The last of five complete lessons on linear sequences. Looks at patterns of squares or lines that each form a linear sequence. Adapted from a resource by another TES user called flibit (who has made some excellent resources). Printable worksheets included.

A challenging set of puzzles, that mainly require pupils to use their knowledge of the properties and area rule of a parallelogram, but also involve finding areas of triangles. Includes a few ideas adapted from other sources, one of which is Don Steward’s superb Median blog, the other I’m afraid I can’t remember. Please review if you like it, or even if you don’t!

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 finding percentages of an amount using non-calculator methods, by relating them to the key percentages of 10%, 25% and 1%. See the cover image to get an idea of the intention of the lesson. Activities included: Starter: A set of questions to recap on finding 50%, 25%, 75%, 10%, 5%, 20% and 1% of an amount. Main: Some slides to introduce the idea of using the key percentages to find other percentages. A worksheet to consolidate these ideas, followed by three flowcharts in the style of the cover image, where pupils are given a starting number and work out all the percentages. The starting numbers get progressively more difficult. I use this as a non-calculator task, but it could be used with calculators too. An extension task where pupils work out some percentages not included in the flowcharts, by combining percentages. Plenary: A great discussion question, looking at four possible ways to calculate 75% of a number. Printable worksheets and answers included. Please review if you buy as any feedback is 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 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 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 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 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 knowledge of gradient and y-intercept to find the equation of a line. Progresses from positive integer gradients to fractional and/or negative gradients. Examples, printable worksheets and answers included. 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 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 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 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 designed to introduce the concept of an equation. Touches on different equation types but doesn’t go into any solving methods. Instead, pupils use substitution to verify that numbers satisfy equations, and are therefore solutions. As such, the lesson does require pupils to be able to substitute into simple expressions. Activities included: Starter: A set of questions to check that pupils can evaluate expressions Main: Examples of ‘fill the blank’ statements represented as equations, and a definition of the words solve and solution. Examples and a worksheet on the theme of checking if solutions to equations are correct, by substituting. A few slides showing some variations of equations using carefully selected examples, including an equation with no solutions, an equation with infinite solutions, simultaneous equations and an identity. A sometimes, always never activity inspired by a similar one form the standards unit (but simplified so that no solving techniques are required). I’d use the pupils’ work on this last task as a basis for a plenary, possibly pupils discussing each other’s work. Printable worksheets and answers included. 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 number pyramids, with an emphasis on pupils forming and solving linear equations. An excellent way of getting pupils to think about equations in an unfamiliar setting, and to create their own questions and conjectures. Activities included: Starter: A mini-investigation on three-tier number pyramids, to set the scene. One combination is best dealt with using a linear equation, and sets pupils up to access the more challenging task to come. Main: A prompt for pupils to consider four-tier number pyramids. Although this task has the potential to be extended in different ways, I have provided an initial focus and provided some responses that pupils could give, so you can get a clear idea of how the investigation might progress. I would spend the rest of the lesson responding to pupils’ work and questions, and probably get pupils to make posters of their findings or discuss their work with other pupils. Please review if you buy as any feedback is appreciated!

At least a lesson’s worth of activities on the theme of quadratic sequences. Designed to come after pupils have learnt the basics (how to use and find an nth term rule of a quadratic sequence). Gives pupils a chance to create their own examples and think mathematically. There are four activities included: Activity 1 - given sets of four numbers, pupils have to order them so that they form quadratic sequences. Designed to deepen pupils understanding that the terms in a quadratic sequences don’t necessarily always go up or down. Activities 2 and 3 - on the same theme of looking at the sequences you get when you pick and order three numbers of choice. Can you always create a quadratic sequence in this way? What if you had four numbers? Could be used to link to quadratic functions. Activity 4 - inverting the last activity, can pupils find possible values for the first three terms and a rule, given the fourth term? A chance for pupils to generate their own examples and possibly do some solving of equations in more than one variable. Where applicable, worked answers provided.