Algebra, Lesson 2
A Variable Can Move
An unknown can be one number. A variable can travel through a rule and reveal a whole pattern.
Predict first. Then move one input through the expressions, table, and graph.
Rule A: y = 2x + 1. Rule B: y = x + 4.
Choose before the graph appears.
| x | A | B |
|---|
Move x and compare the two outputs.
See a variable as movement
Answer all five before the linked representations are explained.
Build the rule
Two numbers shape a line
Change the step size m and the starting output b. One rule updates the formula, table, point, and line.
| x | y |
|---|
Read the structure of a linear rule
Complete the five ideas before checking how m and b control the whole family.
Reverse the rule
Walk backward through the machine
The forward rule doubles an input, then adds 3. Start with an output and undo the actions in reverse order.
Start at the output. Undo the last operation first.
Reason backward, then verify forward
Answer all five before the inverse process is unpacked step by step.
The invariant connection
Next: move a shape without stretching it.
Geometry turns rules into actions on space and asks what survives.