456: A and B

The problem speaks for itself.

A nice pair of questions from @pdaro. What do you think your students will say? #mathchat pic.twitter.com/mLtGRZei3O

— David Wees (@davidwees) May 10, 2015

455: Another Proof Without Words

n³ - 1 is always a multiple of n - 1 #ProofWithoutWords pic.twitter.com/CkOKg0wD6O

— Roy Wright (@Sted304A) April 14, 2015

454: Fraction Sum

Seems like a tough problem.

"Wait a minute. That would make it easier ..."

 source.

453: Kong Size Cereal Box

What do you think? Where's the mistake and why do you think they presented it this way?

source:

Via @mburnsmath, a math mistake. Does it reveal something interesting about how people think about math? 

— Michael Pershan (@mpershan) May 4, 2015

452: Rose Petals

Go to this page at Desmos, and hit play. Explain what you see and why it is behaving that way.

There is obvious symmetry in the figure at each value of a but should we be defining something new to describe the sequence of images? A dynamic symmetry, of sorts?
Source:

https://t.co/WJMf86X3BA hit play. explain why this is true. cc: @MathCurmudgeon @Desmos #mathchat

— Dylan Kane (@math8_teacher) May 3, 2015

451: Growth Rate

Population of organism after n minutes is $P(n) = k*9^{(\frac{n}{2})}$.
What is the growth factor?

... algebraically stated, what is the ratio of P(t+1):P(t)?

Source:

#SATPrep Population of organism after n min is P(n)=k•9^(n/2) P( t+1):P(t)? #mathchat 

— David Marain (@dmarain) April 30, 2015

450: One-third of a triangle

You've been asked to shade one-third of this triangle.

And how do you know?
Here's a response:

• Is this a valid way to get one-third of the triangle?
• Does this technique require that we stipulate a right triangle?
• Does this technique require that we stipulate an isosceles one?
• Do the lines have to be parallel to each other?
• Do the lines have to be parallel to a side for this to work? 
• Perpendicular to a side for this to work?

• How might we generalize this method (if it can be generalized)?

sources:

Try to shade 1/3 of this triangle. How do you know it is 1/3? #mathchat #elemmathchat pic.twitter.com/KaLtPglBfV

— David Wees (@davidwees) May 2, 2015

@davidwees this may be more than you want pic.twitter.com/Azlkv1kwAw

— David Sawtelle (@davesawtelle) May 2, 2015