A complete lesson on area of rectilinear shapes, with a strong problem solving and creative element. Activities included: Starter: See cover slide - a prompt to think about properties of shapes, in part to lead to a definition of rectilinear polygons. Main: A question for pupils to discuss, considering which of two methods gives the correct answer for the area of an L-shape. A worksheet showing another L-shape, 6 times with 6 different sums. Pupils try to figure out the method used from the sum. A second worksheet that is really hard to describe but involves pupils thinking critically about how the area of increasingly intricate rectilinear shapes can have the same area. This sets pupils up to go on to create their own interesting shapes with the same area, by generalising about the necessary conditions for this to happen, and ways to achieve this (without counting all the squares!) A third worksheet with more conventional area questions, that could be used as a low-stakes test or a homework. Most questions have the potential to be done in more than one way, so could also be used to get pupils discussing and comparing methods. Plenary: A final question of sorts, where pupils have to identify the information sufficient to work out the area of a given rectilinear shape. Printable worksheets and answers included. I’ve also included suggestions for key questions and follow up questions in the comments boxes at the bottom of each slide. Please review if you buy as any feedback is appreciated!

A complete lesson looking at the associative and commutative properties of multiplication. Activities included: Starter: A simple grid of times table questions, includes ‘reversals’ (eg 7 times 9 and 9 times 7) to get pupils thinking about the commutative property. Main: Visual examples to get pupils thinking about commutativity of multiplication and non-commutativity of division. Pupils could explore further using arrays or Cuisenaire rods. Visual examples to get pupils thinking about associativity of multiplication and non-associativity of division. Pupils could explore further using pictorial representations. Three short activities where pupils make use of the commutative and associative properties of multiplication to make calculations. The last provides opportunities for pupils to create their own puzzles. Plenary: A maths ‘trick’ that uses the same properties. Please review 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 introducing quadratic equations. The lesson looks at what quadratic equations are, solving quadratic equations when there isn’t a term in x, and ends with a more open ended, challenging task. Activities included: Starter: Two questions to get pupils thinking about the fact that positive numbers have two (real) square roots, whereas negative numbers have none. Main: A discussion activity to help pupils understand what a quadratic equation is. They are presented with equations spit into 3 columns - linear, quadratic and something else, and have to discuss what features distinguish each. Examples, quick questions and two sets of questions for pupils to try. These include fraction, decimal and surd answers, but are designed to be done without a calculator, assuming pupils can square root simple numbers like 4/9 or 0.64. Could be done with a calculator if necessary. Some questions in a geometric context, culminating in some more challenging problems where pupils look for tetromino-type shapes where area = perimeter. There is scope here for pupils to design their own, similar puzzles. I haven’t included a plenary, as I felt that the end point would vary, depending on the group. Slides could be printed as worksheets, although everything has been designed to be projected. Answers included. Please review if you buy, as any feedback is appreciated!

A complete lesson on the theorem that the angle in a semicircle is 90 degrees. I always teach the theorem that the angle at the centre is twice the angle at the circumference first (see my other resources for a lesson on that theorem), as it can be used to easily prove the semicircle theorem. Activities included: Starter: Some basic questions on the theorem that the angle at the centre is twice the angle at the circumference, to check pupils remember it. Main: Examples and non-examples of the semicircle theorem, that could be used as questions for pupils to try. These include more interesting variations like using Pythagoras’ theorem or incorporating other angle rules. A set of questions with a progression in difficulty. These deliberately include a few questions that can’t be done, to focus pupils’ attention on the key features of diagrams. An extension task prompt for pupils to create their own questions using the two theorems already encountered. Plenary: Three discussion questions to promote deeper thinking, the first looking at alternative methods for one of the questions from the worksheet, the next considering whether a given line is a diameter, the third considering whether given diagrams show an acute, 90 degree or obtuse angle. Printable worksheets and answers included. Please do review if you buy as any feedback is greatly appreciated!

A complete lesson on types of polygon, although it goes well beyond the basic classifications of regular and irregular. This lesson gives a flavour of how my resources have been upgraded since I started charging. Activities included: Starter: A nice kinesthetic puzzle, where pupils position two triangles to find as many different shapes as they can. Main: A slide of examples and non-examples of polygons, for pupils to consider before offering a definition of a polygon. A slide showing examples of different types of quadrilateral . Not the usual split of square, rectangle, etc, but concave, convex, equilateral, equiangular, regular, cyclic and simple. This may seem ‘hard’, but I think it is good to show pupils that even simple ideas can have interesting variations. A prompt for pupils to try and draw pentagons that fit these types, with some follow-up questions. A brief mention of star polygons (see my other resources for a complete lesson on this). Slides showing different irregular and regular polygons, together with some follow-up questions. Two Venn diagram activities, where pupils try to find polygons that fit different criteria. This could be extended with pupils creating their own Venn diagrams using criteria of their choice. Could make a nice display. Plenary: A table summarising the names of shapes they need to learn, with a prompt to make an educated guess of the names of 13, 14 and 15 sided shapes. Minimal printing needed and answers included where applicable. I have also added key questions and suggested extensions in the notes boxes. Please review if you buy as any feedback is very much appreciated.

A complete lesson with a focus on angles as variables. Basically, pupils investigate what angle relationships there are when you overlap a square and equilateral triangle. A good opportunity to extend the topic of polygons, consider some of the dynamic aspects of geometry and allow pupils to generate their own questions. Prior knowledge of angles in polygons required. Activities included: Starter: A mini-investigation looking at the relationship between two angles in a set of related diagrams, to recap on basic angle calculations and set the scene for the main part of the lesson. Main: A prompt (see cover image) for pupils to consider, then another prompt for them to work out the relationship between two angles in the image. A slide to go through the answer (which isn’t entirely straight forward), followed by two animations to illustrate the dynamic nature of the answer. A prompt for pupils to consider how the original diagram could be varied to generate a slightly different scenario, as a prompt for them to investigate other possible angle relationships. I’ve not included answers from here, as the outcomes will vary with the pupil. The intention is that pupils then investigate for themselves. Plenary: Another dynamic scenario for pupils to consider, which also reinforces the rules for the sum of interior and exterior angles. Please review if you buy as any feedback is appreciated!

A complete lesson on the theme of balancing equations. There is no solving involved, and the idea is that this lesson would come before using balancing to solve equations. Activities included: Starter: Pupils are presented with a set of number statements (see cover slide) and then prompted to discuss how each statement has been obtained. Pupils then create a similar diagram with an initial number statement of their choice, then could swap/discuss with another student. Main: Pupils are shown an equation and try to create other equations by balancing. They can use substitution to verify whether their new equations are valid. I would follow this up with a whole-class discussion to clarify any misconceptions. Four sets of equations that have been obtained by balancing, pupils have to identify what has been done to both sides each time. A ‘spot the mistake’ worksheet which incorporates the usual misconceptions relating to manipulating and balancing equations. Plenary: A taster of balancing being used to solve equations. Possible key questions, follow up and extension questions included in notes boxes at bottom of slides. 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 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 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 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!