19
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, ...
- 5,352
16
votes
Confusing variables with units in simple equations
A practical suggestion: make sure your own equations are dimensionally consistent, and your students will be more likely to make theirs consistent as well, thus avoiding mistakes like these.
In ...
- 2,961
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 ...
- 111
10
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:
$$3 \text{cm} + x = 5 \text{cm}$$
Solution:
$x = 2 \text{cm}$ => correct.
$x = 0.2 \text{dm}$ => ...
- 2,237
7
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 ...
- 7,475
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})^...
- 1,832
6
votes
Confusing variables with units in simple equations
There are two things that can be done to really drive this point to someone first learning algebraic equations.
Focus on how the units of both sides of the equation must be equal. This might seem ...
- 161
4
votes
Confusing variables with units in simple equations
I think the way to help this kind of student is to get them in the habit of reading the equation correctly. The equation $d=6t$ does not say that
1 mile is the same as 6 hours,
it says that
the ...
- 12.8k
4
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-...
- 12.8k
4
votes
Confusing variables with units in simple equations
One possible method is to have students simply do t vs d value tables.
"If t is 1, what value does d have to have to make the equation true?" So starting with given values for t, figuring ...
- 189
3
votes
Confusing variables with units in simple equations
Personally, I would emphasize translating natural statements very carefully, one word at a time. Starting with the fact that the verb "to be" (is) is the thing that translates to the equals ...
- 26.6k
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 ...
- 441
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 ...
- 3,160
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 ...
- 1,832
2
votes
Confusing variables with units in simple equations
I posted an answer earlier, but after more thought, here's a different approach that I think might be better.
Student: $d=6t$ means 1 mile is the same as 6 hours.
Teacher: Really? So if you plug in 1 ...
- 12.8k
1
vote
Confusing variables with units in simple equations
I would say that your students are completely right:
In general life it's completely normal to write six seconds as $6s$ or thirteen meter as $13m$, so thinking that $6t$ is some way of writing "...
- 2,237
1
vote
Confusing variables with units in simple equations
I'm coming from a physics background. I avoid writing numbers for any measured quantities into equations until the last step where I plug in values to get a final answer. This is because it can be ...
- 475
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 ...
- 817
Only top scored, non community-wiki answers of a minimum length are eligible