Function machines: the momo shop and secret rules
Build a machine that turns plates of momo into a bill, then crack secret machines by comparing their inputs and outputs.
Core concept
In short: Put numbers into a machine, watch what comes out, and guess its rule.
A function gives exactly one output for each input; a linear rule y = mx + c can be found from its table
Topic: Functions and rules
A momo shop charges Rs 30 a plate plus Rs 20 for delivery. The bill is a function of the number of plates: put in x plates, the machine multiplies by 30 and adds 20, and out comes y = 30x + 20 rupees. Every input gives exactly one output. A table of inputs and outputs shows the rule's pattern: each extra plate adds 30, and with no plates the bill is the 20 delivery charge. That is how to crack a secret machine: the step between outputs is m and the output for 0 is c.
What you will learn
- Substitute values into a rule to find outputs.
- Find a linear rule y = mx + c from a table of inputs and outputs.
- Work backwards from an output to find the input.
Before you start
- Multiplying and adding positive and negative numbers.
Materials
- A shop's price list
Equipment
- A notebook for input–output tables
Procedure
- Tap − or + (or −5 / +5) to set the multiplier m and the number added c; tap − or + to change the input x.
- Read the output and the table for inputs 0 to 5.
- Make the momo bill machine and find the bill for 5 plates, then find how many plates cost Rs 80.
- Tap the chip for secret machines A and B, and change m and c until both columns agree.
How this simulation is simplified
- The machines use whole numbers only.