A complete lesson on the graph of tangent from 0 to 360 degrees. I’ve also made complete lessons on sine and cosine 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, and have met the unit circle definitions of sine and cosine. Activities included: Starter: A quick set of questions on finding the gradient of a line. This is a prerequisite to understanding how tan varies for different angles. Main: An example to remind pupils how to find an unknown angle in a right-angled triangle using the tangent ratio, followed by a set of similar questions. The intention is that pupils estimate using the graph of tangent rather than using the inverse tan key on a calculator, to refamiliarise them with the graph from 0 to 90 degrees. Slides to define tan as sin/cos and hence as gradient when using the unit circle definition. A worksheet where pupils construct the graph of tan from 0 to 360 degrees (see cover image). A set of related questions, where pupils use graph and unit circle representations to explain why pairs of angles have the same tan. Pupils can be extended further by making and proving conjectures about pairs of angles whose tans are equal. Plenary: An image to prompt discussion about the “usual” definition of tangent (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 vertically opposite angles. Does incorporate problems involving the interior angle sum of triangles and quadrilaterals too, to make it more challenging and varied (see cover image for an idea of some of the easier problems) Activities included: Starter: A set of basic questions to check if pupils know the rules for angles at a point, on a line, in a triangle and in a quadrilateral. Main: A prompt for pupils to reflect on known facts about angles at the intersection of two lines, naturally leading to a quick proof that vertically opposite angles are equal. Some subtle non-examples/discussion points to ensure pupils can correctly identify vertically opposite angles. Examples and a set of questions for pupils to consolidate. These start with questions like the cover image, then some slightly tougher problems involving isosceles triangles, and finally some tricky and surprising puzzles. A more investigatory task, a sort-of angle chase where pupils need to work out when the starting angle leads to an integer final angle. Plenary: An animation that shows a dynamic proof that the interior angle sum of a triangle is 180 degrees, using the property of vertically opposite angles being equal. Printable worksheets and answers included. Please do review if you buy, as any feedback is helpful!

A complete lesson on using an nth term rule of a linear sequence to generate the first 5 terms in the sequence. Activities included: Starter: Questions to check pupils can evaluate simple algebraic expressions. Main: Introduction to the idea of an nth term rule. Example-question pairs, giving pupils a quick opportunity to try to generate sequences and receive feedback. A set of questions on generating the first 5 terms of increasing sequences, with a progression in difficulty and an extension task. A similar task for decreasing sequences. Plenary: A ‘spot the mistake’ question. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

Classic quiz with questions on area, including parallelograms, triangles, trapezia and composite shapes made with rectangles. Answers on each slide by clicking on orange squares plus on last slide. Hope no-one minds my use of an image of Bob Holness - he will always be the face of Blockbusters to me!

One significant figure estimation is a boring topic, so what better than a rubbish joke to go with it? Pupils answer questions and use the code to reveal a feeble gag. Mistakes on first version now corrected.

Worksheet where answers to questions are used to obtain a 3-digit code (which I set as the combination to a lockable money box containing a prize).

A challenging set of puzzles involving equivalent fractions, probably best for high ability secondary groups. Also offers pupils practice of using divisibility tests, simplifying fractions and working systematically. Please review if you like it, or even if you don’t!

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!

Classic quiz with question on angle rules, including simple parallel lines and knowledge of shape properties. Answers on last slide. Hope no-one minds my use of an image of Bob Holness - he will always be the face of Blockbusters to me!

A powerpoint with worksheets on the profit parabola model. A nice rich task to use with high-ability GCSE students, to deepen their understanding of quadratic functions/maximum points and also to see a real-life application of maths.

Pupils are given two fractions as the start of a sequence, and try to extend it. Could be made easier or introduced using integers rather than fractions, maybe with some decimals and negatives in between. Works as either a ‘low floor high ceiling’ task, or as a way of revising different sequence types and also decimals, negatives and fractions. Particularly for the quadratic sequence, there’s scope to spend time looking at the algebra needed to find solutions. Please let me know if you can think of any other ways to extend the task!

A complete lesson designed to be used to consolidate pupils’ ability to add and subtract a negative number. Activities included: Starter: Some straight forward questions to test if they can remember the basic methods and help identify misconceptions. Main: A set of differentiated questions to give pupils a bit more practice. A game adapted from the nrich website. A closer look at the design of the game, with pupils making a sample space diagram. Plenary: Some final questions to prompt discussion and reflection on how to remember the rules used. Printable worksheets and answers included. Please review if you use this!

Worksheet where answers to questions are used to obtain a 3-digit code (which I set as the combination to a lockable money box containing a prize). Pupils race to finish first and crack the safe.

Non-calculator sums with standard form is a boring topic, so what better than a rubbish joke to go with it? Pupils answer questions and use the code to reveal a feeble gag.

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.

Worksheet where answers to questions are used to obtain a 3-digit code (which I set as the combination to a lockable money box containing a prize). Questions on all aspects of parametric functions as seen in C4

A treasure hunt/follow me activity on circle theorems.

Starts as a dice substitution game but goes a lot deeper by considering the expressions as functions and the effect this has on potential strategies for playing the game. Only suitable for able GCSE students - requires a good grasp of quadratic functions. Nice way of revising and exploring the connection between expressions and functions.

An always, sometimes, never activity looking at various properties of triangles (angles, sides, perimeter, area, symmetry and a few more). Includes a wonderfully sneaky (but potentially confusing!) example of triangle area sometimes being the product of the lengths of all three sides. A good way of stimulating discussion, revising a range of topics and exposing misconceptions. Please review and give feedback, whether you like the activity or whether you don’t!

Maze consists of squares containing identities, some of which are false. Pupils can only pass through squares containing true identities. Identities require ability to expand & factorise quadratic expressions and simplify algebraic fractions, so really only good for a GCSE top set. Extension - pupils find identities of incorrect squares and then design their own maze (there's a good discussion to be had about how to make a good maze - including common misconceptions to fool people).