September 13, 2012

Today was the my first day targeting Linear Relations in my Math 30-3 courses. I have created a list of Big Ideas and Skills for the entire unit, and divided it up to cover approximately 6 days of lessons. In the past, my Applied Math 30 students always had difficulty interpreting graphs, so I decided to start this unit with the creation and interpretation of scatterplots.

My goals for this first day were:

Creating Scatterplots

- independent vs. dependent variables
- (x,y) coordinates
- x- and y-axes
- line or curve of best fit
- outliers
- interpolation / extrapolation visually
- proper scale markings

My question for the day involved a particular crop and fertilizer, along with the following data:

Fertilizer (g/m^{2}) |
Yield (kg) |
---|---|

85 | 5 |

15 | 11 |

20 | 14 |

40 | 15 |

45 | 18 |

25 | 19 |

60 | 20 |

70 | 23 |

75 | 26 |

80 | 29 |

100 | 29 |

105 | 31 |

110 | 34 |

125 | 35 |

120 | 33 |

130 | 31 |

Given this data, what yield can the farmer expect if he uses:

- 85 g/m
^{2}of fertilizer?- 140 g/m
^{2}of fertilizer?If the farmer wants a yield of 35 kg, how much fertilizer should he use?

Students in both classes were initially dumbfounded with no idea how to start. After about 5 minutes, I said, "when you've been given a table of values in previous math courses, what have you often been asked to do?" That was enough to get them going.

All groups created scatterplots, however they also connected all the points with line segments. With a little discussion about trends and the fact that farming data would not represent perfect mathematical patterns, they created lines of best fit.

Here is one group's work:

A few things of note here:

- Initially they were looking for patterns (the blue numbers on the left), perhaps because many of the thinking problems from the past week involved strict mathematical patterns
- The black line on the graph was their first line of best fit. The
red one was their
**second**line of best fit. After some discussion with them, I was unable to figure out their rationale.

At this point we had some discussion in the class about where the line of best fit should be. Once all groups had similar graphs, I pulled up the workbook and highlighted and discussed the terminology that they had indirectly learned about in this question:

- scatterplot
- line of best fit
- correlation
- interpolation
- extrapolation
- outlier

Speaking of outliers, the question asking about the use of 85 g/m^{2} was
great because students initially answered 15 kg (from the table of
values). It wasn't until after creating the scatterplot that they could
see it was an outlier and not representative of the overall trend.

So I didn't address everything I had hoped, but it was a good start. I have a sheet for each class, where I check off the content addressed, so I can decide what to do tomorrow.