[Maths-Education] Ratio and Proportion

[rouletg]

In Ontario (Canada) we regularly go through these (pointless to me) 
exercises in attempting to provide "perfect" definitions for mathematical 
terms.   Our curriculum guidelines and texts have over the past 3 decades 
provided the definition:

Proportion:  a statement of equality between two ratios

To make this work with Dave's example below we need to agree that the 
statement "the proportion of goldfish is 6 out of 24" is a shorthand for:

(number of goldfish) : (number of fish) = 6:24

The Ontario definition also means that there is a proportion between the 
two triangles in Anne's example - ie. there are multiple equalities of ratios

Geoff Roulet


PS.  Now those of you in the UK can "solve" Ontario's problem of the day - 
Does a cone have any faces, vertices, or edges?  If so how many?  This 
appears to be a significant issue for our Junior (grades 4-6) grade teachers.

At 01:23 PM 10/4/01 +0100, Dave Wilson wrote:
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>
>Please help me to understaqnd these 2 words! I don't think that I have 
>ever been particularly bothered about them before, despite years of 
>teaching using texts with chapter titlse like Ratio and Proportion.
>
>I was looking at the NNS Key Stage 3 and read;
>
>Year 7 pupils should use read and write, spelling correctly ratio, proportion.
>
>It then goes on to say;
>
>Proportion compares part to whole
>offering examples - 24 fish in a pond, 6 are gold, 18 black .... the 
>proportion of goldfish is 6 out of 24
>
>and a page later;
>
>Ratio compares part to part
>
>
>These distinctions are not part of my understanding of the words. Am I 
>missing something? Is this something I should know? Am I being mislead in 
>terms of current usage by some hazy recollection of old Euclid/Heath usages?
>
>regards,
>--
>Dave
>Dave Wilson  (D.Wilson@mmu.ac.uk     A letter always reaches its 
>destination                 Dave@zizek.demon.co.uk)              Lacan
>http://s13a.math.aca.mmu.ac.uk
>
>
>
>
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-----------------------------------------------------------
Geoffrey Roulet
Coordinator, Centre for Mathematics, Science and Technology Education
Faculty of Education
Queen's University
Kingston, ON
K7L 3N6
Phone:    613-533-6000 ext. 74935 (Work External)
                74935 (Work Internal)
                613-531-3348 (Home)
Fax:        613-533-6584
e-mail:     rouletg@educ.queensu.ca
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