M2.8.3 For the adult
Number machines
A machine does × 3, then + 1. What comes out if I put in 4?
What this chapter teaches
A number machine does its jobs in order. To go backwards from an output, undo the last job first with its opposite. To find a rule from pairs, look at how the outputs change when the inputs go up by 1.
Three questions to ask
There is no one right wording. Listen for the idea.
- What comes out if you put 4 into a machine that does × 3, then + 1?
- The outputs go up by 2 when the inputs go up by 1. What does that tell you about the rule?
- The output is 22. How can you find what went in?
After the chapter, the learner can
- Find the output of a machine like 'times 3, then add 1'
- Find the rule from pairs of inputs and outputs
- Work backwards from an output to find the input
What they copy into their notebook
A number machine does jobs in order. The input goes in. The output comes out. To go backwards, undo the last job first, with its opposite.