A GSP file (requires Geometer's Sketchpad software to open) which measures, for a right-angled triangle, the sides and ratios sin, cos and tan. The triangle can be changed dynamically. Also shows the graphs of the ratios. Could be used to introduce trigonometric ratios, explain the graphs of sine, cosine and tangent up to 90 degrees or to generate questions on SOHCAHTOA.

A short investigation based on a lovely puzzle I saw a while ago. Requires only knowledge of square numbers to investigate and enjoy, but pupils will need to be able to expand double brackets to understand a proof of the puzzle. Could be used with any age!

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!

An excel file that shows pi as the ratio of circumference / diameter for a circle

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 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!

A complete lesson for first introducing how to find angles in a right-angled triangle using a trig ratio, but as a pupil-led investigation. Intended to come after pupils have practiced identifying hypotenuse/opposite/adjacent and calculating sin/cos/tan. Activities included: Starter: A set of questions to check pupils can correctly calculate sin, cos and tan from a triangle’s dimensions. Main: A structured investigation where pupils: Investigate sin, cos and tan for triangles of different size but the same angles (i.e. similar triangles), by measuring dimensions of triangles and calculating ratios Investigate what happens as the angle varies by measuring dimensions of triangles, calculating ratios, and plotting separate graphs of sin, cos and tan. Using their graphs to estimate angles for conventional SOHCAHTOA questions (i.e. finding an angle given two sides) Plenary: A prompt to get pupils to discuss/reflect on their understanding of the use of trig ratios. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on finding an angle in a right-angled triangle using trig ratios. Designed to come after pupils have been introduced to the ratios sin, cos and tan, and have investigated how the ratios vary. Please see my other resources for complete lessons on these topics. Activities included: Starter: Provided with the graph of y=sinx, pupils estimate sinx for different values of x and vice-versa. Main: Slides to introduce use of scientific calculators to find accurate values for angles or ratios. Examples of the basic method of finding an angle given two sides. Includes graphs to reinforce what is happening. Quick questions for pupils to try and provided feedback. A worksheet of questions with a progression in difficulty. Starts with standard questions, then moves on to more challenging ones (eg finding the smallest angle in a non-right-angled, isosceles triangle). Plenary: A final question to check pupils’ understanding, but also with a combinations/logic element. 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 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 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 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!

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, or range of activities to use, on the theme of Pythagorean triples. A great lesson for adding some interest, depth and challenge to the topic of Pythagoras’ theorem. Activities included: Starter: A set of straight forward questions on finding the third side given two sides in a right-angled triangle, to remind pupils of Pythagoras’ theorem. Main: Slides explaining that Pythagoras’ theorem can be used to test whether a triangle has a right angle. A sorting activity where pupils test whether given triangles contain a right angle. Quick explanation of Pythagorean triples, followed by a structured worksheet for pupils to try using Diophantus’ method to generate Pythagorean triples, and, as an extension, prove why the method works. Two pairs of challenging puzzles about Pythagorean triples. Plenary: A final question, not too difficult, to bring together the theme of the lesson (see cover image). Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

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 the theme of using Pythagoras’ theorem to look at the distance between 2 points. A good way of combining revision of Pythagoras, surds and coordinates. Could also be used for a C1 class about to do coordinate geometry. Activities included: Starter: Pupils estimate square roots and then see how close they were. Can get weirdly competitive. Main: Examples and worksheets with a progression of difficulty on the theme of distance between 2 points. For the first worksheet, pupils must find the exact distance between 2 points marked on a grid. For the second worksheet, pupils find the exact distance between 2 coordinates (without a grid). For the third worksheet, pupils find a missing coordinate, given the exact distance. There is also an extension worksheet, where pupils mark the possible position for a second point on a grid, given one point and the exact distance between the two points. I always print these worksheets 2 per page, double sided, so without the extension this can be condensed to one page! It may not sound thrilling, but this lesson has always worked really well, with the gentle progression in difficulty being enough to keep pupils challenged, without too much need for teacher input. 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 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 for first teaching how to add and subtract fractions with different denominators. Does include some examples and questions involving simplifying at the end, but doesn’t include adding or subtracting mixed numbers. Activities included: Starter: Some quick questions to test if pupils can find equivalent fractions and identify the lowest common multiple of two numbers. Main: Some examples with diagrams to help pupils understand the need for common denominators when adding. A recap/help sheet of equivalent fractions for pupils to reference while they try some simple additions and subtractions. At this stage, they aren’t expected to find LCMs ‘properly’, just to find them on the help sheet. Some example question pairs on adding or subtracting by first identifying the lowest common denominator, starting with the scenario that the LCM is the product of the denominators, then the scenario that the LCM is one of the denominators, and finally the scenario that the LCM is something else (eg denominators of 4 and 6). A set of straightforward questions with a progression in difficulty. The hardest ones require students to simplify the answer. A challenging extension where pupils must find four digits to fit a given fraction sum. Plenary: A final example designed to challenge the misconception of adding numerators and denominators, 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 introducing the area rule for a triangle. Activities included: Starter: Questions to check pupils can find areas of parallelograms (I always teach this first, as it leads to an explanation of the rule for a triangle). Main: A prompt to get pupils thinking (see cover image) Examples and a worksheet where pupils must identify the height and measure to estimate area. Examples and a worksheet where pupils must select the relevant information from not-to-scale diagrams. Simple extension task of pupils drawing as many different triangles with an area of 12 as they can. Plenary: A sneaky puzzle with a simple answer that reinforces the basic area rule. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!