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 powerpoint including examples, worksheets and solutions on plotting coordinates in all 4 quadrants and problem solving involving coordinates. Worksheets at bottom of presentation for printing.

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 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 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 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 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 of area puzzles. Designed to consolidate pupils’ understanding of the area rules for rectangles, parallelograms, triangles and trapeziums, but in an interesting, challenging and at times open-ended way. Activities included: Starter: Some questions to check pupils are able to use the four area rules. Main: A set of 4 puzzles with a progression in difficulty, where pupils use the area rules, but must also demonstrate a knowledge of factors and the ability to test combinations systematically in order to find the answers. Plenary Pupils could peer-assess or there could be a whole-class discussion of the final puzzle, which is more open-ended. 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 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 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 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 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 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 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 on using knowledge of gradient to find the equation of a line perpendicular to a given line. Nothing fancy, but provides clear examples, printable worksheets and answers for this tricky topic. Please review it if you buy as any feedback is appreciated!

A complete lesson on using knowledge of gradient to find the equation of a line parallel to a given line. Examples, activities, printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on finding the gradient of a line that is perpendicular to another. Intended as a precursor to finding equations of lines perpendicular to another. Examples, a range of challenging activities and answers included. Please review it if you buy as any feedback is appreciated!