There is only one main standard for algebra and functions in the fifth grade, but that's more than enough for a month's worth of math lessons.
1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.
This one by itself took two and a half weeks while I was in JL's classroom. He actually taught this really well and thoroughly. By that time in the semester, I was already teaching most of the math (REM: WAY too fast of a progression that time), but he didn't let me teach coordinate graphing because apparently it's a huge thing on the state tests.
Ideas to be mastered involving standard 1.4:
- be completely familiar with positive and negative integers, and probably positive and negative fractions as well
- the idea of an x-axis, a y-axis, and the 2 dimensional plane
- distance on that plane
- how to get from point a to point b
- what exactly point a and point b are (i.e. (x1, y1) standard notation - because switching the x and y coordinate places when writing ordered pairs is a big no-no; basically the conventions writing math symbols)
- how to find the "address" of a point given only a drawing of it on a graph
- know which quadrant is which
- know, with only a glance, that (-1, -10) does not belong in II and why that is the case
There are probably a few other things too, but that's most of it, I believe. See? You really can't get into much depth without multitasking the standards and making as many opportunities to hit each one as possible.
With algebra added on top of functions, it can probably be stretched into another month of lessons. Algebra has relationships with geometry as well as functions, which means functions has relationships with geometry too. And then you've got to touch base with standard line equations, slopes, intercepts, and deciding which pair of coordinates don't fit in a given function.
JL didn't go into geometry with algebra and functions, which is too bad because I think it makes more sense to introduce those things through geometry than just plunking them down in something as abstract as the coordinate plane. Plus, it would help students make much more sense of calculus later on. But I suppose that would have tacked on another month's worth of lessons, which we didn't have since testing was right around the corner. Crazy, yeah?