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 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 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 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 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 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!

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 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 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 complete lesson on using an nth term rule of a quadratic sequence. Starter: A quick quiz on linear sequences, to set the scene for doing similar techniques with quadratic sequences. Main: A recap on using an nth term rule to generate terms in a linear sequence, by substituting. An example of doing the same for a quadratic sequence, followed by a short worksheet for pupils to practice and an extension task for quick finishers. A slide showing how pupils can check their answers by looking at the differences between terms. A mini-competition to check understanding so far. A set of open questions for pupils to explore, where they try to find nth term rules that fit simple criteria. The intention is that this will develop their sense of how the coefficients of the rule affect the sequence. Plenary: A final question with a slightly different perspective on generating sequences - given an initial sequence and its rule, pupils state the sequences given by related rules. No printing needed, although I’ve included something that could be printed off as a worksheet. Please review 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 solving two 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 set of questions to check that pupils can evaluate two step expressions like 2x+3, given a value of x Main: A prompt to discuss the differences between two equations (a one step and a two step with the same solution), to get pupils thinking about how they could approach the latter. Examples and a set of questions on using inverse operations to reverse a two step flowchart and solve its corresponding equation. These have been deigned to further reinforce the importance of BIDMAS when interpreting an algebraic expression, so the emphasis is on quality not quantity of questions. A more challenging task of pupils trying to make an equation with a certain solution. Designed to be extendable to pupils looking for generalistions. Plenary: A prompt to discuss a few less obvious one-step equations (eg x+8+3=20) Printable worksheets and answers included. Please 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 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 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 interior angle sum of a triangle. Activities included: Starter: Some simple recap questions on angles on a line, as this rule will used to ‘show’ why the interior angle sum for a triangle is 180. Main: A nice animation showing a smiley moving around the perimeter of a triangle, turning through the interior angles until it gets back to where it started. It completes a half turn and so demonstrates the rule. This is followed up by instructions for the more common method of pupils drawing a triangle, marking the corners, cutting them out and arranging them to form a straight line. This is also animated nicely. A few basic questions for pupils to try, a quick reminder of the meaning of scalene, isosceles and equilateral (I would do a lesson on triangle types before doing interior angle sum), then pupils do more basic calculations (two angles are directly given), but also have to identify what type of triangles they get. An extended set of examples and non-examples with trickier isosceles triangle questions, followed by two sets of questions. The first are standard questions with one angle and side facts given, the second where pupils discuss whether triangles are possible, based on the information given. A possible extension task is also described, that has a lot of scope for further exploration. Plenary A link to an online geogebra file (no software needed, just click on the hyperlink). This shows a triangle whose points can be moved dynamically, whilst showing the exact size of each angle and a nice graphic of the angles forming a straight line. I’ve listed some probing questions that could be used at this point, depending on the class. I’ve included key questions and ideas in the notes box. Optional, printable worksheets and answers included. Please do review if you buy as any feedback is helpful and 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 for first introducing Pythagoras’ theorem. Activities included: Starter: A set of equations to solve, similar to what pupils will need to solve when doing Pythagoras questions. Includes a few sneaky ones that should cause some discussion. Main: Examples and quick question to make sure pupils can identify the hypotenuse of a right-angled triangle. Optional ‘discovery’ activity of pupils measuring sides of triangles and making calculations to demonstrate Pythagoras’ theorem. Questions to get pupils thinking about when Pythagoras’ theorem applies and when it doesn’t. Examples and quick questions for pupils to try on the standard, basic questions of finding either the hypotenuse or a shorter side. A worksheet with a mild progression in difficulty, from integer sides and answers to decimals. An extension task of a ‘pile up’ activity (based on an idea by William Emeny, but I did make this one myself). Plenary: Some multiple choice questions to consolidate the basic method, but also give a taster of other geometry problems Pythagoras’ theorem can be used for (e.g. finding the length of the diagonal of a rectangle). 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 on subtracting a negative number. Activities included: Starter: Some recap questions on adding a negative number (I always teach this first). Main: A slide showing a number pattern to demonstrate the logic of subtracting 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 deceptively simple puzzle to consolidate the key point of the lesson. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!