A collection of 5 activities involving square numbers that I’ve accumulated over the years from various sources: a puzzle I saw on Twitter involving recognising square numbers. a harder puzzle using some larger square numbers and a bit of logic. a sequences problem that links to square numbers a mini investigation that could lead to some basic algebraic proof work a trick involving mentally calculating squares of large numbers, plus a proof of why it works 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!)

Maze consists of squares containing questions 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 to make the maze harder by including classic misconceptions like divide by 5 to get 5%

A complete lesson designed to be used to consolidate pupils’ ability to add and subtract a negative number. Activities included: Starter: Some straight forward questions to test if they can remember the basic methods and help identify misconceptions. Main: A set of differentiated questions to give pupils a bit more practice. A game adapted from the nrich website. A closer look at the design of the game, with pupils making a sample space diagram. Plenary: Some final questions to prompt discussion and reflection on how to remember the rules used. Printable worksheets and answers included. Please review if you use this!

Starts with the basic tests for numbers up to 10, then looks at tests for higher numbers and finally problem solving using divisibility tests. Also looks at proofs of some of the tests using algebra. Worksheets at end for printing.

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 solving two step equations of the form ax+b=c using the balancing method. Designed to come after pupils have solved using a flowchart/inverse operations. Activities included: Starter: A set of questions to check that pupils can solve one step equations using the balancing method. Main: A prompt for pupils to consider a two step equation. An animated solution to this equation, showing physical scales to help reinforce the balancing idea. An example-problem pair, to model the method and allow pupils to try. A set of questions with a variation element built in. Pupils could be extended by asking them to predict answers, or to explain the connections between answers after finishing them. A related, more challenging task of solving equations by comparing them to a given equation, plus a suggested extension task for pupils to think more mathematically and creatively. Plenary: A closer look at a question, looking at the two different balancing approaches that could be taken (see cover slide). Depending on time, pupils could go back and attempt the previous questions using the second approach. 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 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 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 of more challenging problems involving the sine rule. Designed to come after pupils have spent time on basic questions. Mistake on previous version now corrected - please contact me for an updated copy if you have already purchased this. Activities included: Starter: A set of six questions, each giving different combinations of angles and sides. Pupils have to decide which questions can be done with the sine rule. In fact they all can, the point being that questions aren’t always presented in the basic ‘opposite pairs’ format. Pupils can then answer these questions, to check they can correctly apply the sine rule. Main: A set of eight more challenging questions that pupils could work on in pairs. Each one is unique, with no examples offered, and therefore I’d class this as a problem solving lesson - pupils may need to adopt a general approach of working out what they can at first, and seeing where this takes them. Questions also require knowledge from other topics including angle rules, shape properties, bearings, and the sine graph. I’ve provided full worked answers FYI, but I would get pupils discussing answers and presenting to the class. Plenary: A prompt for pupils to reflect on possible rounding errors. Most of the questions have several steps, so it is worth getting pupils to think about how to avoid rounding errors. I’ve left each question as a full slide, but I’d print them 4-on-1 and 2-sided, so that you’d only need to print one worksheet per pair. 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 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 selection of puzzles, most using the digits 1 to 9 and an element of working systematically to obtain a solution. A few are from the the excellent Nrich website. Based around key skills of adding, subtracting, multiplying and dividing but that doesn't mean they're easy!

Inspired by the Transformers cartoon/film/toys, pupils turn robots into vehicles using a mixture of shape transformations (translations, reflections, rotations and enlargements). Animated answers included. Great homework potential for pupils to design their own!

A fun 'investigation&' using ratio and problem solving skills. Slightly dark theme of thieves sharing the profits of different robberies. Made by another TES user &';taylorda01' (thanks for the resource!) but I wanted to add answers to it.

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.

Worksheet where answers to questions are used to obtain a 3-digit code (which I set as the combination to a lockable money box containing a prize). Pupils race to finish first and crack the safe.

Worksheet where answers to questions are used to obtain a 3-digit code (which I set as the combination to a lockable money box containing a prize).