A complete lesson of more challenging problems involving the sine rule. Designed to come after pupils have spent time on basic questions. Mistake on previous version now corrected - please contact me for an updated copy if you have already purchased this. Activities included: Starter: A set of six questions, each giving different combinations of angles and sides. Pupils have to decide which questions can be done with the sine rule. In fact they all can, the point being that questions aren’t always presented in the basic ‘opposite pairs’ format. Pupils can then answer these questions, to check they can correctly apply the sine rule. Main: A set of eight more challenging questions that pupils could work on in pairs. Each one is unique, with no examples offered, and therefore I’d class this as a problem solving lesson - pupils may need to adopt a general approach of working out what they can at first, and seeing where this takes them. Questions also require knowledge from other topics including angle rules, shape properties, bearings, and the sine graph. I’ve provided full worked answers FYI, but I would get pupils discussing answers and presenting to the class. Plenary: A prompt for pupils to reflect on possible rounding errors. Most of the questions have several steps, so it is worth getting pupils to think about how to avoid rounding errors. I’ve left each question as a full slide, but I’d print them 4-on-1 and 2-sided, so that you’d only need to print one worksheet per pair. Please review if you buy as any feedback is appreciated!

Pupils solve straight forward quadratic equations to reveal a pathetic joke.

Pupils work out answers to questions on a mixture of SOHCAHTOA, sine rule, consine rule and Pythagoras’s theorem to reveal a fairly rubbish joke (although I quite like it).

A complete lesson looking at the effect of multiplying and dividing integers and decimals by 10, 100 and 1000. Activities included: Starter: A prompt for pupils to share any ideas about what the decimal system is. Images to help pupils understand the significance of place value. Questions that could be used with mini whiteboards, to check pupils can interpret place value. Main: A worksheet where, by repeated addition, pupils investigate the effect of multipliying by 10, initially with whole numbers but later with decimals. A slide to summarise these results, followed by some more mini whiteboard questions to consolidate. A prompt for pupils to use a calculator to investigate the effect of multiplying or dividing by positive powers of 10, followed by slides to help pupils reflect on their findings, and provide notes for all pupils. A related game for pupils to play (connect 4). Plenary: A very brief, bulleted summary of the history of the decimal system and the importance of the invention of zero. Printable worksheets included. 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 using cos or tan) for any range. Designed to come after pupils have spent time solving equations in the range 0 to 360 degrees, and are also familiar with the cyclic nature of the trigonometric functions. See my other resources for lessons on these topics. I made this to use with my further maths gcse group, but could also be used with an A-level class. Activities included: Stater: A set of 4 questions to test if pupils can solve trigonometric equations in the range 0 to 360 degrees. Main: A visual prompt to consider solutions beyond 360 degrees. followed by a second example (see cover image) that will lead to a “dead-end” for pupils. Slides to define principal values for sine, cosine and tangent, followed by a summary of how to solve equations for any range. Three example problem pairs to model methods and then get pupils trying. Includes graphical representations to help pupils understand. A worksheet with a progression in difficulty and a challenging extension to create equations with a required number of solutions. Plenary: A prompt to discuss solutions to the extension task.

A complete lesson on the graphs of sine and cosine from 0 to 360 degrees. I’ve also made complete lessons on tangent 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. Activities included: Starter: Examples to remind pupils how to find unknown angles in a right-angled triangle (see cover slide), followed by two sets of questions; the first using sine the second using cosine. The intention is that pupils estimate using the graphs of sine and cosine rather than with calculators, to refamiliarise them with the graphs from 0 to 90 degrees. Although I’ve called this a starter, this part is key and would take a decent amount of time. I would print off the question sets and accompanying graphs as a 2-on-1 double sided worksheet. Main: Slide to define sine and cosine using the unit circle, with a hyperlink to a nice geogebra to show the graphs dynamically. Or you could get pupils to try to construct the graphs themselves by visualising. A set of related questions that I would do using mini-whiteboards, where pupils consider symmetry properties of the graphs. A mini-investigation where pupils look at angles with the same sine or cosine and look for a pattern. Plenary: An image to prompt discussion about the “usual” definition of sine and cosine (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 the theorem that the angle at the centre is twice the angle at the circumference. For me, this is definitely the first theorem to teach as it can be derived using ideas pupils have already covered. and then used to derive some of the other theorems. Please see my other resources for lessons on the other theorems. Activities included: Starter: A few basic questions to check pupils can find missing angles in triangles. Main: A short discovery activity where pupils split the classic diagram for this theorem into isosceles triangles (see cover image). If you think this could overload pupils, it could be skipped, although I think if they can’t cope with this activity, they’re not ready for circle theorems! A link to the mathspad free tool for this topic. I hope mathspad don’t mind me putting this link - I will remove it if they do. A large set of mini-whiteboard questions for pupils to try. These have been designed with a variation element as well as non-examples, to really make sure pupils think about the features of the diagrams. A worksheet for pupils to consolidate independently, with two possible extension tasks: (1) pupils creating their own examples and non-examples, (2) pupils attempting a proof of the theorem. Plenary: A final set of six diagrams, where pupils have to decide if the theorem applies. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on the theorem that opposite angles in a cyclic quadrilateral sum to 180 degrees. Assumes that pupils have already met the theorems that the angle at the centre is twice the angle at the circumference, the angle in a semicircle is 90, and angles in the same segment are equal. See my other resources for lessons on these theorems. Activities included: Starter: Some basics recap questions on the theorems already covered. Main: An animation to define a cyclic quadrilateral, followed by a quick question for pupils, where they decide whether or not diagrams contain cyclic quadrilaterals. An example where the angle at the centre theorem is used to find an opposite angle in a cyclic quadrilateral, followed by a set of three similar questions for pupils to do. They are then guided to observe that the opposite angles sum to 180 degrees. A quick proof using a very similar method to the one pupils have just used. A set of 8 examples that could be used as questions for pupils to try and discuss. These have a progression in difficulty, with the later ones incorporating other angle rules. I’ve also thrown in a few non-examples. A worksheet of similar questions for pupils to consolidate, followed by a second worksheet with a slightly different style of question, where pupils work out if given quadrilaterals are cyclic. A related extension task, where pupils try to decide if certain shapes are always, sometimes or never cyclic. Plenary: A slide showing all four theorems so far, and a chance for pupils to reflect on these and see how the angle at the centre theorem can be used to prove all of the rest. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on the theme of the formula for 1+2+3+…+n, looking at how the rule emerges in different scenarios. Activities included: Starter: A classic related puzzle - counting how many lines in a complete graph. After the initial prompt showing a decagon, two differing approaches to a solution are shown. These will help pupils make connections later in the lesson. This is followed by a prompt relating to the handshaking lemma, which is the same thing in a different guise. Pupils could investigate this in small groups. Main: A prompt for pupils to consider the question supposedly put to Gauss as a child - to work out 1+2+3+…+100. Gauss’s method is then shown, at which point pupils could try the same method to sum to a different total. The method is then generalised to obtain Gauss’s rule of n(n+1)/2, followed by a worksheet of related questions. These include some challenging questions requiring pupils to adapt Gauss’s method (eg to work out 2+4+6+…+100). Plenary: A final look at the sequence Gauss’s rule generates (the triangle numbers). Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching about corresponding, alternate and supplementary angles. Activities included: Starter: Pupils measure and label angles and hopefully make observations and conjectures about the rules to come. Main: Slides to introduce definitions, followed by a quiz on identifying corresponding, alternate and supplementary angles, that could be used as a multiple choice mini-whiteboard activity or printed as a card sort. Another diagnostic question with a twist, to check pupils have grasped the definitions. Examples followed by a standard set of basic questions, where pupils find the size of angles. Examples/discussion questions on spotting less obvious corresponding, alternate and supplementary angles (eg supplementary angles in a trapezium). A slightly tougher set of questions on this theme, followed by a nice angle chase puzzle and a set of extension questions. Plenary: Prompt for pupils to see how alternate angles can be used to prove that the angles in a triangle sum to 180 degrees. Printable answers and worksheets included. Please review if you buy as any feedback is appreciated!

A complete lesson on the interior angle sum of a quadrilateral. Requires pupils to know the interior angle sum of a triangle, and also know the angle properties of different quadrilaterals. Activities included: Starter: A few simple questions checking pupils can find missing angles in triangles. Main: A nice animation showing a smiley moving around the perimeter of a quadrilateral, turning through the interior angles until it gets back to where it started. It completes a full turn and so demonstrates the rule. This is followed up by instructions for pupils to try the same on a quadrilateral that they draw. Instructions for pupils to use their quadrilateral to do the more common method of marking the corners, cutting them out and arranging them to form a full turn. This is also animated nicely. Three example-problem pairs where pupils find missing angles. Three worksheets, with a progression in difficulty, for pupils to work through. The first has standard ‘find the missing angle’ questions. The second asks pupils to find missing angles, but then identify the quadrilateral according to its angle properties. The third is on a similar theme, but slightly harder (eg having been told a shape is a kite, work out the remaining angles given two of the angles). A nice extension task, where pupils are given two angles each in three quadrilateral and work out what shapes they could possibly be. Plenary: A look at a proof of the rule, by splitting quadrilaterals into two triangles. A prompt to consider what the sum of interior angles of a pentagon might be. Printable worksheets and answers included throughout. Please review if you buy as any feedback is appreciated!

Inspired by the TV show, pupils work in teams on a mix of Physical, Skill and Mystery maths puzzles . Game is divided into four zones based loosely on contributions of Greek, Egyptian, Indian and Chinese mathematicians in history. Teams collect crystals that buy a head-start in a final mega-puzzle - a really tough maze.Worksheets for printing at end of presentation which is clickable between menus.

A brief insight into how fractals are created as well as examples in Maths, art and nature. Includes a spreadsheet to investigate. Requires a basic understanding of complex numbers to fully appreciate.

Are you bored of telling students what calculator to get for secondary school maths? Then use this poster!

Looks at switching between different bases and the effect of base on arithmetic and divisibility tests.Plus an excel 'base switch&' calculator. A good enrichment task with a historical/real-life aspect, though probably best for more able pupils.

A selection of puzzles, most using the digits 1 to 9 and an element of working systematically to obtain a solution. A few are from the the excellent Nrich website. Based around key skills of adding, subtracting, multiplying and dividing but that doesn't mean they're easy!

A lesson or two of functional maths activities exploring a visual breakdown of the Budget that I found on the Guardian website recently. Requires knowledge of percentage change and reverse percentage problems. Starts with relatively straight forward calculations but gets a bit more political towards the end!

A hyperlinked list of geogebra interactives I’ve found on a range of maths topics. Not made by me, I’m just sharing in case people find them useful.

Adding, subtracting, multiplying and dividing fractions is a good topic, so what better than a joke to reward pupils' efforts? Pupils answer questions and use the code to reveal a funny gag.

A complete lesson on the 1/2 absinC area rule. Doesn’t include ‘reverse’ problems (I’ve made a separate resource on this). Activities included: Starter: A set of questions on area of triangles using bh/2. Main: An area question for pupils to attempt, given two sides and the angle between them. If they spot that they can use SOH to get the perpendicular height, they have effectively ‘discovered’ the 1/2absinC rule. If they don’t spot it, then the rule can be easily explained at this point. A set of questions designed to be done as a class using mini whiteboards, progressing from identifying the correct information needed to calculate area, to standard questions, to trickier questions (see cover slide for an example). A two-page worksheet (I’d shrink and print as one page) with a similar progression in difficulty, for pupils to consolidate. Includes a suggested extension task in the comments box of the powerpoint. Plenary: A closer look at question one from the worksheet, which links to the graph of sine.