A fun 'investigation&' using ratio and problem solving skills. Slightly dark theme of thieves sharing the profits of different robberies. Made by another TES user &';taylorda01' (thanks for the resource!) but I wanted to add answers to it.

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.

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 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 using calculators to directly make percentage changes, e.g. increasing by 5% by multiplying by 1.05 Activities included: Starter: A recap on making a percentage change in stages, e.g. increasing something by 5% by working out 5% and adding it to the original amount. Main: Examples and quick questions for pupils to try, along with some diagnostic questions to hopefully anticipate a few misconceptions. A worksheet of questions with a progression in difficulty. An extension task/investigation designed to challenge the misconception that you can reverse a percentage increase by decreasing by the same percentage. Plenary: A question in context - working out a restaurant bill including a tip. 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!

A complete lesson on gradient as rate of change, that assumes pupils have already learned how to calculate the gradient of a curve and are familiar with distance-time graphs. Designed to match the content of the 9-1 GCSE specification. Examples and activities on calculating average gradient between 2 points on a curve and estimating instantaneous gradient at a point, in the context of finding rates of change (eg given a curved distance-time graph, calculate the speed) . Printable worksheets and answers included. Please review it 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 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 solving one step equations using the balancing method. Designed to come after pupils have solved using a flowchart/inverse operations, and as such the introductory slides put the two methods side by side, so pupils can relate them. I’ve also uploaded a lesson on balancing (but not solving) equations that would be a good precursor to this lesson. Activities included: Starter: A set of questions to check that pupils can solve one step equations using a flowchart/inverse operations. Main: Two slides showing equations represented on scales, to help pupils visualise the equations as a balancing problem. Four examples of solving equations, firstly using a flowchart/inverse operations and then by balancing. Then a set of similar questions for pupils to try, before giving any feedback. A second set of questions basically with harder numbers. Not exactly thrilling but necessary practice. A more interesting, challenging extension task in the style of the Open Middle website. Plenary: A prompt of an equation that is best solved using the balancing method, rather than inverse operations (hence offering some incentive for the former method). Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on a mixture of area and circumference of circles. Designed to come after pupils have used area and circumference rules forwards (eg to find area given radius) and backwards (eg to find radius given area). Activities included: Starter: Questions to check pupils are able to use the rules for area and circumference. Main: A set of four ‘mazes’ (inspired by TES user alutwyche’s superb spider puzzles) with a progression in difficulty, where pupils use the rules forwards and backwards. A ‘3-in-a-row’ game for pupils to compete against each other, practicing the basic rules. Plenary: Questions to prompt a final discussion of the rules. 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 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 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 on the graph of tangent from 0 to 360 degrees. I’ve also made complete lessons on sine and cosine from 0 to 360 degrees and all three functions outside the range 0 to 360 degrees. Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry, and have met the unit circle definitions of sine and cosine. Activities included: Starter: A quick set of questions on finding the gradient of a line. This is a prerequisite to understanding how tan varies for different angles. Main: An example to remind pupils how to find an unknown angle in a right-angled triangle using the tangent ratio, followed by a set of similar questions. The intention is that pupils estimate using the graph of tangent rather than using the inverse tan key on a calculator, to refamiliarise them with the graph from 0 to 90 degrees. Slides to define tan as sin/cos and hence as gradient when using the unit circle definition. A worksheet where pupils construct the graph of tan from 0 to 360 degrees (see cover image). A set of related questions, where pupils use graph and unit circle representations to explain why pairs of angles have the same tan. Pupils can be extended further by making and proving conjectures about pairs of angles whose tans are equal. Plenary: An image to prompt discussion about the “usual” definition of tangent (using the terminology opposite, adjacent and hypotenuse) and the fuller definition (using the unit circle) Printable worksheets and answers included. 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 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 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 lesson for first introducing the ratios sin, cos and tan. Ideal as a a precursor to teaching pupils SOHCAHTOA. Activities included: Starter: Some basic similarity questions (I would always teach similarity before trig ratios). Main: Examples and questions on using similarity to find missing sides, given a trig ratio (see cover image for an example of what I mean, and to understand the intention of doing this first). Examples, quick questions and worksheets on identifying hypotenuse/opposite/adjacent and then sin/cos/tan for right-angled triangles. A challenging always, sometimes, never activity involving trig ratios. Plenary: A discussion about the last task, and a chance for pupils to share ideas. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!