Algebra A – Week 1 – 2007

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1. opening day algebra activities, order of operations
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Macroscope

1. I feel like teaching algebra well to a bunch of young kids predisposed against mathematics is the most accurate measure of my worth as a teacher. Maybe as a hard-working human being. One of the hardest things I’ve ever tried and failed to do.
2. Illustrative anecdote: I spent thirty minutes revising last year’s Geometry lessons every day this week. I spent two hours revising last year’s Algebra lessons.
3. Help.
4. We used whiteboards day one. That was a good way to kick things off.
5. I feel like I’m close to landing evaluating expressions. Check day four. Using symbols, dingbat fonts as stand-ins for numbers works way better than starting straight into variables.
6. The last slide of the week, what you should know how to do, is one of my better innovations this year. It gave a lot of students some security, something to hold onto in a busy week of busy classes starting busily. (“Okay, great, I know how to do all this.”) Students who had less of a clue at least knew what they didn’t know, which in my book comes in a close second to actually knowing.

Filesharing

1. Keynote (which choosey moms choose)
2. PowerPoint
3. PDF
4. Interactive QuickTime

Microscope

1. First minute of the first day of class be SURE to have something for them to do. Something they can self-initiate. Otherwise, youâ€™ve got 179 more days coming where YOU have to start them working, YOU have to tell them, okay, letâ€™s get down to business.

2. Theyâ€™ll raise their hands and try to tell you but have them write it on the boards.

3. Talk about how different language move subjects and adjectives around differently, how in German the subjects are capitalized, and how youâ€™ve got to learn to interpret these things.

4. Talk about how math is a language also. Cue the groans. Have them write the symbols at the top of the whiteboard.

1. Michael. Jessica. Ask â€˜em whatâ€™s weird about that last problem. â€œNegatives are one of the most annoying parts about the math youâ€™re gonna learn. Youâ€™re gonna be tempted to say, â€˜Whatâ€™re these good for?â€™ often.â€

2. So I originally wanted them writing down all the pluses and minuses, cancelling all the way, but, graphically, no one could keep anything straight. The answers were all, like, one or two off due to smudging or whatever. So I just had them instead TALLY the pluses and TALLY the minuses and then compare the difference.

3. Follow up question: if the team starts fifteen yards away from the goal, do they score?

4. We talked here about â€œloving to love is goodâ€ as well as â€œgood things happening to good people.â€ That second one caught the best response, the most nods.

5. NEXT YEAR: talk here about how â€œminus a negativeâ€ is the same as adding.

1. Free meals for life.

2. Have a different student come up to fill in each row.

3. Kinda fun, first-week timewaster. â€œThat little popping sound you just heard … that was your mind totally getting blown.â€

4. Tried this for the first time this year. The animation is important. Youâ€™re like, whatâ€™s square + triangle. The smarter kids will guess 7.

1. French fries.

2. Did we change the area at all as we cut up the square?

3. How do we turn 2/9 into /36?

4. Really cool giving them their own worksheet for this so they could draw it.

5. Discuss with a friend or neighbor or the inside of your own head what fraction is shaded here. (Lots of kids suggest 1/9.)

6. Here, Iâ€™ll make it easier for you.

7. Discuss with a friend or neighbor or the inside of your own head what fraction is shaded here.

8. Here, Iâ€™ll make it easier for you.

9. Can I divide anything out of the top and bottom?

10. Talk about how the negatives act like switches, how every two negatives cancel each other out. Or have them figure it out the long way and ask them if they notice anything about the answer and the NUMBER of negative signs.

11. Iâ€™d like to do this every week, I think. This is what weâ€™ve done, where you oughtta be.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. I have horrible news to pass on to you. Manero’s closed. I was just informed of this by my CT (that’s the second bit of bad news, the abbreviation) relatives. Big platter of steak pieces and amazing garlic bread, gone.

2. Tony Lucchese

September 3, 2007 - 3:12 am -

When discussing multiplication with negatives, how much explanation do you use? Your football scenario provides an easy example of negative times negative with the application of say two 15-yard penalties. I’m sure students would intuitively “get” that. But negative times negative really only equals positive to avoid breaking the distributive property. Do you explain this convention, or just ask for rote memorization? Is there a concrete example that helps them remember?

3. Jackie

September 3, 2007 - 4:49 am -

Tony,

I’ve seen one example (in the IMP curriculum) hot & cold cubes.
So for (-3) * (-5)
If one takes away three groups of five cold cubes, the net temp. change is an increase of 15 degrees.

Some kids seem to understand this, some just rely on prior memorized knowledge.

4. A. Mercer

September 3, 2007 - 7:32 am -

Nice to see that whiteboards in Mathematics is not just for elementary anymore…

Sad to see some of the stuff used in PRIMARY (using dingbat symbols to intro variables) have to be reused in high school because the kids never got comfortable with letter variables. ARGHHHHHHH!

5. Tony, I teach rote memorization.

I don’t know what to say in my defense.

There’s something going on in my head at all times, though, wondering just how strictly to teach these things, ’cause the closer I hew to the book’s definition of (e.g.) planes (“a surface such that, given any two distinct points on the surface, the surface also contains the unique straight line that passes through those points.”) and the deeper I push into abstraction, the more kids I lose. I make math more familiar at the expense of a lot of good formal learning. Someday, at the pearly gates of mathematics, I’ll have to answer for that, I’m sure.

I mean, I lie awake at nights sometimes over it, but I tell ’em planes are a like a sheet of plywood that’s as thin as you can cut it and runs on forever in every direction and I teach ’em that multiplying negatives just works like that.

And then I jump into application as soon as possible.

6. Taylor the Teacher

September 3, 2007 - 8:26 am -

Although I have to confess to skipping some of the math-y stuff, I love your language analogy for teaching math. This exactly what we should all be doing — interdisciplinary thinking.

I am feeling chastised for not applying more math in the teaching of grammar, which I know certain math brains can do. Some students like the grammar parts of English class because it’s more rule-based. It’s not as rule-based as math, or half as rule based as we English teachers make it out to be, but for the kid with a math brain it can really help them with English.

Unfortunately, I’m not math brained enough myself to cook those lessons up.

Taylor

7. Matt

October 25, 2007 - 1:55 pm -

I gave your sheet “Evaluating Expressions sampler” to my fourth graders today as we were learning about variables. I just made a few tiny changes, but left it almost completely intact. They were completely motivated when I told them that it was high school work. And many were able to complete it correctly.

I told them that I would tell you!

Thanks.