🎢 This is how I've been teaching proportional reasoning in physics, slightly different than how I've seen, which I will tentatively name the "Expel the Intruder" method. We start with this warm up situation, and need to compare the range of B vs. C. 1/ - ThreadSky

afreeparticle.com • 87 days ago

🎢 This is how I've been teaching proportional reasoning in physics, slightly different than how I've seen, which I will tentatively name the "Expel the Intruder" method.

We start with this warm up situation, and need to compare the range of B vs. C.

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almostretired2025.bsky.social•87 days ago

📌

almostretired2025.bsky.social•87 days ago

This is interesting! Thanks so much for sharing.

afreeparticle.com•87 days ago

This example is 4x the height, but will allow them to answer the warm up on their own.

They tend multiply stuff immediately, thus the colors and the command to immediately "Expel the Intruder" are necessary, to leave the base expression intact.

Students just need to check 3 things to move on.

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helenrey.bsky.social•87 days ago

SO interesting - thanks for all this!

It's a 'curse of the expert' thing for me that if H is x 4 then sqr is x 2. Obviously it's x 2, but not to them...

afreeparticle.com•87 days ago

Now we still have the original "base" expression intact! So the factor of 2 has a clear meaning. It's what you multiply the original range by to get the new range.

Now students can use this example to answer the warm up (If they didn't figure it out by other means, but they can still do it!)

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afreeparticle.com•87 days ago

I do try to convince them that you are allowed to rearrange the equation like that through algebra, but most of their algebra skills aren't that great unfortunately.

This is the worksheet I use to check understanding:

https://docs.google.com/document/d/1WlnfXfEqPzHvz4VNeQUySlM5L65gY0Z1_mj4JmVtBsY/edit?usp=sharing

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afreeparticle.com•87 days ago

I've tried the Rule of Ones / Factors of Change method, but they never understood what their answer meant, and I think it looked too much like plugging in values for them.

https://jacobsphysics.org/2019/02/22/the-factor-of-change-method-for-semiquantitative-reasoning-aka-berthas-rule-of-ones/

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jonathanbyrd.bsky.social•87 days ago

Thank you. This is good insight-building.

malmeida.bsky.social•87 days ago

This is pretty much how I do it (at least for myself, not a huge emphasis in my class). Only worked ok for students in my experience but you're much more scaffolded than I was.

I like it because of ties into transformation of functions

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