# four winds maths

maths resources for the more able pupils in the 8 - 14 age-group

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maths resources for the more able pupils in the 8 - 14 age-group

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maths resources for the more able pupils in the 8 - 14 age-group

At one stage in my teaching career I was responsible for setting the maths paper for entry to the school at 11+. At another stage I was responsible for preparing year 6 pupils for the range of maths papers which they needed to pass for entry to senior schools at 11+. Although the actual maths papers which these pupils took did vary to some extent, on the whole they tended to follow a fairly standard format. In the run-up to the exam season I would give pupils a weekly practice paper; this seemed sufficient for them to develop the necessary exam technique. In case they might be useful to anyone else, I have assembled here some of the practice papers I created. There are 8 papers altogether : papers A1, A2, B1, B2, C1 and C2 (the letters denote increasing difficulty) are fairly standard fare; papers M1 and M2 are multiple-choice papers (a few schools set papers in this format). For the first six papers, the mark available for each question is clearly shown on the paper, with the marks available for the whole paper totalling exactly 100; the multiple-choice papers have a maximum possible mark of 50 (1 mark for each of the 50 questions). Each of the papers is accompanied by a complete set of answers.
nb These papers could also be used as end-of-term or end-of-year maths papers for Yr6 or Yr7 pupils.

There are various classroom maths activities, including maths games, which are purely recreational – and no doubt they have their place. But there are maths games which demand a real involvement on the part of the players and which call for both reasoning and imagination(surely two key features of any worthwhile mathematical activity). Some of these are games for two players, where the aim is to win and where competitive excitement can run high; others are solo games, where the aim is to achieve a particular objective and where the satisfaction is a more private one. We have tried numerous games in the classroom, with pupils of different ages and abilities, and have selected eight of our favourites for the collection offered here.
The booklet provides clear instructions for each game, together with the appropriate grid for you to photocopy and laminate. None of the games requires complicated materials and all of them are easy to explain and to put into practice.

This is a set of ten simple posters, designed to be printed on A4 or A3 paper, for classroom display. Topics include : prime numbers, square numbers, powers of 2, Pascal’s triangles, factorials, big number names, byte names, times tables etc. Some teachers have downloaded these and printed them up smaller for sticking into pupils’ maths books.

This Long Multiplication pack contains two different groups of resources, all of which have been used extensively in the classroom :
The Farming Times resources folder includes a full account of one colourful and cheerful approach to teaching grid multiplication. It also includes worked examples, blank grids for classroom use and a useful ‘Farming Times’ spreadsheet (presented here in two version : a Numbers version for Mac users and an Excel version for PC users).
The other folder contains a note on lattice multiplication, including a clear explanation of the well-known and ingenious Gelosia method and, uniquely, an explanation of our own Diamond Grid method (a lattice method for 2-digit by 2-digit multiplication which pupils have found attractively simple). Also included here are the necessary resources for introducing the Diamond Grid method in the classroom, namely blank grids for pupil use, a set of exercises (with answers) and a useful ‘Diamond Grid’ spreadsheet (presented, as before, in two versions).

These investigations come from a variety of sources; some you might have seen before, whilst others are completely original but – they have all been tried and tested in the classroom and found to be practicable, worthwhile and engaging. They’re presented here in a way which makes them easy to grasp and straightforward to carry out in the classroom. Each investigation is clearly outlined, with the aims, practical resources needed, instructions for pupils and expected results all described. Extension activities are suggested where appropriate and photocopiable resource masters are provided where these would be helpful. None of the investigations requires materials beyond the usual classroom ones.
The 18 different investigations are listed with a suggested year-group for each one. However, these are only suggestions, as any of the investigations can be used with a variety of year-groups; for example, some of the earlier ones can be adapted to provide interesting investigations for older pupils.
Each of these investigations is a complete lesson and every one of them has a mathematical point or theme of value; all of them have been tried and tested in the classroom.
‘Maths Investigations’ is provided as a zip folder carrying two zip files, one containing the investigations and the other containing the photocopiable resource masters.
contents 18 investigations : 2 for KS1, 3 for year 3, 3 for year 4, 4 for year 5 and 6 for year 6

Loop Cards are back in fashion! The basic principle (an ingenious idea but by no means a new one) is to devise of a set of mental arithmetic questions and answers which can form an endless loop. These questions and answers are then printed onto cards which can be distributed among the pupils in a class. The loop begins when one pupil reads out the question printed on his card, after which somewhere in the class another pupil recognises that he has the answer on his card. This pupil may now read out the question on his card, which of course another pupil must recognise as the one on his card. Now this pupil takes the loop forward . . . Eventually someone asks a question which is answered by the very first pupil – and the loop is complete! Timing the whole procedure from start to finish adds to the drama. Without doubt, a good set of loop cards in the hands of a well-motivated class can produce a highly-charged and exciting start to any maths lesson. Sadly, the traditional format for these cards was not itself particularly colourful or appealing and so – we’ve reinvented loop cards to make them more attractive and engaging.
The zip file which you can download here contains pdf masters for 16 different sets of loop cards, together with instructions for use etc. As a guide, we’ve noted which loop cards have typically been used with which year-groups, although you may well choose to use them differently.

A collection of cards (ready for printing 2 to a page onto A4 card) with relatively straightforward questions covering a range of number and spatial skills. Useful for early finishers, homeworks (if printed on paper) etc. Originally designed for Year 4 pupils but not labelled as such and so may by used for any group at your discretion. Also : a complete set of answers, ready to be printed onto A4 paper and stapled to form an A5 answer booklet.

nb this download is a sample only . . . the full set is available from my website.
The mini-problems take only a few moments to read – but each one of them presents a small challenge to the solver, an invitation to take in a straightforward set of facts and then to find a way of getting to the desired answer, using only existing skills. The key thing for pupils to grasp is that they need to be creative, to use imagination and experiment, in order to find a way of getting to the answer. None of the problems requires maths skills or knowledge beyond the Key Stage 2 level. Of course, there are skills (in algebra, for example) which can be taught and which would make these problems easier but the aim here is to encourage pupils to make the best use of the skills they already have. The attitude that, when faced with new or difficult problems, the first line of attack should be to use one’s own imagination is an attitude to be encouraged in pupils; this way pupils gain in both confidence and enjoyment.
The problems cover a range of topic areas : number problems (inevitably the largest category), geometric & spatial problems, as well as problems on statistics, probability, logic, sets etc. The difficulty level of the problems is somewhat below the difficulty level of those in eg our ‘no problem’ books.
The printed format is perhaps unusual in that each problem is given within an A6 rectangle, so that there are four mini-problems on each A4 page; cut up into the four separate items (ready to pritt-stick into maths exercise books), these mini-problems make excellent shorter exercises in problem-solving, ideal for individual early finishers or to give to a whole class for class or home working.
By contrast, the answers are not short in format : whilst repeatedly making the point that there is no one correct way to solve any of the problems, suggested approaches are offered for the benefit of those who have been unable to get started on a particular problem or for those who might be interested in comparing an alternative approach with the one they have already found.

This is a book of original, colourful and engaging maths problems, designed to interest any young mathematician. The problems form Part 1 of the book. Part 2 outlines some useful strategies to try when you’re completely stuck; many children have found this to be extremely helpful. Part 3 contains the answers to all questions, along with clear and helpful explanations (often outlining more than one approach).
The 50 problems are on separate pages, making things easy for teachers who wish to email them to pupils eg for homework / prep or for distance learning . . .
. . . and to help teachers or parents who wish to set the problems without giving immediate access to the answers, ‘no problem! book 1’ is supplied here as a whole book and also as separate ‘problem’ and ‘answer’ books.
I originally designed these problems to challenge and extend able pupils in the yr6 – yr8 age group. The landscape format was chosen so that the book could be displayed using desktop computer, laptop, ipad or smartboard.
To tackle the problems in this book, no maths knowledge or skills are required beyond those of a yr6 pupil; in particular, no knowledge of algebra is needed. What is essential, and what the book hopes to develop in pupils, is imagination and confidence – and a willingness to tackle the new and the unfamiliar.

These cards have been created to provide extra useful practice over a range of topics for Year 6 pupils. The zip file contains A4 masters, designed to be photocopied onto card and guillotined to produce separate A5 cards. The zip file also contains A4 masters for the 2-sided A4 answer sheet which contains answers to all the questions. The topic covered by each card is shown at the top of the card. Calculators may be used for some of the questions and these questions are indicated by a small calculator image in the top right-hand corner of the card. These cards have been extensively tried and tested in the classroom and will provide a useful addition to your range of resources for Year 6.

Many pupils find the whole topic of percentages difficult and anxiety-raising. The ‘build-up method’ provides a simple approach to working out percentages. The method is explained in simple terms, with examples to illustrate. A useful footnote reveals a little-known but useful fact about percentages . . .

*The ‘Maths Challenge Cards - Set B’ pdf files which you can download from this site give you the first 10 questions and answers from the complete set of 50. If you would like a copy of the complete set of questions and answers, please go to my website . . .
I originally designed these Challenge Cards for the more able pupils in Year 5. However, I have labelled them alphabetically to give teachers the option of using them with different year-groups. No extra skills are needed beyond those usually taught to year 5 pupils. The aim is to challenge and extend pupils by encouraging them to use their existing skills imaginatively and creatively as they tackle sometimes difficult, new or unfamiliar problems. The cards are of roughly the same difficulty (which means that they do not have to be worked through in any particular order).
The cards are designed to be printed up landscape on A4 card (two A5 Challenge Cards to a page) and the set comes complete with answers. The Challenge Cards have been extensively tried and tested in the classroom and many teachers have found them to be a valuable extra resource. I hope you and your pupils enjoy using them.
note : Although most teachers print straight to card, some have chosen to print on paper at either A5 or A6 size. Easily stuck into the pupil’s maths book, the problems produced this way can be useful for either classroom or home working. Alternatively, problems can be emailed to pupils for homework / prep or for distance learning.
In maths, as in other subjects, able pupils need (and deserve) to be challenged. These cards are designed to do just that; they have already proved popular ‘extender’ material with teachers in the UK and beyond.

*The ‘Maths Challenge Cards - Set D’ pdf files which you can download from this site give you the first 10 questions and answers from the complete set of 50. If you would like to have the complete set of questions and answers, please go to my website . . .
I originally designed these Challenge Cards for the more able pupils in Year 7. However, I have labelled them alphabetically to give teachers the option of using them with different year-groups. No extra skills are needed beyond those usually taught to year 7 pupils. The aim is to challenge and extend pupils by encouraging them to use their existing skills imaginatively and creatively as they tackle sometimes difficult, new or unfamiliar problems. The cards are of roughly the same difficulty (which means that they do not have to be worked through in any particular order).
The cards are designed to be printed up landscape on A4 card (two A5 Challenge Cards to a page) and the set comes complete with answers. The Challenge Cards have been extensively tried and tested in the classroom and many teachers have found them to be a valuable extra resource. I hope you and your pupils enjoy using them.
note : Although most teachers print straight to card, some have chosen to print on paper at either A5 or A6 size. Easily stuck into the pupil’s maths book, the problems produced this way can be useful for either classroom or home working. Alternatively, problems can be emailed to pupils for homework / prep or for distance learning.
In maths, as in other subjects, able pupils need (and deserve) to be challenged. These cards are designed to do just that; they have already proved popular ‘extender’ material with teachers in the UK and beyond.

*The ‘Maths Challenge Cards - Set C’ pdf files which you can download from this site give you the first 10 questions and answers from the complete set of 50. If you would like a copy of the complete set of questions and answers, please go to my website . . .
I originally designed these Challenge Cards for the more able pupils in Year 6. However, I have labelled them alphabetically to give teachers the option of using them with different year-groups. No extra skills are needed beyond those usually taught to year 6 pupils. The aim is to challenge and extend pupils by encouraging them to use their existing skills imaginatively and creatively as they tackle sometimes difficult, new or unfamiliar problems. The cards are of roughly the same difficulty (which means that they do not have to be worked through in any particular order).
The cards are designed to be printed up landscape on A4 card (two A5 Challenge Cards to a page) and the set comes complete with answers. The Challenge Cards have been extensively tried and tested in the classroom and many teachers have found them to be a valuable extra resource. I hope you and your pupils enjoy using them.
note : Although most teachers print straight to card, some have chosen to print on paper at either A5 or A6 size. Easily stuck into the pupil’s maths book, the problems produced this way can be useful for either classroom or home working. Alternatively, problems can be emailed to pupils for homework / prep or for distance learning.
In maths, as in other subjects, able pupils need (and deserve) to be challenged. These cards are designed to do just that; they have already proved popular ‘extender’ material with teachers in the UK and beyond.

*The ‘Maths Challenge Cards - Set A’ pdf files which you can download from this site give you the first 10 questions and answers from the complete set of 50. If you would like a copy of the complete set of questions and answers, please go to my website . . .
I originally designed these Challenge Cards for the more able pupils in Year 4. No extra skills are needed beyond those usually taught to this year-group. The aim is to challenge and extend pupils by encouraging them to use their existing skills imaginatively and creatively as they tackle sometimes difficult, new or unfamiliar problems. The cards are of roughly the same difficulty (which means that they do not have to be worked through in any particular order).
The cards are designed to be printed up landscape on A4 card (two A5 Challenge Cards to a page) and the set comes complete with answers. The Challenge Cards have been extensively tried and tested in the classroom and many teachers have found them to be a valuable extra resource. I hope you and your pupils enjoy using them.
note : Although most teachers print straight to card, some have chosen to print on paper at either A5 or A6 size. Easily stuck into the pupil’s maths book, the problems produced this way can be useful for either classroom or home working. Alternatively, problems can be emailed to pupils for homework / prep or for distance learning.
In maths, as in other subjects, able pupils need (and deserve) to be challenged. These cards are designed to do just that; they have already proved popular ‘extender’ material with teachers in the UK and beyond.