A complete lesson for introducing the area rule of a parallelogram. Activities included: Starter: A couple of area mazes to remind them of the rule for rectangles. Main: A prompt for pupils to discuss or think about what a parallelogram is, followed by 2 questions, where pupils are shown a set of shapes and have to identify which ones are parallelograms. Animated examples showing the classic dissection and rearrangement of a parallelogram into a rectangle, leading naturally to a derivation of the area rule. Animated examples of using a ruler and set square to measure the base and perpendicular height, before calculating area. A worksheet where pupils must do the same. This is worth doing now, to make pupils think carefully about perpendicular height, rather than just multiplying given dimensions together. Examples and a worksheet where pupils must select the relevant information from not-to-scale diagrams. Extension task of pupils using knowledge of factors to solve an area puzzle. Plenary: Spot the mistake discussion question. Nice animation to show why the rule works. Link to an online geogebra file (no software required) with a lovely alternative dissection of a parallelogram Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson for first teaching how to compare fractions using common denominators. Intended as a precursor to both ordering fractions and adding or subtracting fractions, as it requires the same skills. Activities included: Starter: Some quick questions to test if pupils can find the lowest common multiple of two numbers. Main: A prompt to generate discussion about different methods of comparing the size of two fractions. Example question pairs on comparing using equivalent fractions, to quickly assess if pupils understand the method. A set of straightforward questions with a progression in difficulty. A challenging extension where pupils find fractions halfway between two given fractions. Plenary: A question in context to reinforce the key skill and also give some purpose to the skill taught in the lesson. Optional worksheets (ie no printing is really required, but the option is there if you want) and answers included. Please review 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!

A complete lesson on prime factors. Intended as a challenging task to come after pupils are familiar with the process of expressing a number as a product of prime factors (see my other resources for a lesson on this). Activities included: Starter: Questions to test pupils can list all factors of a number using factor pairs. Main: Pupils find all factors of a number using a different method - by starting with the prime factor form of a number and considering how these can be combined into factor pairs. Links well to the skill of testing combinations that is in the new GCSE specification. Possible extension of pupils investigating what determines how many factors a number has. Plenary: A look at why numbers that are products of three different primes must have 8 factors. No worksheets required and answers included throughout. Please review it if you buy as any feedback is appreciated!

A complete lesson on prime factors, but not the usual questions. Intended as a challenging task to come after pupils are familiar with the process of expressing a number as a product of prime factors (see my other resources for a lesson on this). Activities included: Starter: A nice ‘puzzle’ where pupils work out three seemingly unrelated multiplication sums (a good chance to practice another non-calculator skill), only to find they give the same answer. Intended to stimulate some discussion about prime factors. Main: Four mini-activities, where pupils use one number’s prime factor form to obtain the prime factor form of some related numbers. An opportunity for pupils to be creative and come up with their own puzzles. Plenary: A final puzzle to check pupils’ understanding of the key idea of the lesson. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson for first teaching pupils how to express a number as a product of its prime factors using a factor tree. Activities included: Starter: Three puzzles relating to prime numbers, intended to increase pupils’ familiarity with them. Main: Examples and questions (with a progression of difficulty and some intrigue). Plenary A ‘spot the mistake’ question. No worksheets required and answers included throughout. Please review it if you buy as any feedback is appreciated!

A complete lesson on finding a term given its a position and vice-versa. Activities included: Starter: Recap questions on using an nth term rule to generate the first few terms in a linear sequence. Main: Short, simple task of using an nth term rule to find a term given its position. Harder task where pupils find the position of a given term, by solving a linear equation. Plenary: A question to get pupils thinking about how they could prove if a number was a term in a sequence. No worksheets required, and answers are included. Please review it if you buy as any feedback is appreciated!

A complete lesson for first teaching pupils how to find the nth term rule of a linear sequence. Activities included: Starter: Questions on one-step linear equations (which pupils will need to solve later). Main: Examples and quick questions for pupils to try and receive feedback. A set of questions with a progression in difficulty, from increasing to decreasing sequences, for pupils to practice independently. Plenary: A proof of why the method for finding the nth term rule works. Answers provided throughout. Please review it if you buy as any feedback is appreciated!

A complete lesson on gradient as rate of change, that assumes pupils have already learned how to calculate the gradient of a curve and are familiar with distance-time graphs. Designed to match the content of the 9-1 GCSE specification. Examples and activities on calculating average gradient between 2 points on a curve and estimating instantaneous gradient at a point, in the context of finding rates of change (eg given a curved distance-time graph, calculate the speed) . Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on gradient of curves. Examples and questions on calculating average gradient between 2 points on a curve and estimating instantaneous gradient at a point. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on gradient between two points, that assumes pupils have already spent time calculating gradients of lines, and is intended to give pupils an opportunity to use their knowledge of gradient in a slightly more challenging way. The examples and activities involve using knowledge of coordinates and gradient to find missing points on a grid. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson on using SOHCAHTOA and Pythagoras’ theorem with problems in three dimensions. Activities included: Starter: A set of recap questions on basic SOHCAHTOA and Pythagoras. Main: Examples and questions to dscuss, on visualising distances and angles within cuboids and triangular prisms, and understanding the wording of exam questions on this topic. Examples and quick questions for pupils to try, on finding the angle of a space diagonal. A worksheet, in three sections (I print this, including the starter, two per page, two sided so that you have a single page handout), with a progression in difficulty. Starts with finding the space diagonal of a cuboid, where the triangle pupils will need to use has been drawn already. The second section looks at angles in a triangular prism, and pupils will need to draw the relevant triangles themselves. The third section has exam-style questions, where pupils will need to identify the correct angle by interpreting the wording of the question. (eg “find the angle between the diagonal AE and the plane ABCD”). An extension task looking at the great pyramid of Giza. Plenary: A final question to add a bit more depth, looking at the most steep and least steep angles up a ramp. Printable worksheets and worked answers included. Please review 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 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 the theorem that tangents from a point are equal. 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 Angles in alternate segments are equal so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: Instructions for pupils to discover the theorem, by drawing tangents and measuring. Main: Slides to clarify why this theorem usually involves isosceles triangles. Related examples, finding missing angles. A set of eight questions using the theorem (and usually another theorem or angle fact). Two very sneaky extension questions. 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 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 perpendicular bisector of a chord passes through the centre of a circle. 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 Angles in alternate segments are equal Tangents from a point are equal so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: An animation reminding pupils about perpendicular bisectors, with the intention being that they would then practice this a few times with ruler and compass. Main: Instructions for pupils to investigate the theorem, by drawing a circle, chord and then bisecting the chord. Slides to clarify the ‘two-directional’ nature of the theorem. Examples of missing angle or length problems using the theorem (plus another theorem, usually) A similar set of eight questions for pupils to consolidate. An extension prompt for pupils to use the theorem to locate the exact centre of a given circle. 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 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!