# "Tools" (literarily) for solving linear or quadratic equations

Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to learn the hard way that they, say, use |-1 to subtract 1 from both sides of an equation. Of course I know the notation, but the operation was too obvious for me.)

My idea was to increase their mental capacity of using the toolbox I will teach by literarily naming the tools with a, duh, similar household tool. (Or other things.) For example, |-1 would be the saw, since you saw off the same on both sides.

My course at the moment deals with solving quadratic equations but I first have to re-teach them all the forgotten stuff...

My list so far:

stop sign - to remember traffic rules: +- yields to */ yields to ^ yields to ([])

worker helmet - Danger! E.g. a root is defined as positive, but still a quadratic equation has (up to) two solutions

= reflexivity - ???

= symmetry - Mirror

= transitivity - Chain

Commutativity of *,+ - ???

Associativity of *,+ - ???

Distributivity - wrench (screws ([]) off or on)

Inserting known values - funnel

Simplifying equation - rake

same action on both sides of = sign - saw

collect (x+a/2)^2 from x^2+a*x+b - hammer

extract square root - tongs

general catch-em-all formula - Robot

And when they are done with this, Vieta's theorem dynamite, blows every equation with integer solutions skyhigh! (This theorem is so useful, yet so little known or taught...)

If you like to improve or fill in on some of my random associations (the hammer is...silly), feel free to use comments, but my question is rather:

Can you suggest a reference where "my" concept (make it stick by association), best specific for quadratic equations (otherwise I can google myself, since the general concept is well known), already has been fleshed out, even tested?

Vaguely related: since I have to do everything step by step

• It is an interesting idea and it reminds me of the classical technique of memorization of long lists of unrelated objects by taking a mental walk on a familiar road and attaching one object to every landmark on that road. That technique does work, but requires some training by itself and is good just for what it is intended for: memorization when logical relations don't exist or are beyond one's comprehension. IMHO, mathematics is exactly the opposite of that and part of the reason some people never get it is exactly trying to memorize where one needs to understand, so be careful! Nov 27, 2023 at 23:25
• I agree with fedja and would go further: I strong dis-recommend introducing such terminology. Even if you manage to succeed, your students will have learned a completely novel vocabulary. If they master your method they will be unable to communicate with anyone besides you. Nov 28, 2023 at 5:19
• THX for your sensible objections - I trained chess for decades now, but I'm definitely new in the tutor business. Nov 28, 2023 at 9:24