I'm loving teaching (a 1 year course of ) Algebra 1 for the first time. It's fun to be the first person to show the kids all the stuff I take for granted they know later on.
Recently, we started solving one-step then two-step equations. Maybe everyone does this, but I found it helpful to start with a goofy story. I told them I bought them a special present (it was just some random object in the room), and I wanted to give it to them, but I first had to wrap it up. So I put it in a box, then I put the lid on the box (some plastic tub I had laying around), then since it was see-through, I wanted to wrap it up (I had an old sheet laying around), and then I had to put a bow on it (some random string I cut up). Then I asked them what were the steps to what I had just done. They repeated them. Then I asked them, if they wanted to get the present out, what specifically did they have to do and in what order. So we went through untieing the bow, unwrapping, opening the lid, and taking the present out of the box.
Then I linked this to a 2 step equation on how you have to undo what's being done to x and in the opposite order that you had "wrapped up" x. This seemed to work (so far).
A few days later we worked on combining like terms and "challenging" distributive property types like:
5 - 2(3x - 4) = 20. YEESH! That distributing the negative was a challenge. I explained it 3 different ways, and different ways seemed to work for different kids. One kid was okay with: okay, cover up the "5" and just look at the "-2(3x-4)", what would it become? Then it's just "adding 5 in front of that operation".
I'll see how they did on homework tomorrow.
I do a similar routine with pi and other approximations.
ReplyDeleteI draw the letter pi on the board, then draw a suitcase around it. Draw a sturdy handle.
Then I'll write an equation for circle area: A = [pi] * r * r. I draw the suitcase around pi.
We substitute our number (5) for r.
A = [pi] * 5 * 5
A = [pi] * 25
Then it is time to take pi out of the suitcase.
A = 3.14159 * 25
A = 15.70795
Then we'll do a pi problem with a handful of steps, and I'll assign different clusters of kids different values of pi. We open our suitcases on the first step, with our different sized pi's, do the steps in unison, and compare the answers at the end. This shows how the number of digits used can compromise the answer if you approximate too early.
Just thought I'd share. Your box story was great, and reminded me of my suitcase.
I really like the activity of exploring what happens if you round too early and too much.
ReplyDeleteMs. Cookie
I usually base this on subtracting numbers from a total, eg start with eleven, subtract four, subtract another three. Some kids go 11 - 7 straight away; others go 11 - 4 - 3 and they all agree that 11 - (4 + 3) MUST mean the same as 11 - 4 - 3, so see that the negative MUST distribute over the bracket.
ReplyDeleteThanks for the (11-4-3) tip. I was trying to get that message across from them, but I didn't approach it in just quite THAT way .... so I'll try that on Monday when I see them again.
ReplyDeleteMs. Cookie
I have a colleague that does shoes and socks. He brings it up when he covers other inverse operation pairs (like square and square root, log and exp). It seems to stick with them. I likve to use imaginary balances to help them solve equations - and there are actually online versions (nlvm out of Utah State) that works well.
ReplyDelete