Tuesday, September 6, 2011

Linking Linear Functions and Quadratic Functions

In hopes of reconciling the big gap that often seems to divide linear and quadratic algebra, I used a variation of this activity today and it worked out well. I gave the kids a linear pattern, followed by a square of that pattern, and the kids had to make the connection and figure out that their linear function now transformed into a quadratic one. Then I tagged on some extra dots in a third pattern and they had to figure out that the third pattern now had extra constants.

We used today's activity as a segue into how to expand/simplify quadratic expressions, and they were so excited! (These 8th-graders saw some pieces of quadratic skills last year, but they were happy to be introduced to the box method of multiplication today.)

I made this file (as linked above) to be a follow-up activity to use during a future class, to reinforce the connections they've already made today. After that, I think I'll be ready to go into how to find quadratic equations from a table of values!!

PS. In the interest of less scaffolding, I'm going to hand this sheet to the kids with only the last problem showing. If they can do it, they should try to do it without looking at the problems before; otherwise they can move through the scaffolded "hints" and return to that problem...

PPS. The earlier activity I used is here. I think it's nice to start with a square relationship because the kids can immediately visualize that it will end up looking "quadratic"...


  1. Couple thoughts...

    1) Don't tell kids that #3 is related to #1 and #2 -- let them figure that out (and they will, especially if they're working together). If they don't figure it out you have it as a walk-around pointer, and eventually kids will realize problems relate to one another :)

    2) I'm a big non-fan of forcing the "standard form" of a quadratic. The form y = (3x+2)(2x+1) actually carries more information, since you can describe where it came from, while y = 6x^2 + 7x + 2 can't be picked apart as well.

    Why is standard form so important? (I am curious -- what is everyone's opinion on this?) It isn't until they're faced with adding or subtracting stuff like (3x+2)(2x+1) + (x+3)^2 or such that I think a standard form starts to have a reason for being. I say let any form of the answer be correct at this point.

    Good luck and keep posting!

  2. Hi Bowen,

    Yes - I agree! There was a bit too much scaffolding on this. Sadly I've already run this off... I'll have to black it out manually :)

    By the way I taught kids how to find quadratic equations using Legrange's method today like you showed us. It was a hit! We're ready for some projecty things very soon...

  3. I just posted my earlier activity (see above). Do you have thoughts on that? There's a bit less scaffolding there.