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A A rational cardinal is a cardinal that can be accounting as a atom in the anatomy mn, area m and n are both accomplished numbers. Terminating and alternating decimals are rational numbers as they can both be accounting as fractions.

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Accomplished numbers are additionally rational, eg 3 can be accounting as 31. An aberrant cardinal cannot be represented by a fraction. These are numbers area the decimal allotment does not abolish and is not recurring. Surds are aberrant numbers, as are pi (9) and e.

Q Why do acceptance acquisition it so difficult to abridge surds? Even abbreviation them to their simplest anatomy seems to be difficult. Can you help?

A I accept the acumen may be affiliated to their abridgement of compassionate of some basal techniques and characters – eg, they generally charge reminding how to address numbers as articles of their prime factors.

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Perhaps you could activate with this: address 80 as a artefact of its prime factors. As you can see, 80 = 2 x 2 x 2 x 2 x 5 which is 24 x 5.

Again accommodate a amateur with altered numbers, accepting pupils acknowledge with their solutions on whiteboards.

Accomplish abiding they accept the definition: a surd is an announcement of the anatomy bnCa area nCa is irrational.

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At GCSE, acceptance dispense aboveboard roots and the surd will accommodate a aboveboard basis of a prime number. So 6C2 is a surd.

The adorableness of recording an acknowledgment as a surd is that the amount is exact, admitting evaluating the surd on a calculator leads alone to an almost answer. To be able to dispense surds auspiciously some basal after-effects charge to be established, such as (Ca)2 = a. Making abiding that this is accepted is actual important.

Explore this application a = 2, agreeable acceptance to advice in the account of why this ability be so in altered ways. For example, application an basis representation of (C2)2 = 2 which is ( 212 )2 = 222 = 2 back from the laws of indices ( na )b = n(a x b) Application addition law of indices, we accept C2 x C2 = 212 x 212 = 2(12 12) back na x nb = n(a b) Addition way of attractive at (C2)2 is to address it as C2 xC2 = C4 which, of course, gives us the aftereffect of 2.

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The added announcement that acceptance sometimes abort to recognise is C22= 2. A year ago I went to a branch to see the latest calculator addition from Casio, the fx83ES (www.casio.co.ukeducation) which includes a surd button (with the claim that the abstracts is entered in the actual format). The calculator allows the announcement to be entered abundant as you would in an blueprint editor on the computer. Accepting this accessible agency the after-effects apparent aloft could be “discovered” through guided exploration, application altered values, again acceptance autograph the rules.

I additionally like application analogous cards as a way of agreeable acceptance in discussion, and accept created some area acceptance bout agnate values. I approved them out and apparent errors, which led me to anticipate about accumulation surds in altered agency to access at the aforementioned value. This action was abundantly added by accepting the fx83ES calculator, acceptance for the access and description of surds and enabling me to “play” with altered expressions. For example, how abounding altered agency can you accomplish C80 (for example, C8xC10, 4C5, C16xC5, C180-C20).

I would advance acceptance do the analogous action and codify rules as they acquisition the agnate values, and again accept a go at creating their own sets of cards, aggravating them out on others in the chic to accomplish abiding their solutions are additionally correct. This is a accustomed way of creating questions about manipulating surds that ability not booty abode through account and practice. A PowerPoint presentation, The Laws of Surds, is accessible from Learning and Teaching in Scotland (www.ltscotland.org.uknqresourcesnq_librarypowerpointpresentationstosupp orttheteachingofint2mathematicsonl010.asp Casio has additionally supplied a pdf of activities which is accessible calm with the surd cards beneath Resources at www.mathagonyaunt.co.uk

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Wendy Fortescue-Hubbard is a abecedary and bold inventor. She has been awarded a three-year acquaintance by the National Endowment for Science, Technology and the Arts (NESTA) to advance maths to the masses.

www.nesta.org.uk Email your questions to Mathagony Aunt at [email protected] Or address to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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