Maths Learning Difficulties, Dyslexia and Dyscalculia by Steve Chinn

Author:Steve Chinn
Language: eng
Format: epub
ISBN: 9781784509897
Publisher: Jessica Kingsley Publishers
Published: 2018-09-30T16:00:00+00:00

Images, symbols and concepts

Mathematicians often look for ways to represent numbers and ideas about numbers in as succinct a way as they can devise. The number of zeros written after the 1 for the yottabyte is 24, which takes a while to write. The symbol code used to replace the writing of all those zeros is the ‘index’, so 1 000 000 000 000 000 000 000 000 becomes 1024 where 24 is the index.

The other vocabulary for this is ‘10 to the power of 24’, which I quite like as the word ‘power’ suggests to me that something powerful is going on.

The logic behind powers can be seen in the sequence (or pattern) below:

1 = 100 (one)

10 = 101 (ten)

100 = 10 × 10 = 102 (hundred)

1000 = 10 × 10 × 10 = 103 (thousand)

10 000 = 10 × 10 × 10 × 10 = 104 (ten thousand)

100 000 = 10 × 10 × 10 × 10 × 10 = 105 (hundred thousand)

1 000 000 = 10 × 10 × 10 × 10 × 10 × 10 = 106 (million)

The logic extends to dividing by 10 and powers of 10. The code is modified by including a minus sign in front of the index, for example, 10-2 means ‘divide by 100’ or 1/100 and 10-6 means divide by one million or 1/1 000 000.

The sequence is:

106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6

Note the index in the middle is 0. 100 is 1.

Recognising patterns makes understanding and remembering more effective.

These tasks are very much about place value. They are often not well understood. Children rely on mnemonics, like ‘100 has 2 zeros so when you multiply a number by 100 you add 2 zeros to the number’, for example 267 × 100 = 26700. If I wanted to interpret the mnemonic literally, and many students will react that way, then I might do:

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