- ONE: twenty-eight times
- TWO: twenty times
- THREE: fifteen times
- FOUR: thirty-one times
- FIVE: thirty-two times
- SIX: twenty-nine times.

What is the probability he will get a 6 on the next roll?

180 Days of Ideas for Discussion in Math Class. (as of 9July2014, we're in overtime!)

Sullivan bought a die at the magic shop. He
rolls it 155 times and gets the following results:

What is the probability he will get a 6 on the next roll?

- ONE: twenty-eight times
- TWO: twenty times
- THREE: fifteen times
- FOUR: thirty-one times
- FIVE: thirty-two times
- SIX: twenty-nine times.

What is the probability he will get a 6 on the next roll?

Once upon a time, the world's smartest person (Marilyn vos Savant, IQ: 228) received a question for her newspaper column …

Marilyn's answer was surprising to many people. What do you think?

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Craig. F. Whitaker, Columbia, MD

Marilyn's answer was surprising to many people. What do you think?

Your teenage son has a fast car.

He knows that friction is determined by the weight of the car over the wheels, the "normal" force. He also knows that additional weight means that the car can't accelerate as fast, but he's also having problems with the rear tires spinning out. He's convinced that having Fat Eddie sit in the back will help his quarter-mile time.

Will the extra weight help him or hurt him?

He knows that friction is determined by the weight of the car over the wheels, the "normal" force. He also knows that additional weight means that the car can't accelerate as fast, but he's also having problems with the rear tires spinning out. He's convinced that having Fat Eddie sit in the back will help his quarter-mile time.

Will the extra weight help him or hurt him?

Defend your answer! Here's your claim ... what's your warrant?

Give an example or a situation to bolster your position

Give an example or a situation to bolster your position

- The Department of Education conducted an observational study to determine the average salary of high school teachers in each of the United States
- A paint company conducted a double-blind experiment to determine which of two types of exterior paint was more resistant to rain.
- The lab conducted an experiment to determine whether the throat culture was positive for strep.
- In a study of medications designed to slow the rate of balding in men, a placebo group had better results than the control group.
- A meta-analysis was conducted to determine the population of New Zealand.
- A case-control experiment was used to determine the average family size in Utah.

A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine that you are in charge of deciding how the raises should be determined.

Use an atbash cipher decoder: http://rumkin.com/tools/cipher/atbash.php

- What are some variables you should consider?
- Describe mathematically as many different methods you can think of to distribute the raises. (We came up with nine; can you beat that?)
- What information will you need to compute those raises according to your various methods?
- Which of your methods do you feel is the most fair?

Use an atbash cipher decoder: http://rumkin.com/tools/cipher/atbash.php

- zm vjfzo znlfmg, gdl gslfhzmw vzxs.
- vjfzo kvixvmgztv yzhvw lm hzozib.
- mvklgrhn: 1p, 1p, 1p, 1p, Ldmvi'h hlm: 6p.
- R'n lmv lu gsv vnkolbvvh: 0p, 0p, 0p, 0p, nv: 10p
- kilwfxgrergb tlzoh: 1p, 1p, 2p, 2p, 4p
- olggvib, zoo li mlgsrmt.
- olggvib, 0p, 1p, 2p, 3p, 4p.
- zokszyvgrxzo liwvi, 0p, 1p, 2p, 3p, 4p.
- vnkolbvv'h xsrow'h gvhg hxlivh rm gsv olxzo hxsllo ... ru gsviv'h ml rnkilevnvmg, ml ylmfh.

For the following functions, think about "How to graph like a math teacher."
Math teachers want to sketch graphs quickly and efficiently and choose
values of x that work "nicely" in the equation and generate integer
values of y, thus making it easier to graph.

What are your favorite examples of this?

- Which points are best found by inspection?
- Which points are best found by substitution?
- Which points are best found by symmetry?

$y = \lvert x \rvert$

$y = \lvert x \rvert - x$

$y = 2\lvert x+2 \rvert$

$y = \dfrac{1}{2}\lvert x-3 \rvert$

What are your favorite examples of this?

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