359: Lines and Diagonals

There's sequences all over the place. What are they?

Does your sequence predict the 20th case?

And the 11th and 12th?

358: Division and Remainders

Is that diagram correct?

What if the question were 13 ÷ 5 = 2 R3? Could we diagram it in the same way?

357: Box Office Receipts for The Interview.

"Sony doesn't say" .... but do we have enough information to tell anyway?

‘The Interview’ Brings In $15 Million on Web 
LOS ANGELES —
“The Interview” generated roughly $15 million in online sales and rentals during its first four days of availability, Sony Pictures said on Sunday.

Sony did not say how much of that total represented $6 digital rentals versus $15 sales. The studio said there were about two million transactions over all. 

source. @ddmeyer

356: Partridge in a Number Tree

You know the song. "And a Partridge in a Pear tree." What patterns of numbers can we find here?

The first partridge.

If you look at the total gifts each day, what sequence of numbers is this?

Four Calling Birds, calling out numbers ...

How many different ways are there to find the total number of gifts given over the twelve days?

355: Millionaire

Would you guess? $250,000 if correct and $100,000 if she refuses to try for it.

354: How to Teach Division

So, students. You've had a chance to weigh in on addition and multiplication.

What is the best way to do division?

353: How to Teach Multiplication

There are several ways to teach multiplication. Many people seem to feel that students know best how they learn, so I'm asking students to weigh in on this particular issue.

Which method is best? Is there a difference between what we should be doing with elementary students and with high school students? With how much and with what do students need to graduate high school and enter the RealWorld?

Hindu Lattice Method	Grid Method
Standard Algorithm	Japanese Sticks

352: How to Teach Addition

Everyone seems to have an opinion and now, students, we're asking for yours.

Scott Macleod says, "We now live within multidirectional conversation spaces in which 12-year-olds can reach audiences at scales that previously were reserved for major media companies, large corporations, and governments. We all now can have a voice. We all now can be publishers. We all now can find each other’s thoughts and ideas and can share, cooperate, collaborate, and take collective action."

So how should addition, and by extension subtraction, be taught?The standard algorithm or by piecewise addition?

Weigh in on the "Letter to Jack".

How would you teach these two problems?

351: Balance 6

Weights 1lb through 6lbs.
Where should we start?

350: Primes

This little puzzle, via @mathmovesu, asks for three consecutive prime numbers.

Is the guess and check method the best way to go here?

Which prime numbers are candidates and which ones can we safely ignore?

349: Hole-in-One Insurance

If the average golfer is able to get a hole-in-one once in approximately 3000 rounds of golf (18 holes apiece), then what is the probability of any one of 100 average golfers getting a hole-in-one on the 5th hole during the weekend golf tournament?

What's the best way to find this out if you're the insurance company that will write this policy?

348: Homer's Pythagorean proposition

$1782^{12}+1841^{12}=1922^{12}$

Wait, didn't Fermat say this was impossible?
What's a three-second way to tell that this equation is false?

347: Combinatorics

Consider eight objects. We will choose them one at a time, two at a time, three at a time, and so on.

Which of these will result in identical numbers of ways?
Why?

346: Casting the Play

The cast of a school play that requires 4 girls and 3 boys is to be selected from 7 eligible girls and 9 eligible boys.

• Will it be a different calculation if the boys are willing to play girls' parts, as in Shakespeare's time? If so, how will it be different?

345: Fair or Foul?

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

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

Is this die loaded?
What is the probability he will get a 6 on the next roll?

344: Monty Hall

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

 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?

343: Forces and Friction

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?

342: Algebret

That takes care of four letters.

twenty-two to go ....

341: Sensible or Not? Study Types

Defend your answer! Here's your claim ... what's your warrant?
Give an example or a situation to bolster your position  

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

340: Giving Raises

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.

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

source: illustrativemathematics.org

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

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

334: Which values of x do we choose? Absolutes

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.

• 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?

333: Which values of x do we choose? Radicals

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.

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

$y = \sqrt{x+2}$

$y = \sqrt{1-x}$

$y = \sqrt[3]{2x+1}$

What are your favorite examples of this?

332: Which values of x do we choose? Rational functions

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.

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

$y = \dfrac{4}{(x+2)(x+11)}$

$y = \dfrac{1}{x^2+1}$

$y = \dfrac{1}{x^-1}$

$ y = \dfrac{x+2}{x^2-4}$

$y=\dfrac{x^2-1}{x^2+1}$

What are your favorite examples of this?

331: Which values of x do we choose? Trigonometry.

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.

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

$y = sin(3\theta)$

$y = \Big{sin(\theta)}^2$

$y = sin^{-1}(\theta)$

$r = 3sin(3\theta)$

What are your favorite examples of this?

330: Which values of x do we choose? Linear Functions

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.

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

$y = \dfrac{1}{3}x + 7$

$y = \dfrac{2}{7}(x + 4)$

$y = \dfrac{x + 2}{5}$

What are your favorite examples of this?

329: Which values of x do we choose? Quadratics

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.

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

$y = (x+2)(x-4)$

$y = -(x+1)(x+5)$

$y = x^2 + 6x + 9$

$y = \dfrac{1}{4}(x+5)^2$

What are your favorite examples of this?

328: Which values of x do we choose? Conics

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.

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

$x^2+y^2=25$ 

$\dfrac{(x-1)^2}{9}+\dfrac{(y+2)^2}{16} = 1$

$\dfrac{(x-4)^2}{9}-\dfrac{(y-4)^2}{16} = 1$

What are your favorite examples of this?