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We have produced our Challenge Cards specifically for the more able pupils in the 8 – 14 age range. There are four sets, Set A, Set B, Set C and Set D. To tackle these problems, no extra skills are needed beyond those usually taught to pupils in year-groups 4, 5, 6 and 7. The starting-point for any particular pupil or group of pupils will depend upon a number of factors, most importantly how much problem-solving has already been done and for this reason (and to give teachers maximum flexibility in their use), the Challenge Card sets have been labelled A to D, rather than by year-groups. Ideally, pupils should start with whichever set they find moderately challenging and progress from there. 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 in each set are of roughly the same difficulty (which means that they do not have to be tackled in any particular order).

The cards are designed to be printed up landscape on A4 card (giving two A5 cards per page) and each 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. We hope you and your pupils enjoy using them.

note : Although most teachers print straight to card, some have chosen to print on paper. With the problems at either A5 or reduced to A6 in size, they are easily stuck into the pupil's maths book, making them 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 Challenge Cards

# no problem! books 1 & 2

These are two books of original, colourful and engaging maths problems, designed to interest and challenge any young mathematician. In both books the aim is to help pupils develop imagination and confidence in problem-solving, together with a willingness to tackle the new and the unfamiliar.

The two books are arranged in similar fashion, with the problems and then the answers forming the main sections. The problems are presented straightforwardly, so that the solver knows what he / she is supposed to find; no hints are offered at this stage on how to tackle a particular problem, the aim being to encourage experiment and originality. The answers section contains answers to all questions, along with clear and helpful explanations of how a particular answer has been reached; often more than one approach is outlined and sometimes different approaches are compared; the aim throughout is to encourage individual initiative. 'no problem! book 1' also contains a section outlining some useful strategies to try when the would-be solver is completely stuck; 'no problem! book 2' has an FAQs section suggesting, with examples, answers to questions often asked about problem-solving, particularly in relation to this age-group.

In both books, 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. The page format is designed for ease of use with desktop computer, laptop, ipad or smart board. And to help teachers or parents who wish to set the problems without giving immediate access to the answers, each of the 'no problem!' books is supplied as a zip folder containing both a copy of the book as a whole and also separate 'problem' and 'answer' books.

The materials in these two books was originally designed to challenge and extend able pupils in the yr6 – yr8 age group. None of the problems requires maths knowledge or skills beyond those of a yr6 pupil; in particular, no knowledge of algebra is needed. The problems have been well tried and tested in the classroom and by home learners.

# Maths Investigations

Perhaps the importance of regular involvement in both problem-solving and investigative maths for young mathematicians is no longer a matter for debate. But these things are not just valuable components of anyone's development in the subject; they also offer a glimpse of what it is that real mathematicians get up to. The days have surely gone when a thorough grounding in arithmetic skills is all that is required for pre-senior school pupils. However, planning and preparing for investigative work is time-consuming and so in a busy world this area can often be neglected. Our Maths Investigations pack offers a collection of worthwhile investigations with both the planning and the preparation of necessary photocopiable materials already done for you.

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. These are ideal for any teacher or parent looking for ready-to-use but valuable maths investigations.

These investigations have been used with a variety of age-groups; a suggested year-group is listed for each but in practice any of them can be used with a range of pupils. Each one provides about the right amount of activity for a complete lesson but equally any of them can also be used as the starting-point for further activities.

# Maths Games

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 Maths Games 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.

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. These problems are somewhat easier than 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 answer-book is 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.

# mini-problems

# grids, templates etc

This pdf contains a range of useful grids, templates and blanks (square grids, isometric grids, hexagon grids, co-ordinate grids, circle grids, venn diagram blanks, digital clock blanks, ºC thermometer blanks) together with selections of important number sets (number grids, square numbers, prime numbers, powers of 2, factorials, pascal's triangle, common fractions to percentages).

Some grids (eg square grids, isometric grids) are in full-page A4 format; others (smaller grids) are printed 2, 4, 6 or 8 to a page for class use.

# Year 6 practice cards

The Year 6 Practice Cards have been created to provide extra useful practice over a range of topics for your Year 6 pupils. They are designed to be printed up as A5 cards and each set comes complete with answers. For your information, the topic covered by any particular card is shown at the top. 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.

# long multiplication pack

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).

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