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.

Basically colouring by numbers, but with questions on Pythagoras' theorem. Actually created by one of my pupils!

A powerpoint including examples, worksheets and solutions on 3D sketching of prisms and other solids, nets of 3D solids, drawing on isometric paper and plans/elevations. Worksheets at bottom of presentation for printing.

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.

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.

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!

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 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 trapezium area rule. Activities included: Starter: Non-calculator BIDMAS questions relating to the calculations needed to area of a trapezium. A good chance to discuss misconceptions about multiplying by a half. Main: Reminder of shape properties of a trapezium Example-question pairs, giving pupils a quick opportunity to try and receive feedback. A worksheet of straight forward questions with a progression in difficulty, although I have also built in a few things for more able students to think about. (eg what happens if all the measurement double?) A challenging extension task where pupils work in reverse, finding measurements given areas. Plenary: Nice visual proof of rule by relating to the rule for the area 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 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 for first teaching how to divide fractions by whole numbers. Activities included: Starter: A simple question in context to help pupils visualise division of fractions by whole numbers. Main: Some example and questions for pupils to try. A set of straightforward questions. A challenging extension where pupils must think a lot more carefully about what steps to take. Plenary: A final example designed to challenge the misconception of division leading to an equivalent fraction, and give a chance to reinforce the key method. Worksheets and answers included. 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 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!