16
votes
Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?
The usual physics convention is that variables have units built into them, so you don't need to (indeed, shouldn't) write the units separately. For example, Wikipedia writes
In classical mechanics, ...
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11
votes
What does research indicate about how one should treat units in elementary school?
The CRA approach says to move from concrete to pictorial to abstract concepts. The idea of numbers without units or identifiers is treating numbers as an abstraction, and a positive goal. You start ...
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9
votes
Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?
As far as the centimeters are concerned, I believe that both are possible, but there's a catch:
$$3 cm+x=5 cm$$
Solution:
$x = 2 cm$ => correct.
$x = 0.2 dm$ => correct.
$x = 0.02 m$ => ...
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7
votes
Accepted
How to teach that $10000x^2$ c$^2$m$^2$ is wrong?
But $x^2$ m$^2$ and $10000x^2$ c$^2$m$^2$ are arguably both correct.
The prefix ‘centi’ means a hundredth, and the convention \begin{align}\text{cm}^2:={}&(\text{cm})^2\\={}&(10^{-2}\text{ m})^...
- 1,802
6
votes
Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?
This must certainly depend on the context. In the examples you present here, the units/dimensions do nothing, so I would just go ahead and forget them, taking them back in use to check if the answer ...
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3
votes
How to explain square meters?
Peter answered how to explain the ideas to students. So I'll answer your second question:
Is "square meter" a badly-phrased term? What would be a more appropriate term?
It's not badly-...
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2
votes
How to teach that $10000x^2$ c$^2$m$^2$ is wrong?
Although being a bit late to the question...
The underlying problem I see is that we first expose our students to a math symbology where single letters are used to name things, and that simply ...
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2
votes
How to teach that $10000x^2$ c$^2$m$^2$ is wrong?
I wanted to synthesize some of the discussion happening in the comments into an answer.
To me, a statement like
$$(100x\ \text{cm})^2 = 10\,000x^2\ \text{c}^2\text{m}^2$$
indicates that the student ...
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2
votes
Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?
I sometimes come across equations like
I) $3 \text{ cm} + x \text{ cm} = 5 \text{ cm}$
where I would write
II) $3 \text{ cm} + x = 5 \text{ cm}$.
Aside from the fact that option I allows the units to ...
- 1,802
1
vote
How to explain square meters?
For the first, give them a shape that is 1 meter on a side. Then let them try to fill it with four shapes that are each .25 m on a side.
For the second, get several other shapes that are 1 square ...
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