A complete lesson on using sin, cos and tan to find an unknown side of a right-angled triangle. Designed to come after pupils have been introduced to the trig ratios, and used them to find angles in right-angled triangles. Please see my other resources for complete lessons on these topics. Activities included: Starter: A quick reminder and some questions about using formulae triangles (e.g. the speed, distance, time triangle). This is to help pupils to transfer the same idea to the SOHCAHTOA formulae triangles. Main: A few examples and questions for pupils to try, on finding a side given one side and an angle. Initially, this is done without reference to SOHCAHTOA or formulae triangles, so that pupils need to think about whether to multiply or divide. More examples, but this time using formulae triangles. A worksheet with a progression in difficulty, building up to some challenging questions on finding perimeters of right-angled triangles, given one side and an angle. A tough extension, where pupils try to find lengths for the sides of a triangle with a given angle, so that it is has a perimeter of 20cm. Plenary: A prompt to get pupils thinking about how they are going to remember the rules and methods for this topic. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated! Error on previous version now fixed. If you have bought this already and want the amended version, please message me and I will email the file directly.

A complete lesson with examples and activities on calculating gradients of lines and drawing lines with a required gradient. Printable worksheets and answers included. Could also be used before teaching the gradient and intercept method for plotting a straight line given its equation. Please review it if you buy as any feedback is appreciated!

A complete lesson on drawing nets and visualising how they fold. The content has some overlap with a resource I have freely shared on the TES website for years, but has now been augmented and significantly upgraded,as well as being presented in a full, three-part lesson format. Activities included: Starter: A matching activity, where pupils match up names of solids, 3D sketches and nets. Main: A link to an online gogebra file (no software required) that allows you to fold and unfold various nets, to help pupils visualise. A question with an accurate, visual worked answer, where pupils make an accurate drawing of a cuboid’s net. Rather than answer lots of similar questions, pupils are then asked to compare answers with others and discuss whether their answers are different and/or correct. The same process with a triangular prism. A brief look at other prisms and a tetrahedron (the latter has the potential to be used to revise constructions if pupils have done them before, or could be briefly discussed as a future task, or left out) Then two activities with a different focus - the first looking at whether some given sketches are valid nets of cubes, the second about visualising which vertices of a net of a cube would meet when folded. Plenary: A brief look at some more elaborate nets, a link to a silly but fun net related video and a link to a second video, which describes a potential follow up or homework task. Printable worksheets and answers included where appropriate. Please review if you buy as any feedback is appreciated!

A complete lesson on introducing 3-figure bearings. Activities included: Starter: A quick set of questions to remind pupils of supplementary angles. Main: A quick puzzle to get pupils thinking about compass points. Slides to introduce compass points, the compass and 3-figure bearings. Examples and questions for pupils to try on finding bearings fro m diagrams. A set of worksheets with a progression in difficulty, from correctly measuring bearings and scale drawings to using angle rules to find bearings. Includes some challenging questions involving three points, that should promote discussion about different approaches to obtaining an answer. Plenary: A prompt to discuss how the bearings of A from B and B from A are connected. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for introducing mean, median and mode for a list of data. Activities included: Mini whiteboard questions to check pupil understanding of the basic methods. A worksheet of straight forward questions. Mini whiteboard questions with a progression in difficulty, to build up the skills required to do some problem solving... A worksheet of more challenging questions, where pupils are given some of the averages of a set of data, and they have to work out what the raw data is. Some final questions to stimulate discussion about the relative merits of each average. Printable worksheets and answers included. Please review it if you buy as any feedback is appreciated!

A complete lesson (or maybe two) on finding an original amount, given a sale price or the value of something after it has been increased. Looks at both calculator and non-calculator methods. Activities included: Starter: A set of four puzzles where pupils work their way back to 100%, given another percentage. Main: Examples, quick questions for pupils to try and a worksheet on calculator methods for reversing a percentage problem. Examples, quick questions for pupils to try and a worksheet on non- calculator methods for reversing a percentage problem. Both worksheets have been scaffolded to help pupils with this tricky topic. A challenging extension task where pupils form and solve equations involving connected amounts. Plenary: A final question to address the classic misconception for this topic. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to add and subtract fractions with different denominators. Does include some examples and questions involving simplifying at the end, but doesn’t include adding or subtracting mixed numbers. Activities included: Starter: Some quick questions to test if pupils can find equivalent fractions and identify the lowest common multiple of two numbers. Main: Some examples with diagrams to help pupils understand the need for common denominators when adding. A recap/help sheet of equivalent fractions for pupils to reference while they try some simple additions and subtractions. At this stage, they aren’t expected to find LCMs ‘properly’, just to find them on the help sheet. Some example question pairs on adding or subtracting by first identifying the lowest common denominator, starting with the scenario that the LCM is the product of the denominators, then the scenario that the LCM is one of the denominators, and finally the scenario that the LCM is something else (eg denominators of 4 and 6). A set of straightforward questions with a progression in difficulty. The hardest ones require students to simplify the answer. A challenging extension where pupils must find four digits to fit a given fraction sum. Plenary: A final example designed to challenge the misconception of adding numerators and denominators, 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 on sharing an amount in a ratio. Assumes pupils have already learned how to use ratio notation and can interpret ratios as fractions - see my other resources for lessons on these topics. Activities included: Starter: A set of questions to recap ratio notation, equivalent ratios, simplifying ratios and interpreting ratios as fractions. Main: A quick activity where pupils shade grids in a given ratio( eg shading a 3 x 4 grid in the ratio shaded:unshaded of 1:2). The intention is that they are repeatedly shading the ratio at this stage, rather than directly dividing the 12 squares in the ratio 1:2. By the last question, with an intentionally large grid, hopefully pupils are thinking of a more efficient way to do this… Examples and quick questions using a bar modelling approach to sharing an amount in a a given ratio. A set of questions on sharing in a ratio, with a progression in difficulty. Includes the trickier variations of this topic that sometimes appear on exams (eg Jo and Bob share some money in the ratio 1:2, Jo gets £30 more than Bob, how much did they share?) A nice puzzle where pupils move matchsticks(well, paper images of them) to divide a grid in different ratios. Plenary: A final spot-the-mistake question, again on the theme of the trickier variations of this topic that pupils often fail to spot. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on finding the nth term rule of a quadratic sequence. This primarily focuses on one method (see cover slide), although I’ve thrown in a different method as an extension. I always cover linear sequences in a similar way and incorporate a recap on this within the lesson. Starter: To prepare for the main part of the lesson, pupils try to solve a system of three equations with three unknowns. Main: A recap on finding the nth term rule of a linear sequence, to prepare pupils for a similar method with quadratic sequences. Examples on the core method, followed by a worksheet with a progression in difficulty for pupils to practice. I’ve included two versions of the worksheet - a simple list of questions that could be projected, or a much more structured worksheet that could be printed. Worked solutions are included. A worked example of an alternative method, that could be given as a handout for pupils who finish early to try on the questions they’ve already done. Plenary: A proof of why the method works. I’d much rather show this at the start of the lesson, but in my experience this usually overloads students and puts them off if used too soon! Please review if you buy as any feedback is appreciated!

A complete lesson on compound interest calculations. Activities included: Starter: A set of questions to refresh pupils on making percentage increases. Main: Examples and quick questions on interest. Examples and a worksheet on compound interest by adding on the interest each year. Examples and a worksheet on compound interest using the direct multiplier method. A challenging set of extension questions. Plenary: A prompt for pupils to think about the graph of compounded savings with time. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on using knowledge of gradient and y-intercept to plot a line, given its equation. 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 areas of composite shapes involving circles and/or sectors. Activities included: Starter: A matching activity using logic more than area rules. Main: Two sets of challenging questions. Opportunity for pupils to be creative/artistic and design their own puzzles. Plenary: Discussion of solutions, or pupils could attempt each other’s puzzles. Printable worksheets and answers included. Please review it 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!

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!

The first of two complete lessons on distance-time graphs that assumes pupils have done speed calculations before. Examples and activities on calculating speed from a distance-graph and a matching activity adapted from the Mathematics Assessment Project. Printable worksheets and answers included. Please review it if you download as any feedback is appreciated!

A powerpoint including examples, worksheets and solutions on probability of one or more events using lists, tables and tree diagrams. Also covers expectation, experimental probability and misconceptions relating to probability. Also includes some classics probability games, puzzles and surprising facts. Worksheets at bottom of presentation for printing.

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.

A complete lesson for first teaching what mixed numbers and improper fractions are, and how to switch between the two forms. Activities included: Starter: Some quick questions to test if pupils can find remainders when dividing. Main: Some examples and a worksheet on identifying mixed numbers and improper fractions from a pictorial representation. Examples and quick questions for pupils to try, on how to convert a mixed number into an improper fraction. A set of straight forward questions for pupils to work on, with an extension task for those who finish. Examples and quick questions for pupils to try, on how to simplify an improper fraction. A set of straight forward questions for pupils to work on, with a challenging extension task for those who finish. Plenary: A final question looking at the options when simplifying improper fractions with common factors. Worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on using Pythagoras’ theorem for 3-dimensional scenarios. Activities included: Starter: Two questions involving a spider walking along the faces of a cuboid. For the first question, pupils draw or use a pre-drawn net and measure to estimate the distance travelled by the spider. This leads into a discussion about finding exact distances using Pythagoras’ theorem, followed by a second question for pupils to apply this method to. Main: Highly visual example and quick questions for pupils to try on finding the space diagonal of a cuboid. A set of questions with a progression in difficulty, starting with finding space diagonals of cuboids, then looking at problems involving midpoints and different 3D solids. An extension where pupils try to find integer dimensions for a cuboid with a given space diagonal length. Plenary: Final question to discuss and check for understanding. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on solving equations of the form sinx = a, asinx = b and asinx+b=0 (or with cos or tan) in the range 0 to 360 degrees. Designed to come after pupils have spent time looking at the functions of sine, cosine and tangent, so that they are familiar with the symmetry properties of these functions. See my other resources for lessons on these precursors. I made this to use with my further maths gcse group, but could be used with A-level classes too. Activities included: Starter: A set of four questions, effectively equations but presented as visual graph problems, to remind pupils of the symmetry properties of sine and cosine and the fact that tangent repeats every 180 degrees. Main: An example to transition from a visual problem to a formal, worded problem, and a reminder of the symmetry properties of sine and cosine. Five examples of solving trigonometric equations of increasing difficulty, including graphical representations to help pupils understand. A set of similar questions for pupils to do independently. I’ve made this into a worksheet where the graphs are included, to scaffold the work. Includes an extension task where pupils create equations with a required number of solutions. Plenary: A “spot the mistake” that addresses a few common misconceptions. Printable worksheets and answers provided. Please review f you buy as any feedback is appreciated!