A complete lesson for first teaching how to divide fractions by whole numbers. Activities included: Starter: A simple question in context to help pupils visualise division of fractions by whole numbers. Main: Some example and questions for pupils to try. A set of straightforward questions. A challenging extension where pupils must think a lot more carefully about what steps to take. Plenary: A final example designed to challenge the misconception of division leading to an equivalent fraction, 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 how to divide whole numbers by fractions. Activities included: Starter: A set of recap question to test if pupils can simplify improper fractions. Main: Some highly visual examples of dividing by a fraction, using bar modelling (more to help pupils feel comfortable with the idea of dividing by a fraction, than as a method for working them out). Two sets of straightforward questions, the first on dividing by a unit fraction, the second on dividing by a non-unit fraction, moving from integer answers to fractional answers. An extension where pupils investigate divisions of a certain format. Plenary: Two more related examples using bar modelling, to reinforce the logic of the method used for division by a fraction. Answers included to all tasks. Please review if you buy as any feedback is appreciated!

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 complete lesson for first teaching the concept of equivalent fractions. Activities included: Starter: Some ‘fill the blank’ multiplication and division questions (basic, but a prerequisite for finding equivalent fractions with a required denominator or numerator). Main: Visual examples using shapes to introduce concept of equivalent fractions. A worksheet where pupils use equivalent fractions to describe the fraction of a shape. Examples and quick-fire questions on finding an equivalent fraction. A worksheet with a progression in difficulty on finding an equivalent fraction. A challenging extension task where pupils look at some equivalent fractions with a special property. Plenary: A statement with a deliberate misconception to stimulate discussion and check pupils have understood the key concepts. Worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on a mixture of area and circumference of circles. Designed to come after pupils have used area and circumference rules forwards (eg to find area given radius) and backwards (eg to find radius given area). Activities included: Starter: Questions to check pupils are able to use the rules for area and circumference. Main: A set of four ‘mazes’ (inspired by TES user alutwyche’s superb spider puzzles) with a progression in difficulty, where pupils use the rules forwards and backwards. A ‘3-in-a-row’ game for pupils to compete against each other, practicing the basic rules. Plenary: Questions to prompt a final discussion of the rules. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to simplify a fraction. Activities included: Starter: Some quick questions to test if pupils can find the highest common factor of two numbers. Main: A short activity where pupils sort a selection of fractions into two groups, based on whether they are simplified or not. Example question pairs to quickly assess if pupils understand how to simplify. A set of straightforward questions with a progression in difficulty. A challenging extension where pupils must arrange four digits to create fractions that simplify to given fractions. Plenary: Some questions in context to reinforce the key skill and also give some purpose to the process of simplifying fractions. Optional worksheets and answers included. Please review if you buy as any 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 (or maybe two) for introducing the circumference rule. Activities included: Starter: Prompts for pupils to discuss and share definitions for names of circle parts. Main: Link to an online geogebra file (no software required) that demonstrates the circumference rule. Quickfire questions to use with mini whiteboards. A worksheet of standard questions with a progression in difficulty. A set of four challenging problems in context, possibly to work on in pairs. Plenary: Pupils could discuss answers with another pair, or there could be a whole-class discussion of solutions (provided) Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A few activities on the theme of proving Pythagoras’ theorem, including a version of Perigal’s dissection I took from another TES user. The intention is to encourage discussion about what proof is, and to move pupils from nice-looking but hard to prove dissections to a proof they can make using relatively simple algebra (expanding and simplifying a double bracket). Please review if you use it, like it or even hate it!

A game to get pupils using key words and help them develop a greater appreciation of the important features of a diagram. I’ve created a series of simple images using two, three or four lines. Pupils cut these into individual cards, then take it in turns to pick one and describe the image to the other. The other sketches what they think the image looks like. They then reveal and discuss any differences. The game could be extended by pupils designing their own images, or used on other topic, eg circle theorems. As a bonus, they can finish off with a bit of route inspection! If anyone has a more catchy name for the game I’m open to suggestions!

A complete lesson designed to first introduce the concept of angle. The lesson is very interactive, with lots of discussion tasks and no worksheets! Activities included: Starter: A link to a short video of slopestyle footage, to get pupils interested. The athlete does a lot of rotations and the commentary is relevant but amusing. The video is revisited at the end of the lesson, when pupils can hopefully understand it better! Main: Highly visual slides, activities and discussion points to introduce the concepts of angle as turn, angle between 2 lines, and different types of angle. Includes questions in real-life contexts to get pupils thinking. A fun, competitive angle estimation game, where pupils compete in pairs to give the best estimate of given angles. A link to an excellent video about why mathematicians think 360 degrees was chosen for a full turn. Could be followed up with a few related questions if there is time. (eg can you list all the factors of 360?) Plenary: Pupils re-watch the slopstyle video, and are then prompted to try to decipher some of the ridiculous names for the jumps (eg backside triple cork 1440…) Includes slide notes with suggestions on tips for use, key questions and extension tasks. No printing required for this one! Please review if you buy as any feedback is appreciated!

A complete lesson or maybe two, where pupils consider how perimeter varies for rectilinear shapes. Sounds simple but it involves pupils investigating and using algebra to form and solve equations. Designed to follow on from another lesson I’ve put on the TES website about perimeter, although it works as a stand alone lesson too. Activities included: Starter: A quick task to get pupils thinking about when perimeter varies and when it doesn’t. Main: Three similar-but-different scenarios for pupils to investigate, by drawing different shapes that fulfil given criteria, before trying to spot patterns and generalise about perimeter. One of these scenarios is a ‘non-example’, in that the exact perimeter cannot be found. These scenarios are each formalised using some basic algebra, to model how to approach the next task. I’ve also attached a Geometer’s Sketchpad file which has these questions shown dynamically. If you don’t have GSP, no problem, as I have endeavoured to show the same information within the powerpoint. A set of related perimeter questions, requiring pupils to form simple equations to answer. Includes a few more non-examples, to help deepen pupils’ understanding of the algebra involved. Plenary: A prompt for pupils to reflect on the subtly different ways algebra has been used within the lesson. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

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!

A complete lesson on perimeter, with a strong problem solving element. Incorporate a set of on-trend-minimally-different questions and several opportunities for pupils to generate their own questions. Also incorporates area elements, to deliberately challenge the misconception of confusing the two properties of area and perimeter. Activities included: Starter: A few basic perimeter questions, to check pupils know what perimeter is. Main: Pupils come up with a variety of shapes with the same perimeter, then discuss answers with partners. Designed to get pupils thinking about which answers could be different, and which must be the same. A slight variation for the next activity - pupils are given diagrams of pentominoes (ie same area) and work out their perimeters. Raises some interesting questions about when perimeter varies, and when it doesn’t. A third activity based on diagrams a bit like the cover image. Using shapes made from different arrangements of identical rectangles, pupils work out the perimeters of increasingly elaborate shapes, some of which can’t be done. Questions have been designed so that only slight alterations have been made from one diagram to the next, but the resulting perimeter calculations are varied, interesting and sometimes surprising (IMO!). Has the potential to be extended by pupils creating their own shapes and trying to work out when it is possible to calculate the perimeter. Plenary: A closer look at the impossible questions, using a couple of different methods. Printable worksheets and answers included, where appropriate. Please review if you buy as any feedback is appreciated!

A complete lesson on solving one step equations using inverse operations. Does include some decimals, as I wanted to give a more complete example set and make it hard for pupils to just use trial and error to find solutions. As such, I would let pupils use calculators. Activities included: Starter: A short task where pupils match up simple one step ‘flll the blank’ statements, flow charts and equations. Then a prompt for them to discuss the solutions to these equations. I would expect them to at least know that to solve means finding numbers that make the equation true, and even if they have no prior knowledge of solving methods, they could verify that a given number was a solution to an equation. See my other resources for a lesson on introducing equations. Main: Some diagnostic questions to be used as mini whiteboard questions, where pupils turn one step equations into flow charts. Examples and a set of questions on using inverse operations to reverse a flowchart and solve its corresponding equation. A more open ended task of pupils creating their own questions, plus an extension task of creating equations with the largest possible answer, given certain criteria. Plenary: A prompt to discuss an example of an equation that can’t be solved using inverse operations. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on solving two step equations using inverse operations. Does include some decimals, as I wanted to give a more complete example set and make it hard for pupils to just use trial and error to find solutions. As such, I would let pupils use calculators. Activities included: Starter: A set of questions to check that pupils can evaluate two step expressions like 2x+3, given a value of x Main: A prompt to discuss the differences between two equations (a one step and a two step with the same solution), to get pupils thinking about how they could approach the latter. Examples and a set of questions on using inverse operations to reverse a two step flowchart and solve its corresponding equation. These have been deigned to further reinforce the importance of BIDMAS when interpreting an algebraic expression, so the emphasis is on quality not quantity of questions. A more challenging task of pupils trying to make an equation with a certain solution. Designed to be extendable to pupils looking for generalistions. Plenary: A prompt to discuss a few less obvious one-step equations (eg x+8+3=20) Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

An open-ended lesson on number pyramids, with the potential for pupils to practice addition and subtraction with integers, decimals, negatives and fractions, form and solve linear equations in two unknowns and create conjectures and proofs. I used this lesson for an interview and got the job, so it must be a good one! The entire lesson is built around the prompt I’ve uploaded as the cover slide. I have provided detailed answers for some of the responses that pupils could give, so you can get a clear idea of how the investigation might progress. I would spend the lesson responding to pupils’ work and questions, and probably get pupils to make posters of their findings or discuss their work with other pupils. Suitable for a range of abilities. Please review if you buy as any feedback is appreciated!

A complete lesson on solving two step equations of the form ax+b=c, ax-b=c, a(x+b)=c and a(x-b)=c using the balancing method. Designed to come after pupils have solved using a flowchart/inverse operations. Activities included: Starter: A few substitution questions to check pupils can correctly evaluate two-step expressions, followed by a prompt to consider some related equations. Main: A slide to remind pupils of the order of operations for the four variations listed above. Four example-problem pairs of solving equations, to model the methods and allow pupils to try. A set of questions for pupils to consolidate, and a suggestion for an extension task. The questions repeatedly use the same numbers and operations, to reinforce the fact that order matters and that pupils must pay close attention. A more interesting, challenging extension task in the style of the Open Middle website. Plenary: A set of four ‘spot the misconception’ questions, to prompt a final discussion/check for understanding. Printable worksheets and answers included. 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).