Everything needed for tree diagrams at Higher Tier - a presentation on probability rules for addition and subtraction, a PowerPoint on drawing tree diagrams, and a worksheet for the learners to answer questions on tree diagrams. All photographs (c)2015 Colin Billett

Big bundle of worksheets/activities to revise or practise trigonometry of right angled triangles, with Pythagoras and sin, cos and tan for finding lengths of sides or angles. In Word or PDF. Great for homework or assessment of learning in the classroom. Now on KS3 but always needs revising in KS4, especially on the new GCSE 9-1 specifications. • apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right- angled triangles

KS3 Presentation warm up, two more sequences sets on PowerPoint, and two worksheets, the second quite challenging. Plus a ‘sticks and dots’ pattern set with lots of pictures. • generate terms of a sequence from either a term-to-term or a position-to-term rule • recognise arithmetic sequences and find the nth term • recognise geometric sequences and appreciate other sequences that arise. And all good for lower tier at GCSE.

Maths Key Stage 2. Lots of questions in the style of SATs from right across the range of papers. Great for revision, practice, or checking learning at later stages, for example KS3 or Foundation GCSE. Using mathematics to solve problems using all four rules. In Word and PDF for ease of editing or printing.

PowerPoint presentations on using the grid method, plus a poster and an investigation into multiplying diagonals. Worksheets to practice multiplying and factorising two brackets, and lots of questions on solving quadratic equations, including GCSE examples. Plus questions on matching quadratic graphs to expressions. All answers provided either in Word and/or PowerPoint. Everything you need for a couple of lessons at least.

KS4 GCSE Foundation and Higher Tiers. Three PowerPoint presentations including multiple choice quiz. Plus two worksheets of GCSE exam-style questions. • generate terms of a sequence from either a term-to-term or a position-to-term rule • recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer, and r is a rational number >0) • deduce expressions to calculate the nth term of linear sequences

Everything for introducing negative numbers in KS2, especially for Year 4 but great for revision in Year 5 or above. PowerPoint to move on from counting numbers, adding zero and negative numbers. Lots of opportunity for open questions and direct questioning. PowerPoint includes ten questions for the learners to do as a group or individually. Powerpoint also given as a PDF so that it will open on any system, and look the same. Worksheet covers the specs - counting through zero, done on number lines presented in a variety of ways. Plus games to give the learners colourful, active and kinaesthetic learning. Year 4 programme of study Number – number and place value Statutory requirements Pupils should be taught to count backwards through zero to include negative numbers Year 5 programme of study Number – number and place value Statutory requirements Pupils should be taught to: interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Images © Colin Billett

Mathematics Key Stage 2 Year 6: use negative numbers in context, and calculate intervals across zero solve number and practical problems that involve all of the above. Everything you need to introduce the next stage, and give learners plenty of practice.

Ordering of fractions for Year 3 of KS2. Revision of work in Year 2, then a PowerPoint presentation with identical worksheet. Use the PowerPoint as answers, or for class work on an interactive board. Great for discussion of equivalences, percentages or decimal equivalences. Entirely suitable as revision in later years. Specs: 'compare and order unit fractions, and fractions with the same denominators' Notes and guidance (non-statutory) They begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval. Full lesson of activity.

Dividing a fraction by a fraction. Ever wonder why we 'flip and multiply'? Not many people seem to do so, and learners are too happy to follow the rules, and forget the rules. 'When do I do this and when do I do that?' Here is a colourful diagrammatic presentation that recaps on dividing by unit fractions, then goes on to illustrate why we multiply by the denominator, and divide by the numerator, ie 'flip and multiply'. Give your learners the 'why' and they might remember the 'when'! Questions at every point for class discussion and teacher explanation, and a set of questions at the end for learners to try, with full answers. Plus differentiated worksheet, two exercises, one just proper fractions, one mixed numbers.

Presentation with 52 slides and around fifty questions covering basic concepts of percentages, including fractional and decimal equivalents. Simple questions to develop fluency, misconceptions to correct, simple applications and written problems. Each slide followed by solution slide. Plus a clone of the questions in Word and as a PDF for further practise. So around 100 questions in total, with plenty of repetition and plenty of new questions slotted in. Plus answers for printing or otherwise. Originally produced for Functional Skills Levels 1 & 2 but entirely suitable for other groups. Easily editable into four different lessons for revisiting at a later date.

Ratio can be difficult for the learners, and especially so since it has become a more significant element of GCSE. Using tables to help structure the questions is a new and extremely useful approach, one that many learners have found beneficial. The questions are all adapted and reconfigured from past papers, and although originally set at GCSE they are equally useful for KS3. The files consist of a presentation to demonstrate the method, plus worksheets at both Foundation and Higher Tier. All files are also included as PDFs so will appear the same on any operating system. If some of the questions look relatively easy, there can be a huge difference between papers - those aimed at the top grades and those questions aimed at the middle.

A very full set of resources to use and apply Pythagoras' Theorem in a wide range of situations, from simple triangles to finding the length of a line on a co-ordinate grid. PowerPoint presentation with early slides reminding learners of the principles and knowledge. Later questions apply the knowledge and lead on to generalisations. Plus extra worksheets on finding perimeter of polygons and finding the area of a circle drawn on a co-ordinate grid. Surds and use of pi encouraged in line with 2015 UK curriculum. Plus a multiple choice starter to check learning before they begin, with six questions, and another multiple choice activity to use for homework, or as a simple starter in a following lesson.

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).