Adding, subtracting, multiplying and dividing fractions is a good topic, so what better than a joke to reward pupils' efforts? Pupils answer questions and use the code to reveal a funny gag.

A powerpoint including examples, worksheets and solutions on plotting coordinates in all 4 quadrants and problem solving involving coordinates. Worksheets at bottom of presentation for printing.

Maze consists of squares containing questions (on addition, subtraction, multiplication and division of fractions) with answers, some of which are wrong. Pupils are only allowed to pass through squares containing correct answers. Extension - pupils design their own maze (I like to discuss how they can make their maze harder by including classic misconceptions). Extra worksheet included to help pupils think about misconceptions (warning - this may well confuse weaker pupils!)

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 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 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 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 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!

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 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 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 identifying the y-intercept of a linear function. Intended as a precursor to using gradient and y-intercept to plot a linear function, but after pupils have plotted graphs with a table of values (ie they have seen equations of lines already). A good way of getting pupils to consider gradient without formally being ‘taught’ it. Activities included: Starter: A puzzle about whether two boats (represented on a grid) will collide. Main: Examples and three worksheets on the theme of identifying y-intercept. The first could just be projected and discussed - pupils simply have to read the number off the y-axis. The second is trickier, with two points marked on a grid, and pupils extend this (by counting squares up and across) until they reach the y-axis. The third is a lot more challenging, with the coordinates of 2 points given on a line, but no grid this time (see cover image). Could be extended by giving coordinates of two points, but one either side of the y-axis (although I’m going to do a whole lesson on this as a context for similarity, when I have time!) Plenary: A look at how knowing the equation of a line makes finding the y-intercept very easy. Examples, printable worksheets and answers included. Please review it 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 finding the gradient of a line that is perpendicular to another. Intended as a precursor to finding equations of lines perpendicular to another. Examples, a range of challenging activities 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 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 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 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 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 complete lesson (or maybe two) for introducing the area rule of a circle. Activities included: Starter: A mini-investigation where pupils estimate the area of circles on a grid. Main: Quickfire questions to use with mini whiteboards. A worksheet of standard questions with a progression in difficulty. A set of three challenging problems in context, possibly to work on in pairs. Plenary: Link to a short video that ‘proves’ the area rule very nicely. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!