The journey of relationships and change
What is determined when you choose an input?
Begin with locker assignments to discover the function condition. Turn verbal rules into expressions, pairs into tables and points, then find inputs from a chosen output.
Begin with the assignment condition →Connect representations one step at a time
- 1 / 6
What if one input has two answers?
Distinguish exactly one output per input from missing or split assignments.
- 2 / 6
Which inputs are allowed?
Distinguish allowed inputs, the output set and the outputs actually reached.
- 3 / 6
Writing “double, then add one”
Explain variables and function-value notation, then substitute consistently.
- 4 / 6
One relationship in tables and points
Turn each table row into a coordinate point and check whether intermediate inputs are allowed.
- 5 / 6
Can a constant output be a function?
Compare proportional, offset, constant and squaring rules using the same criterion.
- 6 / 6
Finding inputs from an output
Distinguish evaluating a function from finding inputs meeting an output condition.
Next, ask how much the output changes
Once you can read an output for an input, you can compare how much output changes as input increases. Full introductory courses on constant change, linear functions and equation transformations remain future work. Here we find matching inputs in tables.
Review finding inputs from outputs →Optionally explore the existing function lab →No score locks the next story. Explain a different example in words or drawings and revisit what you need.