EquationQuest ✕
◆ EquationQuest Learn 🎓 Teach 🗺️ Adventure 🤝 Together 🔁 Review ⋯ More 🧭 My Journey Teach the Cast Some of EquationQuest’s cast are still learning. When you teach them, YOU learn it best — catch what they get wrong, then quiz them.
✕ Teach Lever You be the teacher — Lever is still learning. Helping Lever figure it out is the practice. (Lever's progress stays on this device; nothing is sent anywhere.)
🎓 In a minute you'll be the teacher. Get ready to teach Lever: maintaining balance.
An equation is a balance. Whatever you do to one side, you do to the other, so it stays level. To get x alone in x + 3 = 11, take 3 from BOTH sides.
Teach the connections
Show how the equation-solving ideas connect You've helped them one at a time. The real understanding is how the ideas CONNECT — teach that next.
Undo (inverse operations) × Lever (keep both sides balanced)
Undo says "subtract 3 to peel it off." Lever says "keep both sides equal." How are those one move?
You apply the inverse to BOTH sides at once — that's what keeps it balanced AND undoes the step They're separate rules — first you undo, then later you re-balance Undo works on one side; Lever fixes the other side afterward
Undo then says: “To solve x + 3 = 11, I'll subtract 3 from just the left — Undo handles that side.” — is that right?
No — an inverse must hit BOTH sides (11 − 3 = 8), or the scale tips Right, undo the left side only
The link: "do the inverse to both sides" is ONE move — Undo names the operation, Lever names why both sides.
One move, two names: undo it — everywhere at once.
Spread (distribution (clear parentheses)) × Solo (isolate the variable)
In 2(x + 3) = 10, why can't Solo isolate x until Spread has gone first?
x is trapped inside the parentheses — distributing (2x + 6) frees it so it can be isolated They're unrelated — you can isolate x while it's still in the parentheses You isolate first, then distribute what's left
Spread then says: “2(x + 3) = 10, so x + 3 = 10 and x = 7 — I'll just isolate straight away.” — is that right?
No — distribute first (2x + 6 = 10), THEN isolate → x = 2 Sure, x = 7
The link: distribution comes BEFORE isolation — Spread clears the way Solo walks through.
First clear the parentheses, then set x free.
Capstone — solve 2(x + 3) = 10 together One equation, three ideas. Bring in the right cast member for each step of 2(x + 3) = 10.
First: the x is stuck inside parentheses. Who frees it?
Who do you bring in?
Spread — distribute: 2x + 6 = 10 Solo — isolate x while it's still bracketed Flipper — flip the sign
Next: peel the +6 away. Who keeps it legal?
Who do you bring in?
Undo + Lever — subtract 6 from BOTH sides: 2x = 4 Spread — distribute again subtract 6 from the left only
Finally: x is stuck to a 2. Who gets x alone?
Who do you bring in?
Solo — divide both sides by 2: x = 2 Spread — distribute the 2 Undo — add 2 to both sides
The synthesis: distribution opened it, the inverse-on-both-sides kept it balanced, and isolation finished it — three cast members, one solution.
x = 2 — and now they see the ideas aren't separate tricks; they're one chain.
Put it together in the tools →
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