- (
*Community*) Start learning names, and get them learning each other's names. - (
*Expectations*) Don't spend much time on the syllabus; there are more important things to do. (Have them read it, and then you can quiz them on it the next day, or just ask for their questions.) - (
*Learning, Expectations*) If you use group activities (which are a very effective way to help groups of students learn), then you want to introduce students to this on day one. - (
*Curiosity*) An activity that helps them see what's coming in the course would be especially nice.

Our classes start in

**First day activity for Calculus I**

I have them graph a parabola (y=x

^{2}), then draw a tangent to it at x=3. (Some don't know what that means, so I walk around checking.) And then

*its slope. After they're done, I get to talk about what makes actually finding the slope hard - such a good intro to the course. And they've had time to review graphing a parabola.*

**estimate****First day activity for Linear Algebra**

I have them solve a system of 3 equations in 3 variables. I ask them to:

- Write down a description of the process,
- Solve the system,
- Now figure how to check whether your answer is correct. (Naysayers, has the group done enough to be sure that the answer is correct?)
- Extra: What does each equation represent geometrically? What does the solution represent geometrically?

**First day activity for Geometry**

I taught geometry earlier this summer for the first time. I had them draw a triangle (and make sure it was different than their neighbor's). Find the midpoints of each side (they could measure or fold). Connect each midpoint to the opposite vertex. I hoped most would do it well enough that the 3 connecting lines would intersect at one point. My goals were to highlight: vocabulary, shapes, construction (which we were not doing with straightedge and compass - yet), conjecture, and the possibility of proof.

**First day activity for Precalculus**

I've been thinking for the last few weeks about what I'd like to do for Precalculus. I have found exciting activities in the past that turned out to be way too hard, and intimidated the students. I have a lovely fractions activity, but that doesn't represent what we'll do going forward.

I am working hard to create an activity that looks at functions (and circles too) from 4 perspectives: equations, graphs, tables of values, and stories. I have 7 types of relationships (linear, quadratic, polynomial, rational, exponential, periodic, and circles). I don't have stories yet for the polynomial and rational. (My eternal gratitude to anyone who can give me a story I like for either of these.) And I won't show an equation for the periodic. (A trig function wouldn't make sense yet. But we'll get to discuss that.) So that makes 25 "clue sheets".

I have 40 students, who I'll put in 10 groups of 4. Each group will start with two clue sheets. [So 5 of the sheets will not be handed out at first. I can label those as graphs on the back, keep them at the front, and let student turn them over once they're pretty sure they didn't find a graph match to their set.] Each will describe a different type of function/relation from one perspective and ask them to do a few things. Then they pair up with a clue sheet for each pair, and go looking for the matching clue sheets (same function/relation, different perspective). They go back to their group and explain to each other what they found. (I'll have extras up front, so anyone done early can work on a 3

^{rd}function/relation.) When we're done, we'll have a summary of the function types we'll be studying all semester.

I dreamed some of this up late last night. When I started working today, I worried that it would be too hard. (I make up some crazy stuff sometimes when I'm falling asleep.) So my goal as I put this together has been to scaffold it enough. I am assuming some comfort with linear functions, and some familiarity (but not comfort) with quadratics and exponentials. They may not have encountered the others. (And most will not know any trig.)

I put my

Edited (8/17): This is a great activity, but too complex for day one. I will do it on day two. On day one, we will review linear functions in a similar, but much simpler way. Here is my handout.

**My Goals**:

- Review plugging values in for x to find y. (Do they remember that b
^{0}=1? What else might trip them up?) - Review graphing.
- See functions/relations in the context of modeling a situation.
- Identify functions/relations by type.
- See precalculus as a place to strengthen their understanding of all of this.

If you use this activity, please let me know what changes you decide to make and how it goes.

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