Hard Parts Day 65

7/29/2019 Hard Parts Day 65

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Theres the desire for a nice, clean way to do this every time, but what do you

want us to do, just Guess? And then you want to tell us not to guess? Whatsgoing on here?

o There needs to be more clarity about what it is that were aiming for here.

Do whatever it is that you think you need to do to solve the problem

Pause: I need to clarify my teaching assumptions.Theres a shortcut. Why not give kids the shortcut?

Well, they wouldnt remember it or its purpose. Its hard to position something as a

shortcut.Yes, we would. I always remember things when theyre given in a clear series of steps.

Oh, yeah? Then why cant you solve equations?

Heres the justification:

Being smart means not just knowing how to solve one particular problem, but

figuring out how to use the tools that you have.

You guys have the tools for solving this problem, you just dont know it yet. It takes time for your mind to organize itself, though, and the way that it does that

is by working out.

Doing something hard will force you to realize what exactly it is that yourelearning,

In short:

The coach will tell you the moves, and give you comments on your technique.

But to get good, you need to practice playing the game.

The game is answering questions that are different from anything youve everseen before.

The only way to get good at that is by trying to answer questions that are different

from anything youve ever seen before.

Yeah, at the end of the day Ill always give you feedback about what was good

and what wasnt with what you were doing.

Lesson Plan:1. Warm Up

a. Practice with the stuff that theyre good at.

b. I mean, except for the kids who arent good at that stuff yet.c. Lets give a problem with some tricky numbers.

2. Problem Statement

a. You guys can go forwards, right? Equation Points.

b. What about the other way? Points Equation?

c. An easy example: (0, 0), (1, 5), (2, 10), (3, 15)

d. A tougher example: (4, 13)e. A tougher example (4, 13), (9, 33)

3. Practice

a. One point problems


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b. Two point problems

i. Gapless

ii. Missing Stepsiii. Write a procedure

4. Wrap Up

a. Procedure?b. Reality Check

Period 2: Today youre going to learn how to make predictions when youre not given a

perfect set of data.

Notes:

CME has a nice touch, having kids up the mathematical complexity by finding the

balance point, which is a good exercise for finding the mean.

I like the dice problem from their Alg2 curriculum.

I also like the idea that wed have a problem for which they wouldnt have such astrong intuition.

There seem to be two components here: the idea that there are good enoughrules, and how do you find them systematically.

Hard Parts

Yesterday the kidoos werent into it. My take is that they didnt see the

constraints of the problem, and so found the exercise sort of foolish.

The major skill needed in this lesson is finding the equation of a line, and thatcould remain a tripping point for people who are just getting the hang of this

thing.

My instructions for how to handle the dice experiment are a bit lousy. They needsome working. (Add up the numbers that you roll? Probably just show an

example.)

Lesson Plan

1. Warm Up

a. Practice finding equations from linesb. How about one where they have to guess

c. How about one thats downward sloping

d. Then, into the dice experiment

2. Dice Experimenta. Roll 1 die. Record what you roll

b. Roll 2 dice. Add up all the numbers that you roll. (e.g. if you roll a 5 and a6, record 11)

c. Roll 3 dice. Same

d. Keep on going until you see a pattern.

e. What do you predict the sum of all the faces will be if you rolled 47 dice?3. Another data set? (What data set???)


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a. Copy the data from CMEs stuff

b. Or from their feet and height

c. Which of these equations is closest?d. It passes through the balance point

e. Then figure out a reasonable slope.

4. Practicea. Give em a handout

b. Maybe Arlington Algebra

c. Discovering Algebra?5. Wrap Up

a. When could you use what you learned today?

Period 3: Were trying to find out how to translate a graph around the plane. Specifically,

a trig function, but well study every function.

1. Warm Upa. Evaluating Trig Values

b. Graphing a circle of radius 1c. Graph something else, like y = sqrt(x)

d. Graph y = sqrt(x-2)

2. The initial observationa. Find an equation that fits this graph

b. Find an equation that fits this graph

c. The graphs are shifted to the right a bunch. The other is shifted down.

3. What are the rules? Why?4. Practice

a. Find reasonable equations for the graphs. Use a graphing calculator.

5. Wrap Upa. Trig Functions

b. How do we smoosh this so it fits the moon pattern?

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Hard Parts Day 65