Printable worksheets and answers included. Could also be used before teaching the gradient and intercept method for plotting a straight line given its equation. Please review it if you buy as any feedback is appreciated!

A complete lesson on drawing nets and visualising how they fold. The content has some overlap with a resource I have freely shared on the TES website for years, but has now been augmented and significantly upgraded,as well as being presented in a full, three-part lesson format. Activities included: Starter: A matching activity, where pupils match up names of solids, 3D sketches and nets. Main: A link to an online gogebra file (no software required) that allows you to fold and unfold various nets, to help pupils visualise. A question with an accurate, visual worked answer, where pupils make an accurate drawing of a cuboid’s net. Rather than answer lots of similar questions, pupils are then asked to compare answers with others and discuss whether their answers are different and/or correct. The same process with a triangular prism. A brief look at other prisms and a tetrahedron (the latter has the potential to be used to revise constructions if pupils have done them before, or could be briefly discussed as a future task, or left out) Then two activities with a different focus - the first looking at whether some given sketches are valid nets of cubes, the second about visualising which vertices of a net of a cube would meet when folded. Plenary: A brief look at some more elaborate nets, a link to a silly but fun net related video and a link to a second video, which describes a potential follow up or homework task. Printable worksheets and answers included where appropriate. Please review if you buy as any feedback is appreciated!

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!

The first of two complete lessons on distance-time graphs that assumes pupils have done speed calculations before. Examples and activities on calculating speed from a distance-graph and a matching activity adapted from the Mathematics Assessment Project. Printable worksheets and answers included. Please review it if you download as any feedback is appreciated!

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.

A powerpoint with a series of lessons on GCSE vectors, with examples, activities and finally exam questions. Includes a few resources adapted from TES user payphone and another from jensilvermath.com.

A complete lesson on using Pythagoras’ theorem for 3-dimensional scenarios. Activities included: Starter: Two questions involving a spider walking along the faces of a cuboid. For the first question, pupils draw or use a pre-drawn net and measure to estimate the distance travelled by the spider. This leads into a discussion about finding exact distances using Pythagoras’ theorem, followed by a second question for pupils to apply this method to. Main: Highly visual example and quick questions for pupils to try on finding the space diagonal of a cuboid. A set of questions with a progression in difficulty, starting with finding space diagonals of cuboids, then looking at problems involving midpoints and different 3D solids. An extension where pupils try to find integer dimensions for a cuboid with a given space diagonal length. Plenary: Final question to discuss and check for understanding. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

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!