This is the way that CME introduces functions, and I like it. Kids try to find functions that fit the tables (and at this early stage, any way of expressing the relationship between input and output is acceptable, whether or not it uses variables).
There are two things that I like about it:
- It sets us up for moving into fitting data to functions, and in their curriculum their next move isn’t composition of functions, inverse, domain, range, etc. Rather, it’s line of best fit. I like that.
- It introduces the entire menu of functions immediately. We’ll study each of these in depth later, but the whole year is right there in these tables: linear, quadratic, exponential, logarithmic, radical functions.
One thing that I might adjust is give them a slot for “What happens when the input is 100?” ala dan meyer’s handout for linear relationships (see Week 10).
I think a good follow-up activity could be one that groups tables into families. We could give students little cards with tables on them and they could be tasked with grouping them. This feels like a Malcolm Swan activity…