I taught in a range of schools for many years before moving into FE, where I found creative and imaginative approaches just as rewarding with adults. Most of my resources are concerned with giving control to the learner, through a range of methods. Some are great for just giving them experience of examination questions, and the chance to discuss these with other learners. I now concentrate on spreading the range of creations from UK KS1 to KS4, and across the Common Standards.
I taught in a range of schools for many years before moving into FE, where I found creative and imaginative approaches just as rewarding with adults. Most of my resources are concerned with giving control to the learner, through a range of methods. Some are great for just giving them experience of examination questions, and the chance to discuss these with other learners. I now concentrate on spreading the range of creations from UK KS1 to KS4, and across the Common Standards.
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.
Maths GCSE Foundation & Higher. Surds & irrational numbers, three activities or investigations in shape and measure.
Finding the length of a the side of a square that leads to an irrational number.
Comparing ratios of paper sizes to derive the ratio of length to width for A4 paper.
Finding the area and perimeter of the pieces of a tangram.
All good stuff that leads the learner through different process to derive lengths and areas using surds, and to add and simplify with surds.
Needs knowledge of Pythagoras, which is KS3. So great for revising Pythagoras with surds.
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.
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.
Lots of resources covering fractions in KS2, so great for revision in KS3 and Foundation GCSE.
Equivalent fractions, ordering fractions, and four rules of fractions. Addition and subtraction moves from same denominator, through one denominator a multiple of the other, to different denominators. Multiplication and division develops in the same way - simple stages. I've lots of stuff free on fractions, so check the free stuff first if you like. Save 77%!
Four games to play to reinforce solving simple equations and substitution, so quite suitable for year 6 and key stages 3 or 4.
Throw the dice, and match the equation to the score. Claim that tile, and the next person throws.
All solutions are in the range of 1 - 6, so easy arithmetic.
But game can be adapted any way you like - solve all the equations first, then play the dice game to make three in a row, or four in a row.
The second set is throw the dice and substitute the scores into the expressions, then find the numbers in the grid.
Give feedback please, on suggested improvements.
Simple set of slides to demonstrate finding bearings when given some information, and locating things when given two bearings. Follows on from my introduction resource.
For worksheets covering foundation, higher, measuring, trigonometry etc, plus a plenary/revision quiz, go to my premium resource. This contains a whole selection of questions adapted from exam questions, and covers the whole of this aspect of the syllabus.
https://www.tes.com/teaching-resource/maths-gcse-bearings-and-scale-drawings-two-differentiated-worksheets-plus-plenary-quiz-in-pp-11505938
GCSE Maths, bearings. A set of PowerPoint slides to introduce the topic, teaching enough for learners to try some themselves.
All images (c) Colin Billett 2017
A follow on from this, introducing the geometric aspect, is also free.
And a couple of worksheets plus a plenary/revision quid are available for two pounds only!
https://www.tes.com/teaching-resource/maths-gcse-bearings-two-differentiated-worksheets-plus-plenary-quiz-in-pp-all-with-answers-11505938
Step by step look at multiplication of mixed numbers, building on multiplication of proper fractions and addition, to create a simple algorithm. Clear presentation plus two sided worksheet progressing from multiplication of common fractions to multiplication of mixed numbers. Both as PDF for ease of showing on muliple devices.
See my other stuff for presentations on PowerPoint of division, and addition and subtraction.
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.
Clear presentation with lots of opportunities to engage the learners, and questions for the class to try.
40+ slides that take the learners from simple problems to seeing why we do what we do when we divide fraction by fractions.
Dividing by unit fractions in this presentation. Dividing by non-unit fractions, and mixed numbers, to come later.
Great for first introduction in KS3, or revision in KS4.
Simple presentation for Year 6 division of fractions by whole number - clear presentation using the one I did for multiplication. Plus a worksheet that should consolidate the skills, and somewhat differentiated.
Specs: 'divide proper fractions by whole numbers for example, [1/3 ÷ 2 = 1/6]'
National Curriculum Maths year 6, but also essential for revision in KS3, and great for lower tiers of Foundation GCSE. 'Multiply simple pairs of proper fractions, writing the answer in its simplest form'.
Guidelines say: 'Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as numbers, and as equal parts of objects, for example as parts of a rectangle.'
Clear step-by-step presentation with questions and answers built in for class discussion and question/answer session. Everything for at least one lesson and some consolidation.
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.
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!
Fifty slides in a PowerPoint for class discussion of equivalent fractions leading to simple addition of fractions. Nothing complicated - made for class activity and discussion. Get the learners to answer on mini-whiteboards or simply answering each question.
Fully illustrated, with answer pictures for each question, as well as repeat slides for the learners to come up with answers. And designed for working in the head of the learner rather than pencil and paper. (Too much time is often spent with pencils and not enough talking.)
Two simple multiple-choice quizzes covering addition and subtraction. The first is simple halves, quarters and eighths; the second covers halves, third, sixths, fifths and tenths. Aimed at year 5, but great for revision in year 6 before they search for common denominators. And good for KS3 and KS4 revision.
Illustrated throughout, with answer slides after each question.
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’
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.
