Wednesday, September 2, 2020

Lesson 1-3: Ordered Pairs as Points (Day 13)

This is what I wrote last year about today's lesson:

Lesson 1-3 of the U of Chicago text is called "Ordered Pairs as Points." (It appears as Lesson 1-2 in the modern edition of the text.) The main focus of the lesson is graphing points on the plane. Indeed, we have another description of a point:

Third description of a point:
A point is an ordered pair of numbers.

The idea of graphing points on a coordinate plane is a familiar one. But sometimes I wonder whether we should make students graph points and lines so soon in their Geometry course.

Once again, here's how I think about it -- the students coming to us just finished Algebra I. Some of them struggled just to earn a grade of C- or D- (whatever the lowest allowable Algebra I grade is in your district is so that the students can advance to Geometry). The students who just barely passed Algebra I are tired of seeing algebra. They may look forward to Geometry where they won't have to see so much algebra -- and then one of the first things we show them is more algebra.

Then there's also the issue, first brought up by David Joyce, that students should use similarity to show why the graph of a linear equation is a line. This idea appears in the Common Core standards for eighth grade, but it's awkward in high school. Graphing linear equations is a first semester Algebra I topic while similarity is a second semester Geometry topic -- and it's difficult to justify delaying graphing linear equations by three semesters just to conform to Joyce's wishes.

In the past, I've tried -- and failed -- to teach linear graphs after similarity. (This includes the year I was at the old charter school, when I tried to follow the eighth grade standards, but I left the class before graphing equations.) This year, my plan is simple -- I will conform to the order of the U of Chicago text. The U of Chicago text introduces linear graphs in Lesson 1-3, and so that's when I'm teaching it.

The bonus question asks about longitude and latitude. I've already located my own coordinates as being near 34N, 118W.


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