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 selection of puzzles, many from the Junior or Intermediate Maths Challenges. Includes animated solutions. Good for promoting discussion and stimulating interest as starters, plenaries or extension. Powerpoint has clickable contents page to choose and move between puzzles.

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!

Inspired by the Transformers cartoon/film/toys, pupils turn robots into vehicles using a mixture of shape transformations (translations, reflections, rotations and enlargements). Animated answers included. Great homework potential for pupils to design their own!

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 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 defining, recognising and extending linear sequences. Activities included: Starter: Pupils discuss whether six sets of numbers are sequences, and if so, what the rules are. Main: Slides to define linear sequences, followed by mini whiteboard questions and a worksheet of extending linear sequences. A fun puzzle a bit like a word search (but where you try to find linear sequences). Plenary: Another nice puzzle where pupils try to form as many linear sequences as they can from a set of numbers. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on the concept of an equation of a line. Intended as a precursor to the usual skills of plotting using a table of values or using gradient and intercept. Examples, printable worksheets and answers included. Please review it 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 set of challenging activities using Pythagoras’ theorem. Activities included: Starter: Given two isosceles triangles, pupils work out which one has the larger area. Main: Examples/practice questions, followed by two sets of questions on the theme of comparing area and perimeter of triangles. Both sets start with relatively straight forward use of Pythagoras’ theorem, but end with an area=perimeter question, where pupils ideally use algebra to arrive at an exact, surd answer. Plenary: Not really a plenary, but a very beautiful puzzle (my take on the spiral of Theodorus) with an elegant answer.

A complete lesson on interior angles of polygons. Activities included: Starter: A slide showing examples and non-examples of interior angles, for pupils to think about a definition, followed by a set of images where pupils must identify any interior angles (sounds easy and dull, but isn’t!) Main: A recap of visual proofs of why the interior angles of a triangle sum to 180 degrees and those of a quadrilateral sum to 360 degrees, leading to the obvious question of “what next?” Prompts for the usual “investigation” into the sum of interior angles for polygons, by splitting into triangles. A set of questions designed to be done with mini whiteboards, starting with basic sums of interior angles, interior angles of regular polygons and finally a few variations (see cover image). A four-part worksheet (one page if printed two-a-side and two-sided) with a similar progression in difficulty. Plenary: A slide summarising the rules encountered, together with some key questions to check for any misconceptions. Printable worksheets and answers included. I’ve also included suggested questions and extensions in the notes boxes at the bottom of each slide. 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 on gradient of curves. Examples and questions on calculating average gradient between 2 points on a curve and estimating instantaneous gradient at a point. Printable worksheets and answers included. Please review it 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 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, 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 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 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 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 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!