Good point. I would think it probably distracts. I admit I'm very much a part-whole thinker; I'm less at home with the ratio interpretation ... a deficiency on my part ... @germinalmaths.bsky.social has a much better natural affinity with this aspect of fractions than me. - ThreadSky

segarrogers.bsky.social • 32 days ago

Good point. I would think it probably distracts. I admit I'm very much a part-whole thinker; I'm less at home with the ratio interpretation ... a deficiency on my part ... @germinalmaths.bsky.social has a much better natural affinity with this aspect of fractions than me.

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germinalmaths.bsky.social•30 days ago

Actually your strategy of equating numerators then comparing denominators is a valid way to compare any two fractions. We can incorporate ratio here: eg In your earlier example, scaling both parts of 5/13 to obtain 7/(91/5). Since 91/5 > 11, 7/11 > 7/(91/5), ie 7/11 > 5/13.

segarrogers.bsky.social•30 days ago

I’m laughing … I so struggle to think like this!

profsmudge.bsky.social•30 days ago

Yes, but.... We can see by inspection that 7/11 > 5/13; we don't need scaling here. And such a multiplicative relation between fractions is not as fundamental as the multiplicative relation within a fraction, which is a key idea and one which, I think, we tend to neglect.

germinalmaths.bsky.social•30 days ago

Agreed on all points. One is more than 1/2, the other less. I chose that fraction pair as Segar had used it earlier. I also wanted to widen the initial discussion on “units” to include comparison of numerators as well as denominators.

germinalmaths.bsky.social•30 days ago

For me, building fraction sense, as you put it, is vital. Extending the ways in which we understand and work with fractions and how those relate to our existing number sense.

profsmudge.bsky.social•30 days ago

Yes, as here perhaps
https://satisfry.blogspot.com/2024/09/fra01-some-fraction-pairs.html

segarrogers.bsky.social•30 days ago

Could you say more about ‘the multiplicative relation within a fraction’?

profsmudge.bsky.social•29 days ago

I think I just mean seeing the N and D as a ratio, as you might compare the (relative) heights of two people (and rather than seeing N and D as just telling us about a number of pieces of a certain size)

segarrogers.bsky.social•29 days ago

I’d argue there aren’t many resources to help teachers teach this interpretation.

segarrogers.bsky.social•29 days ago

Sounds like a fishing trip for ‘do you have any?’ ;-)

profsmudge.bsky.social•29 days ago

The number line might help, and more generally perhaps learning about scaling, especially geometric enlargement and similar figures

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