Common Core Standards Define trigonometric ratios and solve problems involving right triangles 6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Everything you need for a full lesson or two to develop trigonometry from the tangent ratio to sine and cosine. Presentations, worksheets, activities and solutions, covering all aspects of the Common Core Standards. Please leave comments, suggestions or corrections.

GCSE Maths Higher Speed Distance and Time questions in PowerPoint. Some a bit easy, to keep the learners going, and some introducing other concepts, like bounds, gradients, and areas under a curve. A new design for use in classroom discussions or on Zoom - questions on the left of the screen with a blank space on the right for filling in the answers - great for letting the learners try their answers to the tutor or the whole class. Two versions - one with solutions after each slide, and one with solutions at the end.

Two PowerPoint lessons on straight line graphs, covering all aspects of GCSE Foundation, then Higher Tier mathematics: 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 identify and interpret gradients and intercepts of linear functions graphically and algebraically Clear presentations with lots of opportunities for learner engagement, and great for use on Zoom or other distance learning opportunities. Can be used simultaneously with learners in a classroom and at home.

Fractions four rules KS2 -Year 3 'Add and subtract fractions with the same denominator within one whole.' 'Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.' Presentation and lots of activity, and plenty of resources for you to adapt and make your own. Worksheets, fractions cards, all differentiated. Word and PDF - whatever works for you.

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’

Multiple resources to look at, and learn, equivalent fractions, from KS2 to GCSE Foundation. Colourful presentations including ‘fraction chains’, lots of authentic types of questions, and lots of activities for colouring in fractions. Everything for a wide range of abilities, right up to KS4. Year 3 - recognise and show, using diagrams, equivalent fractions with small denominators. Year 4 - recognise and show, using diagrams, families of common equivalent fractions. Year 5 - compare and order fractions whose denominators are all multiples of the same number; identify, name and write equivalent fractions of a given fraction, represented visually,. Year 6 - use common factors to simplify fractions; use common multiples to express fractions in the same denomination; compare and order fractions.

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!

These have been enormously popular. I teach a number of people who are far more artistically minded than mathematical, so I produced some visual displays to illustrate equivalences. Run the PowerPoint, or print off some slides for display. I've also added a few posters by way of example of how you might use the individual slides. For classroom activity I’ve included five pages of shapes to colour for fractions etc to keep or display. Everything included in editable format, so use as many slides as appropriate for your year group, or change the shapes pages as required. All images ©2015 Colin Billett

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

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.

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.

Two ways of approaching recognition and identifying properties of 3D shapes at KS1. Either match the shape from the description, or name and identify the properties of the shape. I've split them into the Year 1 and Year 2, and done one with the solids required in both years. Some can be simply given out, and some could be printed on card and cut out for a matching activity. All in Word or PDF. Plus a word search in two versions. 'Pupils handle and name a wide variety of common (…) 3-D shapes including: (…) cuboids, prisms and cones, and identify the properties of each shape (for example, number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces.' Two powerpoints are available on the free down downloads to accompany these worksheets. https://www.tes.com/teaching-resource/maths-key-stage-1-3d-shapes-two-ppt-presentations-recognise-properties-and-recognise-shapes-11201174 All images (c) Colin Billett 2015