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 for first introducing the ratios sin, cos and tan. Ideal as a a precursor to teaching pupils SOHCAHTOA. Activities included: Starter: Some basic similarity questions (I would always teach similarity before trig ratios). Main: Examples and questions on using similarity to find missing sides, given a trig ratio (see cover image for an example of what I mean, and to understand the intention of doing this first). Examples, quick questions and worksheets on identifying hypotenuse/opposite/adjacent and then sin/cos/tan for right-angled triangles. A challenging always, sometimes, never activity involving trig ratios. Plenary: A discussion about the last task, and a chance for pupils to share ideas. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on interior angles of polygons. Activities included: Starter: A slide showing examples and non-examples of interior angles, for pupils to think about a definition, followed by a set of images where pupils must identify any interior angles (sounds easy and dull, but isn’t!) Main: A recap of visual proofs of why the interior angles of a triangle sum to 180 degrees and those of a quadrilateral sum to 360 degrees, leading to the obvious question of “what next?” Prompts for the usual “investigation” into the sum of interior angles for polygons, by splitting into triangles. A set of questions designed to be done with mini whiteboards, starting with basic sums of interior angles, interior angles of regular polygons and finally a few variations (see cover image). A four-part worksheet (one page if printed two-a-side and two-sided) with a similar progression in difficulty. Plenary: A slide summarising the rules encountered, together with some key questions to check for any misconceptions. Printable worksheets and answers included. I’ve also included suggested questions and extensions in the notes boxes at the bottom of each slide. 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 on bearings problems with an element of trigonometry or Pythagoras’ theorem. Activities included: Starter: Two sets of questions, one to remind pupils of basic bearings, the other a matching activity to remind pupils of basic trigonometry and Pythagoras’ thoerem. Main: Three worked examples to show the kind of things required. A set of eight problems for pupils to work through. Plenary: A prompt for pupils to reflect on the skills used during the lesson. Printable worksheets and answers included. Please review if you buy as any feedback is 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 on the concept of an equation of a line. Intended as a precursor to the usual skills of plotting using a table of values or using gradient and intercept. Examples, printable worksheets and answers included. Please review it 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 number pyramids, with an emphasis on pupils forming and solving linear equations. An excellent way of getting pupils to consolidate methods for solving in an unfamiliar setting, and for them to think mathematically about what they are doing. Activities included: Starter: Slides to introduce how number pyramids work, followed by a simple worksheet to check pupils understand (see cover slide) Main: A prompt to a harder question for pupils to try. They will probably use trial and improvement and this will lead nicely to showing the merits of a direct algebraic method of obtaining an answer. A second, very similar question for pupils to try. The numbers have simply swapped positions, so there is some value in getting pupils to predict how this will impact the answer. A prompt for pupils to investigate further for themselves, along with a few suggested further lines of inquiry. There are lots of ways the task could be extended, but my intention is that this particular lesson would probably focus more on pupils looking at combinations by rearranging a set of chosen numbers and thinking about what will happen as they do this. I have made two other number pyramid lessons with slightly different emphases. Plenary: A prompt to a similar looking question that creates an entirely different solution, to get pupils thinking about different types of equation. Please review 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 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!

A complete lesson on using a table of values to plot a linear function. Nothing fancy, but provides clear examples, printable worksheets and answers. Please review it if you buy as any feedback is appreciated!

A complete lesson on exterior angles of polygons. I cover exterior angles after interior angles, so I should point out that the starter does rely on pupils knowing how to do calculations involving interior angles. See my other resources for a lesson on interior angles. Activities included: Starter: Some recap questions involving interior angles and also exterior angles, but with the intention that pupils just use the rule for angles on a line, rather than a formal definition of exterior angles (yet). Main: A “what’s the same,what’s different” prompt followed by examples and non-examples of exterior angles, to get pupils thinking about a definition of them. A mini- investigation into exterior angles. Prompts to establish and then prove algebraically that exterior angles sum to 360 degrees for a triangle and a quadrilateral. The proofs could be skipped, if you felt this was too hard. A worksheet of more standard exterior angle questions with a progression in difficulty. Plenary: A slide animating a visual proof of the rule, followed by a hyperlink to a different visual proof. Printable worksheets and answers included. I’ve also included suggested questions and extensions in the notes boxes at the bottom of each slide. Please review if you buy as any feedback is appreciated!

A complete lesson on solving one step equations using the balancing method. Designed to come after pupils have solved using a flowchart/inverse operations, and as such the introductory slides put the two methods side by side, so pupils can relate them. I’ve also uploaded a lesson on balancing (but not solving) equations that would be a good precursor to this lesson. Activities included: Starter: A set of questions to check that pupils can solve one step equations using a flowchart/inverse operations. Main: Two slides showing equations represented on scales, to help pupils visualise the equations as a balancing problem. Four examples of solving equations, firstly using a flowchart/inverse operations and then by balancing. Then a set of similar questions for pupils to try, before giving any feedback. A second set of questions basically with harder numbers. Not exactly thrilling but necessary practice. A more interesting, challenging extension task in the style of the Open Middle website. Plenary: A prompt of an equation that is best solved using the balancing method, rather than inverse operations (hence offering some incentive for the former method). Printable worksheets and answers included. 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!

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 increasing or decreasing by a percentage. Activities included: Starter: A template for pupils to work out lots of different percentages of £30 Main: Examples and a set of straight-forward questions making percentage changes. A connect 4 game for pupils to play in pairs, taking it in turns to work out percentage changes and win squares on a grid. A few questions to discuss about the game. A puzzle where pupils arrange numbers and percentage change statements to make a loop. Plenary: Some examples looking at making a percentage decrease a different way - eg decreasing by 25% by directly working out 75% Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

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 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!