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 gradient between two points, that assumes pupils have already spent time calculating gradients of lines, and is intended to give pupils an opportunity to use their knowledge of gradient in a slightly more challenging way. The examples and activities involve using knowledge of coordinates and gradient to find missing points on a grid. Printable worksheets and answers included. 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!

A collection of 5 activities involving square numbers that I’ve accumulated over the years from various sources: a puzzle I saw on Twitter involving recognising square numbers. a harder puzzle using some larger square numbers and a bit of logic. a sequences problem that links to square numbers a mini investigation that could lead to some basic algebraic proof work a trick involving mentally calculating squares of large numbers, plus a proof of why it works Please review if you like it or even if you don’t!

A complete lesson on finding percentages of an amount using non-calculator methods. Looks at finding 50%, 25%, 75%, 10%, 5%, 20% and 1%. Activities included: Starter: A set of questions where pupils convert the percentages above into their simplified, fraction form. Main: Some examples and quick questions on finding percentages of an amount for pupils to try. A set of questions with a progression in difficulty, from finding simple percentages, to going in reverse and identifying the percentage. The ‘spider diagrams’ are my take on TES user alutwyche’s spiders. An extension task where pupils arrange digits (with some thought) in order to make statements true. Plenary: A nice visual flow chart to reinforce how the calculations required are connected. Printable worksheets and answers included. Please review if you use as any feedback is appreciated!

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 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 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 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 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 using SOHCAHTOA and Pythagoras’ theorem with problems in three dimensions. Activities included: Starter: A set of recap questions on basic SOHCAHTOA and Pythagoras. Main: Examples and questions to dscuss, on visualising distances and angles within cuboids and triangular prisms, and understanding the wording of exam questions on this topic. Examples and quick questions for pupils to try, on finding the angle of a space diagonal. A worksheet, in three sections (I print this, including the starter, two per page, two sided so that you have a single page handout), with a progression in difficulty. Starts with finding the space diagonal of a cuboid, where the triangle pupils will need to use has been drawn already. The second section looks at angles in a triangular prism, and pupils will need to draw the relevant triangles themselves. The third section has exam-style questions, where pupils will need to identify the correct angle by interpreting the wording of the question. (eg “find the angle between the diagonal AE and the plane ABCD”). An extension task looking at the great pyramid of Giza. Plenary: A final question to add a bit more depth, looking at the most steep and least steep angles up a ramp. Printable worksheets and worked answers included. Please review if you buy as any feedback is appreciated!

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 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 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 for introducing the area rule of a parallelogram. Activities included: Starter: A couple of area mazes to remind them of the rule for rectangles. Main: A prompt for pupils to discuss or think about what a parallelogram is, followed by 2 questions, where pupils are shown a set of shapes and have to identify which ones are parallelograms. Animated examples showing the classic dissection and rearrangement of a parallelogram into a rectangle, leading naturally to a derivation of the area rule. Animated examples of using a ruler and set square to measure the base and perpendicular height, before calculating area. A worksheet where pupils must do the same. This is worth doing now, to make pupils think carefully about perpendicular height, rather than just multiplying given dimensions together. Examples and a worksheet where pupils must select the relevant information from not-to-scale diagrams. Extension task of pupils using knowledge of factors to solve an area puzzle. Plenary: Spot the mistake discussion question. Nice animation to show why the rule works. Link to an online geogebra file (no software required) with a lovely alternative dissection of a parallelogram 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 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!