GCSE Mathematics - Foundation and Higher Tier. Finding the equation of a line through two points and perpendicular lines. A worksheet/activity that reminds learners of the algebraic form of a straight line, and goes on to finding the equation of a line joining two points and find the equations of perpendicular lines. Lots of GCSE style questions. Foundation Tier Plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points or through one point with a given gradient. Higher Tier Plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel and perpendicular lines; find the equation of the line through two given points or through one point with a given gradient.

Expanding Binomials and Factorising Quadratic Expressions Objectives: To be able to: • expand products of two binomials • factorise quadratic expressions of the form x2+ bx + c, including the difference of two squares All the research says that girls learn best by understanding, and that by far the best approach to expanding and factorising is by using the grid method. I’ve done this very successfully for years, and retention is greatly improved by giving as little input as possible, and giving the learners challenges to complete. Plus an investigation to give that stretch and challenge. A full set of resources for learning how to expand and factorise, with a PowerPoint that can be used for class discussion. Plus some extra exercises for homework or assessment in a subsequent lesson. And a reminder of multiplication and addition of positive and negative numbers for a quick warm-up. All answers included!

KS3/KS4 ‘Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons.’ A simple example of a triangle sum proof, an investigation into angle sums in both PowerPoint and Word, for classwork or individual work, and plenty of questions for learners to try. Plus a PowerPoint illustrating a variety of tessellation for learners to consider the geometry involved, and hence deduce necessary angle properties.

The motivation for this was the difficulty Foundation learners have with averages of grouped data, and no doubt many Higher learners too. I’ve spent years trying to demonstrate the interval in which the median lies, and watched learners who appeared to follow the method for mean of grouped data, only to watch them go to pieces on tests. So this time I went for kinaesthetic and colourful, my main aim always. The documents are in Word so you can cut my photo if you want. I’ve thrown in a couple of real questions, and there are plenty more about, but very easy to make up in this style. All images (c)2015 Colin Billett

An illustrated introduction to ratio and proportion from the objectives of GCSE. Includes a few typical GCSE questions, but suitable for all levels.

A straightforward presentation that provides images, formulas, and then tables to be completed with answers. Covers the subject matter of Functional Skills level two, but the questions on the exams may well be more complex. And useful at almost any stage in the curriculum, for recap, review, just a bit of practise.

PowerPoint quiz for revision/recap with ten quick questions and answers. Other topics covered: Number

GCSE Higher Tier says ‘apply systematic listing strategies, including use of the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways)’. A clear, colourful and carefully explained PowerPoint presentation building up the skills from simple matching problems to calculating combinations and permutations in a variety of realistic and original settings, with lots of opportunity for the learner to reflect, apply, and evaluate the problems. Also available in my shop are two differentiated worksheets of adapted exam questions from sample and real GCSE assessments. Plus a PDF version that will work on all operating systems.

Surds are new to the Foundation part of GCSE maths, so I've made a very clear step-by-step PowerPoint that introduces surds, explains irrational numbers, demonstrates how to simplify surds, and gives examples and practice in applying all four rules of arithmetic using surds. Plus rationalising the denominator and more. Throughout the presentation there are groups of questions on each aspect to apply the skills, all with answers. Learners are now expected to appreciate that a surd gives an exact answer rather than a decimal approximation, and an understanding is essential for the new topics in algebra and trigonometry that are now on Foundation. Plus, it could be a very solid introduction to Higher tier surds.

Bearings are on the new GCSE for both foundation and higher tier. I’ve produced worksheets to go with my PowerPoint introductions which you will find for free on TES. The first worksheet covers simple measuring and drawing of bearings, and applying simple geometry. The plenary quiz is great for rounding off the lesson, reviewing learning in a following lesson, or later revision. Two versions, one with immediate answers after each question, and one with answers following all the questions. Both PowerPoints also come as PDFs so will open on any system and look as they should. The second worksheet moves on to trigonometry, covering distances in triangles using Pythagoras, and finding bearings using simple trig ratios in right angled triangles. The second half of the worksheet covers the higher aspect of trig - sine rule and cosine rule to find bearings and distances. Answers also included for both worksheets. The free introductions are found at: https://www.tes.com/teaching-resource/maths-gcse-bearings-doing-the-simple-geometry-for-foundation-11494933 and: https://www.tes.com/teaching-resource/maths-gcse-bearings-introduction-how-to-read-and-write-bearings-colourful-presentation-11491326 All images © Colin Billett, 2017

Everything you need for one or two lessons at KS3 or KS4. A quiz to review formulas and another to introduce and discuss the use of formulas. A PowerPoint presentation with lots of examples for the learners to try in a group setting. Three clearly differentiated worksheets of mostly genuine GCSE questions to ensure learning. Worksheets and PowerPoints also in PDF format so they look the same on any system. All images ©2015 Colin Billett.

Two sets of questions, differentiated by paper, for learners to complete. Plus answers. Counting has always been on Foundation, so quite easy for learners. Sophisticated counting strategies are new to the GCSE higher tier. The specs say: apply systematic listing strategies, including use of the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways) Hence also suitable for revision at A Level Statistics. All questions follow the format of 2017 exams across the boards, and the SAMs and Mocks available.

Maths GCSE Ratio. Part (a) Dividing a given quantity into two parts Introduction suitable for Foundation and Higher Tier, acting as a reminder and revision of KS3 Ratio. Simply as is says - dividing into parts, with PowerPoint introduction and two sets of worksheets.

Finding the volume of cuboids, with a big selection of worksheets, from simple counting of cubes to working backwards from the volume to find other dimensions. Plus questions in the style of SATs and GCSE Foundation.

Developing area and perimeter to look at shapes with same areas but different perimeters, same perimeters but different areas, and equal area and perimeter. Engaging activities for the learners. Covers Year 5, but good for revision and practice at later stages.

Everything needed to introduce algebra in Key Stage 2 (Year 6) or to revise and build upon it in KS 3 or later. Formulas, sequences, missing numbers, number patterns and missing number problems. Presentations, worksheets, activities and assessments covering the whole of algebra in Year 6, and also suitable for older learners. Lots of opportunities for deep thinking, and for differentiation, and all suitable for editing if required. Most have answers. And many questions based on previous SATs. All written to new UK standards (2015). Year 6 Algebra Pupils should be taught to: • use simple formulae • generate and describe linear number sequences • express missing number problems algebraically • find pairs of numbers that satisfy an equation with two unknowns • enumerate possibilities of combinations of two variables. Notes and guidance (non-statutory) Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as: • missing numbers, lengths, coordinates and angles • formulae in mathematics and science • equivalent expressions (for example, a + b = b + a) • generalisations of number patterns • number puzzles (for example, what two numbers can add up to).

Surds and and an understanding of irrational numbers are new to GCSE Foundation, so I’ve produced a clear and simple PowerPoint for classroom use to introduce the topic. Other stuff available on working with surds etc. I’ve added a pdf version to solve the problem of different versions of PowerPoint and some images not working well on ppt.

Maths. Descriptors and specifications for UK Key Stage 4, although equally adequate for KS3. All lovingly put into word clouds using Wordle. I made B/W versions some time ago, but now I've been asked for colour, so here they are. Copyright on final images (c)Colin Billett 2015 And all credit to Wordle, as cited on the website: 'May I make money off of Wordle images? Yes. You may take a Wordle, put it on your book cover, your t-shirt, your campaign poster, what have you. You may get rich off it. If you want to give credit to wordle.net, feel free!' So again, all credit to wordle.net, and many thanks! Any problems, please let me know and I can change the formats.

A set of engaging activities to give the learners the concept of area. National Curriculum Year 4 mathematics. Area by counting squares, area of rectangles as arrays, and addition and subtraction of rectangles to find the area of a rectilinear shape. Statutory requirements Pupils should be taught to: • find the area of rectilinear shapes by counting squares Notes and guidance (non-statutory) They relate area to arrays and multiplication. But also great for revision in Year 5 and above. I've done this sort of thing with Foundation GCSE!