A complete lesson on the alternate segment theorem. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees A tangent is perpendicular to a radius so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: Some basic questions to check pupils know what the word subtend means. Main: Animated slides to define what an alternate segment is. An example where the angle in the alternate segment is found without reference to the theorem (see cover image), followed by three similar questions for pupils to try. I’ve done this because if pupils can follow these steps, they can prove the theorem. However this element of the lesson could be bypassed or used later, depending on the class. Multiple choice questions where pupils simply have to identify which angles match as a result of the theorem. In my experience, they always struggle to identify the correct angle, so these questions really help. Seven examples of finding missing angles using the theorem (plus a second theorem for most of them). A set of eight similar problems for pupils to consolidate. An extension with two variations -an angle chase of sorts. Plenary: An animation of the proof without words, the intention being that pupils try to describe the steps. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated.

A complete lesson on the theorem that a tangent is perpendicular to a radius. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: Some basic recap questions on theorems 1 to 4 Main: Instructions for pupils to discover the rule, by drawing tangents and measuring the angle to the centre. A set of six examples, mostly using more than one theorem. A set of eight similar questions for pupils to consolidate. A prompt for pupils to create their own questions, as an extension. Plenary: A proof by contradiction of the theorem. Printable worksheets and answers included. Please do review if you buy, as any feedback is greatly 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 theorem that angles in the same segment are equal. 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 same segment theorem. Activities included: Starter: Some basic questions on the theorems that the angle at the centre is twice the angle at the circumference, and that the angle in a semi-circle is 90 degrees, to check pupils remember them. Main: Slides to show what a chord, major segment and minor segment are, and to show what it means to say that two angles are in the same segment. This is followed up by instructions for pupils to construct the usual diagram for this theorem, to further consolidate their understanding of the terminology and get them to investigate what happens to the angle. A ‘no words’ proof of the theorem, using the theorem that the angle at the centre is twice the angle at the circumference. Missing angle examples of the theorem, that could be used as questions for pupils to try. These include more interesting variations that incorporate other angle rules. A set of similar questions with a progression in difficulty, for pupils to consolidate. Two extension questions. Plenary: A final set of six diagrams, where pupils have to decide if two angles match, either because of the theorem learnt in the lesson or because of another angle rule. Printable worksheets and answers included. Please do review if you buy as any feedback is greatly 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 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!

A complete lesson on the theme of star polygons. An excellent way to enrich the topic of polygons, with opportunities for pupils to explore patterns, use notation systems, and make predictions & generalisations. No knowledge of interior or exterior angles needed. The investigation is quite structured and I have included answers, so you can see exactly what outcomes you can hope for, and pre-empt any misconceptions. Pupils investigate what happens when you connect every pth dot on a circle with n equally spaced dots on their circumference. For p>1 this generates star polygons, defined by the notation {n,p}. For example, {5,2} would mean connect every 2nd dot on a circle with 5 equally spaced dots, leading to a pentagram (see cover image). Pupils are initially given worksheets with pre-drawn circles to explore the cases {n,2} and {n,3}, for n between 3 and 10. After a chance to feedback on this, pupils are then prompted to make a prediction and test it. After this, there is a set of deeper questions, for pupils to try to answer. If pupils successfully answer those questions, they could make some nice display work! To finish the lesson, I’ve included a few examples of star polygons in popular culture and a link to an excellent short video about star polygons, that references all the ideas pupils have considered in the investigation. I’ve included key questions and other suggestions in the notes boxes. Please review if you buy as any feedback is 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.

This started as a lesson on plotting coordinates in the 1st quadrant, but morphed into something much deeper and could be used with any class from year 7 to year 11. Pupils will need to know what scalene, isosceles and right-angled triangles are to access this lesson. The first 16 slides are examples of plotting coordinates that could be used to introduce this skill, or as questions to check pupils can do it, or skipped altogether. Then there’s a worksheet where pupils plot sets of three given points and have to identify the type of triangle. I’ve followed this up with a set of questions for pupils to answer, where they justify their answers. This offers an engaging task for pupils to do, whilst practicing the basic of plotting coordinates, but also sets up the next task well. The ‘main’ task involves a grid with two points plotted. Pupils are asked to plot a third point on the grid, so that the resulting triangle is right-angled. This has 9 possible solutions for pupils to try to find. Then a second variant of making an isosceles triangle using the same two points, with 5 solutions. These are real low floor high ceiling tasks, with the scope to look at constructions, circle theorems and trig ratios for older pupils. Younger pupils could simply try with 2 new points and get some useful practice of thinking about coordinates and triangle types, in an engaging way. I have included a page of suggested next steps and animated solutions that could be shown to pupils. Please review if you buy as any feedback is appreciated!

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 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 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 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 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 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 of more interesting problems involving perimeter. I guess they’re the kind of problems you might see in the Junior Maths Challenge. Includes opportunities for pupils to be creative and make their own questions. Activities included: Starter: A perimeter puzzle to get pupils thinking, where they make changes to shapes without effecting the perimeter. Main: A set of four perimeter problems (on one page) for pupils to work on in pairs, plus some related extension tasks that will keep the most able busy. A matching activity, where pupils match shapes with different shapes but the same perimeter, using logic. I would extend this task further by getting them to put each matching set in size order according to their areas, to address the misconception of confusing area and perimeter. Pupils are then prompted to design their own shapes where the perimeters are the same. Plenary: You could showcase some pupil designs but much better, use all of their answers to create a new matching puzzle. 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 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!

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 drawing nets and visualising how they fold. The content has some overlap with a resource I have freely shared on the TES website for years, but has now been augmented and significantly upgraded,as well as being presented in a full, three-part lesson format. Activities included: Starter: A matching activity, where pupils match up names of solids, 3D sketches and nets. Main: A link to an online gogebra file (no software required) that allows you to fold and unfold various nets, to help pupils visualise. A question with an accurate, visual worked answer, where pupils make an accurate drawing of a cuboid’s net. Rather than answer lots of similar questions, pupils are then asked to compare answers with others and discuss whether their answers are different and/or correct. The same process with a triangular prism. A brief look at other prisms and a tetrahedron (the latter has the potential to be used to revise constructions if pupils have done them before, or could be briefly discussed as a future task, or left out) Then two activities with a different focus - the first looking at whether some given sketches are valid nets of cubes, the second about visualising which vertices of a net of a cube would meet when folded. Plenary: A brief look at some more elaborate nets, a link to a silly but fun net related video and a link to a second video, which describes a potential follow up or homework task. Printable worksheets and answers included where appropriate. Please review if you buy as any feedback is appreciated!