387: Which Shape Doesn't Belong?

From Talking Math With Your Kids

"Which shape doesn't belong?" is a question that kids of any age can deal with.Each page has four shapes, any of which can be considered "wrong" for some reason. Challenge your kids to find a reason for why each shape might not belong in the group of four.

From Talking Math With Your Kids


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386: Finding Primes the Euler Way

Trying to find a prime number seems difficult. You have to test it against divisibility by all of the primes that are smaller. But what if there were a formula?

Take a counting number, multiply it by itself, subtract it from the result and then add 41

1x1 = 1; 1-1 = 0; 0+41 = 41. That's prime.
2x2 = 4; 4-2 = 2; 2+41 = 43. That's prime.
3*3 = 9; 9-3 = 6; 6+41 = 47. That's prime, too.
4*4=16; 16-4=12; 12+41= 53. That's also prime.

How good is this idea?
Will it ever fail?

385: Demographic Oddity

Can you explain how this is possible? Qatar is only 23.5% women?

Before we get into these issue-specific statistics, we can see in basic demographics something that’s different about living in Saudi Arabia as a woman: Only 42.5 percent of the population is female. There are only five countries in the world (for which we have data) with a smaller percentage of female residents, according to the World Bank: Qatar, where just 23.5 percent of the population is female, the United Arab Emirates (29.9 percent female), Oman (36.4 percent), Bahrain (37.8 percent) and Kuwait (40.2 percent).

If you want to see a reasonable explanation, go to the
source.

384: Inscribed Squares

In terms of "this inscribed in that", what do we have here?
Describe the squares and their sizes compared to the circle.

1. If you were to calculate distances (radii, side lengths) or areas, what given information would you like to start with and what would you like to solve for?

• What "givens -- answer" path would be easiest?
• What "givens -- answer" path would be difficult?
• Which would you choose to give to your fellow students as a collaborative question?

N.B. The original question is slightly different. You can see it below.


Source.
Original image, click to enlarge.

383: Selecting Thoughtfully

source: Don Steward
"this resource follows a fine series of posts on MathArguments180 'which values of x do we choose?' (number 330)

382: Arena Funding

This graph is distorted.

• How is it distorted?
• What change in its message is achieved by this distortion?
• How would you fix it?

381: Just About Half

This graph is distorted.

• How is it distorted?
• What change in its message is achieved by this distortion?
• How would you fix it?
• What would have happened if they'd had more than 50%?

380: Standing Tall

This graph is distorted.

• How is it distorted?
• What change in meaning is achieved by this distortion?
• How would you fix it?

379: We All Scream for My Screen

This graph is distorted.

• How is it distorted?
• What change in meaning is achieved by this distortion?
• How would you fix it?
• Of the several ways to adjust this graph, which is best?

378: Irish Ayes are Happy ...

This graph is distorted.

• How is it distorted?
• What change in meaning is achieved by this distortion?
• How would you fix it?

377: Oil in the Water

This graph is distorted.

• How is it distorted?
• What change in meaning is achieved by this distortion?
• How would you fix it?

376: Graduation Rate Growth

This graph is distorted.

• How is it distorted?
• What change in its message is achieved by this distortion?
• How would you fix it?

375: Pencils and Jars

374: Geometric Transformations

Source:

I thought of another possibility. What could a student who does this be thinking? #mathchat pic.twitter.com/aktviLLeii
— David Wees (@davidwees) January 17, 2015

373: Product Puzzle 4

For the last couple of days, I've been asking you to create a new puzzle. Today, I'd like you to describe HOW to create a puzzle with a unique solution, or two solutions, or three. How did Don Steward create these and KNOW that they only had one solution?

source.

372: Product Puzzle 3

Put algebraic expressions into the cells so that the product is as indicated. That's for warm-up.

That's not what I'm going to ask you to do, though ...

Make a new puzzle with two solutions.

source.

371: Product Puzzle 2

Put integers into the cells so that their product is as indicated. But that's not what I'm going to ask you to do, though ...

Make a puzzle with exactly 3 solutions.

source.

370: Product Puzzle

Put integers into the cells so that their product is as indicated.
source.

369: Transformational Spider

Can you figure out how this works?

source.

368: Number Puzzle

source.

367: Making a Bigger Cylinder

Well?

To increase the volume of a cylinder, is it better to increase the radius or the height? Great conversation starter today. #math #mathchat
— Patrick Honner (@MrHonner) January 9, 2015

Je Suis Charlie

366: Minimal Math Cube

You only get to make one and you've only got 6 sides. What are the six most important items of math in your opinion? What would you put on your Minimal Math Cube?

365: Exponential Fun

If a and b are both positive integers, $a^{a - b}=10^6$,

list all possible ordered pairs (a,b).

What are a couple of different ways to approach this nugget?

What are the "obvious" answers that everyone will miss?

If a,b pos int's, a^(a-b)=10^6, list all possible ordered pairs (a,b)?
Ans:(10,4);(100,97);(1000,998); (1000000,999999)
— David Marain (@dmarain) January 3, 2015

364: Yearly Numerology

Time and Chance

A deck contains 52 cards, 12 court cards, 4 suits, and 13 ranks.
A year contains 52 weeks, 12 months, and 4 seasons of 13 weeks.
If A=1, J=11, Q=12, and K=13, then the values in a deck of cards total 364.

What do you make of that?


The number of gifts given out in "The Twelve Days of Christmas"? 364
On what day of the song is the middle gift given?

363: Without Solving for a Variable

Make similar questions ...

If  x² + y² = 196 and (x - y)² = 36, what is the value of xy?

1. -116
2. -80
3. -8
4. 80
5. 160

362: Adding Fractions Again

How can we approach this beast of a problem without finding LCM?

$\dfrac{1}{1} - \dfrac{5}{6} + \dfrac{7}{12} - \dfrac{9}{20} + \dfrac{11}{30} - \dfrac{13}{42} + \dfrac{15}{56} - \dfrac{17}{72} + \dfrac{19}{90} = \dfrac{a}{b}$

361: Futurama Balancing Act

;-)
It's Futurama ... make your own question but this just doesn't look right to me. Scale, mass, distance. What do you think?

360: Happy New Year 2015

What do you notice about these three equations?

10 x 9 x 8 x 7 ÷ 6 ÷ 5 * 4 * 3 - 2 +1 = 2015
(4 * 7 * 69 ) + 83 = 2015
(69 - 4) * (38 - 7) = 2015

Which one do you like best?

source: @alexbellos