Cleave Books
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Teacher's Notes
The purpose of these resources is to provide material which teachers of mathematics can use in their classrooms. All of the material can be viewed and assessed as to its suitability on the screen and, when something suitable has been found, can be printed out to serve as a master from which the necessary classroom copies can be made. The material is very wide-ranging in content and it will require the teacher to decide where, when and how any of it is to be used. It might be as a homework, a revision, a test, a discussion point, a routine exercise, an information sheet, a maths club activity, a diversionary pastime or serve any other purpose which individual teachers might have. The material does NOT constitute a course, and nor is it designed to support or supplement any particular course.
For convenience, the sheets have been grouped under headings which should convey some idea of what the sheets in the group are concerned with. Those headings are amplified here as a further help. Many, but not all, of the units contain notes and suggestions for the teacher.
When the sheets are viewed on the screen it will be seen that colour has been used in a few places. This has been done because it is available on screen and does aid the reader, especially when trying to look at several things quickly. Colour is NOT necessary for the printed sheets and all have been tested to see that they produce suitable clear black and white copy.
The headings of the topics (given on the left) are linked so that the material available for that topic can be called directly from these notes.
Basic Sheets
These are the staple requirements of any mathematics classroom. What is useful about this collection is the wide variety that can be made available at very short notice, and in small quantities. There is almost no storage problem.
Lined GridsA4 sheets ruled in squares ranging in size from 2 cm to 2 mm together with some other rulings.
Dotted GridsA4 sheets giving an assortment of both square and isometric grids marked out only with dots.
Coordinate GridsSets of coordinate grids: 1st quadrant 0 to 9 with 12 on a sheet; and all four quadrants -5 to 5 with 8 on a sheet. Large versions of each grid are included, suitable for making an ohp transparency. There are also grids for polar coordinates and transformations. Work for these grids is provided under 'Exercises and Practice'.
Artefacts for MathsA collection of things to make and use: protractors, clinometer, puzzles etc.
BIG Number LineA DIY Number Line that would be a useful 'decoration' in any classroom.
Thermometer ScaleComplementary to the above, useful as an introduction to negative numbers in a familiar context.
Pi StripValue of Pi to 1000 decimal places, printed large on a strip for wall-mounting.
Height MeasureA metric/imperial scale intended for wall-mounting for the purpose of measuring personal heights .
Number SquaresThe simple 1 to 100 number square with 6 copies on a sheet. There is also a large copy for ohp purposes. In addition, there is an Eratosthenes' Mask which fits over the large square leaving only the primes revealed. Some notes about activities using number squares are included.
Answer GridsThese are ruled into numbered boxes so that a set of answers to any given set of (short) questions can be entered. It greatly facilitates the marking process. See also notes on 'Individualised Working' at the end.
Information Sheets
These are exactly that. They are sheets which might be considered as suitable for students to have a copy of either, for one-off reference or, to keep in their own note-books.
Fact SheetsIn this first group are: Prime numbers; Random numbers; Factors; Multiplication tables and squares; Value of pi; Units of measurement.
Formulas A collection of Formulas, Facts and Figures often needed in mathematics.
TablesThese give the exact values of numbers raised to various powers
Tables 2For Pythagorean Triplets, Fibonacci Numbers, Polygon Numbers and Factors of Numbers with explanations of their origins etc.
Multiplication MethodsA collection of some methods for doing multiplication that have been devised and used in the past
Word ListA list of over 1500 mathematical words and phrases. NO explanations are given.
MathematiciansA list of over 200 mathematicians and their dates
Lottery ResultsAll results of the UK Lottery since its start; this will be updated from time to time. There are some suggestions for their use in statistics.
Exercises and Practice
In short, lots of work of the kind usually found in mathematics classrooms throughout the world, ranging from basic arithmetic to complex calculations.
Arithmetic PracticeThese sheets are concerned with the all important basic skills and provide opportunities for their practice in a variety of different contexts.
TrigonometryA plentiful supply of worksheets covering many aspects and types of problems in this topic. A range of tests, and answers to all of the work, is also available. There is a comprehensive index to all the material.
DivisionSome carefully structured work on introducing the 'Long Divison' algorithm.
Calculator ExercisesA set of worksheets devised to facilitate and encourage the use of the Specialist Calculators.
CirclesAll the sheets here involve work on the mensuration of the circle.
MensurationOn a mixture of shapes - square, circle, sector, cube, sphere, cylinder.
Flow DiagramsAnother way of tackling some mensuration problems
CoordinatesSome simple introductory practice on the use of coordinates.
Missing Numbers etc.The aim in these sheets is to make the student more aware of the structure of the basic arithmetic operations and using the different inverse relationships.
Graduated ProblemsEach sheet offers (under some suitable umbrella heading) a set of problems graded from the basic to the very difficult. Such sheets could be used for assessment purposes to find out just how far a student has got with certain topics; or as a revision sheet so that a student might find out where his or her gaps are.
MiscellaneousThis is the "can't think where else to put them" department. Look and see.
Other Activities
These are topics and ideas which usually find no real place in any mainstream course of mathematics - though some do get a peripheral mention. All of them can, at the appropriate point, perform a very useful service.
Counting ProblemsMathematical problems of a particular type. Easy to get started but difficult to take to a 'proper' conclusion.
Multiplication Bingo Another way of practicing the use of the basic multiplication tables (2 to 10).
Dominoes Using a well-known game to generate lots of practice with those all important small numbers.
The Dartboard To encourage some (more) arithmetic in the investigation of a well-known game.
Flippin' Sums A very different way of getting some simple number work done.
Ordering by Numbers Getting familiar with the Number Line using a 'game-like' activity.
Geometric PatternsSheets of ideas for drawing shapes based on geometric principles.
TessellationsThese sheets are concerned with helping pupils to get started with making tessellations.
Dictionary ExercisesA set of exercises to help students become familiar with the use of a (particular) mathematics dictionary
Dictionary Exercises 2Another version of the above to deal with the revised edition of the same dictionary.
MisMathsA collection of 'howlers' taken from various media.
Vocabulary ExercisesWork on the origins and real meanings of some words involving numbers.
TangramsAn excellent reason for having some pleasurable practice in 2-D spatial work.
PentominoesAnother reason for practicing some 2-D spatial work.
Shapes BingoTo practice identifying the simpler 2-D and 3-D shapes.
Some Other LessonsSome 'ready made' lessons for those occasions when you haven't got one.
Su DokuLogic work with numbers and NO arithmetic.
The necessary background administration of any class needs all the support and help it can get. Here are some sheets which would enable a teacher to put together a useful diary and record book. Some of the units have an extra page with suggestions on how the sheets might be used.
Diary PagesThese are drawn up to show one week (Mon to Fri) on a sheet. A variety of formats is available - for 4, 5, 6 and 8 periods in a day, or blanks, or simple ruled lines - to accommodate a wide range of preferences.
Recording SheetsWith a wide choice of rulings, the form most suitable to record almost anything that is worth recording (from attendance to reports) should be found here.
Planning SheetsThese are intended to provide a framework to assist in forward planning.
CalendarsJust what it says - and several of them - from 1900 to 2060. Dates of Easter also given.
Individualised Working
Some of the sheets are set out in a particular way to enable the work they contain to be split easily into two parts. It will be obvious which ones they are. Most commonly the work is set out in two columns with odd-numbered problems on the left, and even-numbered problems on the right. With pupils sitting in pairs (or notionally considered to be so) the instructions "pupils on the left do the odd-numbered questions and pupils on the right do the even-numbered ones" will go a long way towards ensuring something like individualised working.

A similar technique can be employed with one of the answer sheets. There is one which contains spaces for 50 answers, arranged odd on the left, even on the right. Suppose some form of oral questioning is to be done, and written responses are required. (An obvious example of this is mental arithmetic.) Using this particular answer sheet the instruction above can be given. Then a prepared set of 50 questions can be read out (at a suitable rate) with the aim of each student being occupied with getting his or her own answer sorted out and written down while the next question is being delivered.

Organisation and Storage
No doubt everyone will have their own way of working with this material, but a few suggestions might be useful for newcomers. Since all the sheets provided through this service are meant to serve as 'master copies' they do need to be readily available. To that end it is no good relying on them being obtainable from the Web at a moment's notice. There can be many reasons why that might let you down, from power-failures to a jammed printer.

It is better to download a selection of suitable sheets whenever an opportunity offers itself. These can then be stored (loose-leaf plastic wallets in a ring-binder are admirable for this) until they are needed. From there they can be taken out, used and re-stored whenever necessary. Kept in that format it is then possible to be certain of finding a particular sheet when it is needed, or to browse through them when desperately seeking inspiration!


The copyright in all of this material belongs to the originators who created it.
The material is made available here for downloading and dissemination for

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