Four dens of algebra. Wake each sleeping bear by passing its quiz. Drag everything.
1 the honey box
When you see x, don't panic. It's a box. Tap it to see what the bear hid in there.
π same box, two disguises β both hold the number 4
2 the machine Β· f(x)
This is the whole idea: x goes in, the rule does something, y comes out. Every number you feed it fills a row in the table.
| x (in) | β rule β | y (out) |
|---|
β drag the pink dot Β· tap a rule to rebuild the machine
3 the balance
The = means both sides weigh the same. Tap a grey weight and a matching one leaves the other side too β until x stands alone.
4 the picture
Every row of the table is a dot. Line the dots up and you get a graph. Bend the line with your fingers β the rule, the table, and the picture all move together.
| x | y |
|---|
β drag the pink dot & the orange dots
5 two paths cross
A system is two lines together. The solution is the single spot where they cross β the one x and y that work for both. Slide the orange line and watch the meeting point move.
β the pink line is fixed Β· slide the orange one
6 more or less
An equation has one answer. An inequality has many β a whole stretch of the number line. The circle is hollow for < or > (not included) and filled for β€ or β₯ (included).
7 the doubling bears
2n means multiply 2 by itself n times. Add one more bear each step to a line and it grows slowly; double the bears each step and it rockets past. That's exponential growth.
β amber = doubling (2n) Β· teal = adding (2n)
8 the bear's leap
Write it as y = (x β r)(x β s). The curve crosses the x-axis at its two roots, r and s, and the tip (the vertex) sits right in the middle. Drag the roots and watch the leap reshape.
β the curve crosses the axis exactly at the roots
9 the shape-shifter
Start with y = xΒ². Small changes move it: (x β h) slides it sideways, + k slides it up or down, and a multiplier a makes it steeper β or flips it upside down. Same bear, new pose.
β the faint curve is the original y = xΒ²
10 the honey rectangle
Multiply (x + p)(x + q) and you get xΒ² + (p+q)x + pq β the area of a rectangle with sides (x + p) and (x + q). Factoring runs it backwards: you know the area, find the sides.
β the two sides build the four-piece area
11 the square's side
If a square has area A, its side is βA. Squaring and square-rooting undo each other. Drag the area and watch the side β the clean answers happen at the perfect squares (1, 4, 9, 16, 25β¦).
β side = βA Β· a whole number only at perfect squares