16 votes
Accepted

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

I think the heuristic \begin{align*} \frac{8}{4} \quad \longleftrightarrow \quad 8 \textrm{ out of every group of } 4 \end{align*} still makes sense if you emphasize that you want $8$ slices of pizza ...
Justin Skycak's user avatar
8 votes

Geometric line: constructing fractions

In Growing Ideas of Number, Crossley provides this diagram, Figure 3.4, in a discussion of the notion of the "geometric line." From the perspective of modern mathematics, all of the points ...
Justin Hancock's user avatar
5 votes

Geometric line: constructing fractions

I don't think this diagram would help kids understand fractions. But I do like how it makes me think. Your problem might be that the 1's are not to scale. If we are given that the 3 lines (or line ...
Sue VanHattum's user avatar
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4 votes

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

Justin Skycak wrote a great answer that you can use with your kids, but I'd like to explain how what you're telling them relates to what they might be seeing right now and later on in school. I'll be ...
Justin Hancock's user avatar
3 votes

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

Justin H has a good answer emphasizing how fractions are a complex topic and we learn more and more about them over the years. To your specific question, I would emphasize the need to spend a ...
Guest troll's user avatar
1 vote

Ratio in Fractional Form

In order to judge whether $5/2$ is correct, you need to specify which ratio you're talking about. There are a lot of ratios that can be made here, one of which is $5/2.$ (There are $3+2=5$ animals in ...
Justin Skycak's user avatar
1 vote

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

We teach that there are two basic ways of understanding division. På norsk they are called delingsdivisjon and målingsdivisjon; sharing division and measurement division would be rough translations. ...
Tommi's user avatar
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