Decoding Mathematics
Decoding draws attention to the structure of the mathematics
Key Stage suitability • Explanation
- FS
- KS1
- KS2
- KS3
- KS4
- FE
- HE
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Secret codes are usually employed when someone wants to make things less clear. The intention here is to employ codes to makes the mathematics clearer. In some cases it is the process of decoding that draws attention to the structure of the mathematics; in other cases, the coding is used as a way of describing the mathematics. In all cases, coding calls for the person engaged in coding or decoding to pay attention to the structure of the mathematics being coded and this may enhance awareness of the mathematics.
Algebra is a kind of coding. The codes in this book are not the usual sort of algebra, which is generalised arithmetic. However, many of them have a similar structure to the usual sort of algebra and working on them could be useful complementary activities.
This book has been designed so you can photocopy activities to give out to your class. Suitable for KS2, 3 and 4.
Several activities come with an invitation to make up more codes of your own. Sometimes this may be comparatively easy; at other times this may be quite challenging, particularly if you want to make up problems that have unique solutions.
ISBN 1 898611 21 1
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The hints and prompts, and suggestions for further activities on pages 23 to 39 outline possible problem-solving strategies and indicate some of the ways in which the decoding tasks could be followed with other mathematical work. The hints and prompts do not give answers: you know when you have cracked the code!
None of the problems require mathematical knowledge outside the National Curriculum for KS2 or KS3. However, a high-level of skill in solving problems is needed to solve some of these problems. They are organised so that the ones near the beginning tend to be shorter and to involve less mathematical knowledge. These judgements are always difficult to make, however.
Mathematical topics include multiplication facts, multiples, primes, squares, cubes and other powers, fractions, rational numbers and manipulation of surds, quadrilaterals and other polygons (including symmetry and similarity), solid shapes, formulae for area and volume and time. Sampling and collecting data about the frequency of letters in English texts is relevant to the Substitution codes task.
The publication has been designed so that you can photocopy activities to give out to your class and pupils can, where appropriate, write answers on the photocopied sheets.
Contents
Multiplication tables
Lists of multiples
Cross numbers
Sequences
Fibonacci-type sequences (1)
Fibonacci-type sequences (2)
Substitution codes
No calculators!
Hidden text 1
Hidden text 2
Hidden text 3
Hidden text 4
Hidden text 5
Fractions
Codes for nearly tone-deaf Counter users
Polygon codes
Cutting squares off a rectangle
Hints and prompts, and suggestions for further activities
