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 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 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!

A complete lesson on inverse operations. Includes questions with decimals, with the intention that pupils are using calculators. Activities included: Starter: Four simple questions where pupils fill a bank in a sum, to facilitate a discussion about possible ways of doing this. Slides to formalise the idea of an inverse operation, followed by a set of questions to check pupils can correctly correctly identify the inverse of a given operation and a worksheet of straight-forward fill the blank questions (albeit with decimals, to force pupils to use inverse operations). I have thrown in a few things that could stimulate further discussion here - see cover image. Main: The core of the lesson centres around an adaptation of an excellent puzzle I saw on the Brilliant.org website. I have created a series of similar puzzles and adapted them for a classroom setting. Essentially, it is a diagram showing boxes for an input and an output, but with multiple routes to get from one to the other, each with a different combination of operations. Pupils are tasked with exploring a set of related questions: the largest and smallest outputs for a given input. the possible inputs for a given output. the possible inputs for a given output, if the input was an integer. The second and third questions use inverse operations, and the third in particular gives pupils something a lot more interesting to think about. The second question could be skipped to make the third even more challenging. I’ve also thrown in a blank template for pupils to create their own puzzles. Plenary: Your standard ‘I think of a number’ inverse operation puzzle, for old time’s sake. Printable worksheets and answers included. Please do review if you buy, as any feedback is appreciated!

A complete lesson on solving two step equations of the form ax+b=c using the balancing method. Designed to come after pupils have solved using a flowchart/inverse operations. Activities included: Starter: A set of questions to check that pupils can solve one step equations using the balancing method. Main: A prompt for pupils to consider a two step equation. An animated solution to this equation, showing physical scales to help reinforce the balancing idea. An example-problem pair, to model the method and allow pupils to try. A set of questions with a variation element built in. Pupils could be extended by asking them to predict answers, or to explain the connections between answers after finishing them. A related, more challenging task of solving equations by comparing them to a given equation, plus a suggested extension task for pupils to think more mathematically and creatively. Plenary: A closer look at a question, looking at the two different balancing approaches that could be taken (see cover slide). Depending on time, pupils could go back and attempt the previous questions using the second approach. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

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 the graphs of sine, cosine and tangent outside the range 0 to 360 degrees. I’ve also made complete lessons on these functions in 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 looked at the graphs of sine cosine and tangent in the range 0 to 360 degrees. This could also be used as a precursor to solving trigonometric equations in the further maths gcse or A-level. Activities included: Starter: A worksheet where pupils identify key coordinates on the graphs of sine and cosine from 0 to 360 degrees. Main: A reminder of the definitions of sine, cosine and tangent using the unit circle, with a prompt for pupils to discuss what happens outside the range 0 to 360 and a slide to make this clear. Three examples of using knowledge of the graphs to effectively solve a trigonometric equation. This isn’t formalised, but done more as a visual puzzle that pupils can answer using symmetry and the fact that the functions are periodic (see cover image). A worksheet with a set of similar questions, followed by a related extension task. Plenary: A brief summary about sound waves and how pitch and volume is determined. 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 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 using calculators to directly make percentage changes, e.g. increasing by 5% by multiplying by 1.05 Activities included: Starter: A recap on making a percentage change in stages, e.g. increasing something by 5% by working out 5% and adding it to the original amount. Main: Examples and quick questions for pupils to try, along with some diagnostic questions to hopefully anticipate a few misconceptions. A worksheet of questions with a progression in difficulty. An extension task/investigation designed to challenge the misconception that you can reverse a percentage increase by decreasing by the same percentage. Plenary: A question in context - working out a restaurant bill including a tip. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated!

A complete lesson, or range of activities to use, on the theme of Pythagorean triples. A great lesson for adding some interest, depth and challenge to the topic of Pythagoras’ theorem. Activities included: Starter: A set of straight forward questions on finding the third side given two sides in a right-angled triangle, to remind pupils of Pythagoras’ theorem. Main: Slides explaining that Pythagoras’ theorem can be used to test whether a triangle has a right angle. A sorting activity where pupils test whether given triangles contain a right angle. Quick explanation of Pythagorean triples, followed by a structured worksheet for pupils to try using Diophantus’ method to generate Pythagorean triples, and, as an extension, prove why the method works. Two pairs of challenging puzzles about Pythagorean triples. Plenary: A final question, not too difficult, to bring together the theme of the lesson (see cover image). Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on the theme of using Pythagoras’ theorem to look at the distance between 2 points. A good way of combining revision of Pythagoras, surds and coordinates. Could also be used for a C1 class about to do coordinate geometry. Activities included: Starter: Pupils estimate square roots and then see how close they were. Can get weirdly competitive. Main: Examples and worksheets with a progression of difficulty on the theme of distance between 2 points. For the first worksheet, pupils must find the exact distance between 2 points marked on a grid. For the second worksheet, pupils find the exact distance between 2 coordinates (without a grid). For the third worksheet, pupils find a missing coordinate, given the exact distance. There is also an extension worksheet, where pupils mark the possible position for a second point on a grid, given one point and the exact distance between the two points. I always print these worksheets 2 per page, double sided, so without the extension this can be condensed to one page! It may not sound thrilling, but this lesson has always worked really well, with the gentle progression in difficulty being enough to keep pupils challenged, without too much need for teacher input. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for introducing the area rule for a triangle. Activities included: Starter: Questions to check pupils can find areas of parallelograms (I always teach this first, as it leads to an explanation of the rule for a triangle). Main: A prompt to get pupils thinking (see cover image) Examples and a worksheet where pupils must identify the height and measure to estimate area. Examples and a worksheet where pupils must select the relevant information from not-to-scale diagrams. Simple extension task of pupils drawing as many different triangles with an area of 12 as they can. Plenary: A sneaky puzzle with a simple answer that reinforces the basic area rule. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on defining, recognising and extending linear sequences. Activities included: Starter: Pupils discuss whether six sets of numbers are sequences, and if so, what the rules are. Main: Slides to define linear sequences, followed by mini whiteboard questions and a worksheet of extending linear sequences. A fun puzzle a bit like a word search (but where you try to find linear sequences). Plenary: Another nice puzzle where pupils try to form as many linear sequences as they can from a set of numbers. Printable worksheets and answers included. Please review it if you buy as any feedback is 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 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 patterns of growing shapes that lead to quadratic sequences. See the cover image to get an idea of what I mean by this. Activities included: Starter: A matching activity relating to representation of linear sequences, to set the scene for considering similar representations of quadratic sequences, but also to pay close attention to the common sequences given by the nth term rules 2n and 2n-1 (ie even and odd numbers), as these feature heavily in the lesson. Main: A prompt to give pupils a sense of the intended outcomes of the lesson (see cover image). An extended set of examples of shape sequences with increasingly tricky nth term rules. The intention is that pupils would derive an nth term rule for the number of squares in each shape using the geometry of each shape rather than counting squares and finding an nth term rule from a list of numbers. A worksheet with a set of six different shape sequences, for pupils to consider/discuss. The nth term rules have been given, so the task is to justify these rules by considering the geometry of each shape sequence. Each rule can be justified in a number of ways, so this should lead to some good discussion of methods. Plenary: Ideally, pupils would share their differing methods, but I’ve shown a few methods to one of the sequences to stimulate discussion. Printable worksheets (2) included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to divide fractions by fractions. Activities included: Starter: A set of questions on multiplying fractions (I assume everyone would teach this before doing division). Main: Some highly visual examples of dividing by a fraction, using a form of bar modelling (more to help pupils feel comfortable with the idea of dividing a fraction by a fraction, than as a method for working them out). Examples and quick questions for pupils to try, using the standard method of flipping the fraction and multiplying. A set of straightforward questions. A challenging extension where pupils must test different combinations and try to find one that gives required answers. Plenary: An example and explanation (I wouldn’t call it a proof though) of why the standard method works. Optional worksheets (ie everything could be projected, but there are copies in case you want to print) and answers included. Please review if you buy as any feedback is appreciated!