Key stage 2 - getting more familiar with fractions: 'compare and order unit fractions, and fractions with the same denominators' Simple stuff for young learners, or revision at later stages.

Colourful presentation with lots of images to show the relationship between mixed numbers and improper fractions, plus two worksheets covering the specs for year 5. A full lesson of stuff. Specification, fractions year 5: 'recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5]' Great for revision in year 6 and above.

KS2 Maths - Year 3 Equivalent Fractions: Year 3 equivalent fractions. recognise and show, using diagrams, equivalent fractions with small denominators Colourful powerpoint for sharing with a whole class, or for printing slides for cutting out and matching the shapes. You can buy them but they cost £25 a set of magnetic ones! Lots of questions to match shapes to fraction concepts, and activities for the learners to do, including writing fraction chains and colouring in a fractions wall. Great for revision in later years.

A full presentation, developing surds to show how to expand two brackets with surds, rationalising the denominator, and using the conjugate (difference of squares) to simplify expressions in number and algebra. Plus two differentiated worksheets that give practice in application and reasoning.

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 National Curriculum Multiplying fractions Year 5 ’multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams’ Clear, concise and colourful presentation giving a variety of real scenarios with appropriate images and photographs to give the learners opportunities the ability to see this topic from a variety of positions. And hopefully the learners will develop alternative ways to find solutions. A PDF version is included to ensure it looks good on any screen with any computer system. Plus a worksheet of questions, and another file with the answers. Meets the criteria for Year 5, but invaluable for revision in year 6 and in Key Stages 3 and 4.

Fractions addition and subtraction with different denominators. KS2 Year 6, but great for revision in KS3, and essential for foundation GCSE, and not a few higher candidates would benefit too. Warm up worksheet that asks the learners to find common multiples and common factors, through word questions. Colourful presentation covering the definitions of a fraction, and why the numerator has to be the same. One example, and then a small selection for the learners to find the lowest common denominator. Finally a worksheet for the learners to try out, or revise, these new skills. Does not include addition of mixed numbers - all simple results less than one. All worksheets in Word and PDF, and all answers included! The presentation has been updated to include an older version of PowerPoint, a revised v2 which might fit better, and a PDF version which will work on any system. Year 6 specs say: ‘use common multiples to express fractions in the same denomination add and subtract fractions with different denominators’

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!

Ten multiple choice quizzes in MS Word covering functional mathematics – algebra and formulas, fractions, decimals, percentages, charts, graphs and tables, area and volume, measure, data handling, ratio, proportion, scale, probability, average and range. Designed for use with Level 2 16+ learners but suitable for lower levels at any age, or bright youngsters! All in Word for self-editing. Plus amplification and tracking sheets. These have been very popular for a long time. All images ©2015 Colin Billett

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

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.

GCSE Mathematics Higher Tier new for 2017 exams. 'recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point' Clear introduction to circle equations on a cartesian grid using Pythagoras' theorem. Lots of opportunity for learners to draw their own using the formula, and extending to equation of radius, finding a perpendicular line, and hence finding the equation of the tangent.

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.

Practical and real-life examples of ratios in context for exploring the mathematics, including equal opportunities issues. Plus worksheets at both foundation and higher tier GCSE to give opportunity to practise skills.

Full set of resources to cover types of number for mathematics national curriculum in Year 5. Great for preparation for SATs in Year 6, or revision at KS3. Four clear PowerPoints with lots of questions and exercises, all with answers. Specifications: ‘Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.’ I’ve tried the files myself on a different computer, and had to adjust the size of text on four or five slides, but very easy to do. And because not all systems work the same I’ve included a PDF of each of the presentations - even easier to show and will always be as intended.

Short presentation to define and demonstrate perimeter, with pages of activities, worksheets, and a full assessment based on previous SATs KS2. Colourful, and can be extended in many ways, with centicubes for example. KS2 – Year 4 - Perimeter Statutory requirements Pupils should be taught to: • measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres Notes and guidance (non-statutory) Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit.

A recap of surds and simplifying expressions with surds, then a full presentation of multiplying brackets and surds, including the conjugate of a binomial. simplify and manipulate algebraic expressions (including those involving surds) by: collecting like terms multiplying a single term over a bracket taking out common factors expanding products of two binomials Lots of points to stop for the learner to try three of four examples, and each questions slide followed by the answers slide. Also suitable for A’level revision! And plus a PDF version should you have problems with the PowerPoint.

Formulas begin in KS2 so by KS3 learners should be able to talk about what one is, and for, and to substitute into more sophisticated formulas. A clear PowerPoint presentation that delivers a set of questions for the learners to answer as part of the lesson, and each with a clear answer. Ranges from very easy to a bit more complex. Plus forty questions of increasing difficulty, arranged in a variety of views - one page, or two pages for more space for working, or two pages for differentiation. Plus answers!