Saturday, October 24, 2015

501: Learning time

Read this post on lost learning time.

Here's his basic point:
... roughly 10 of 60 minutes are not spent learning. 
In one day, roughly 50 minutes.
In a 5 day week, 250 minutes.
In a typical school year, 8,700 minutes not utilized for learning.

Now, let's be realistic and cut that number in half because we all know there are assemblies and other events that cut into learning time throughout the school year. That leaves us with 4,350 minutes of time not spent learning.
  1. Do you agree with his analysis?
  2. How about his calculations?
  3. What should be done?

Monday, October 19, 2015

500: Secret Salary

My employer has nine workers. The nine of us want to determine what our average salary is, but none of us wants to divulge his own salary. Can we find the average without doing so?


499: Blue-Eyed Blondes

If the proportion of blonds among blue-eyed people is greater than among the population as a whole, is it also true that the proportion of blue-eyed people among blonds is greater than among the population as a whole?


498: Circles on a Lattice

On a square lattice, a circle can pass through 2, 3, or 4 points, as in the diagram below. The original question asks for a circle that passes through 5 points, but can you define a circle that passes through other numbers of points? and explain how the circle was created?


Sunday, October 11, 2015

497: Factor Grids

Source: #mathsTLP

496: Determining the Discriminant

How many different solutions can we find?

495: Pythagorean anti-Triples?

Ask your class if there are any Pythagorean anti-Triples: $\dfrac{1}{a^2} + \dfrac{1}{b^2} = \dfrac{1}{c^2}$ ?

If a, b, c are integers, the question seems harder, since 1/3, 1/4, 1/5 would be (to me) obvious answers - leading to the rules for Pythagorean triples and just using their reciprocals.


Saturday, October 10, 2015

494: NetFlix Optimization

An article about the Netflix price hike:

Netflix upped the rate of its “two-screen” plan from $8.99 to $9.99. This plan lets you watch two HD (or regular) streams simultaneously on different devices.  Netflix’s “one-screen” and “four-screen” plans remained unaffected.
Here's the thinking: If Netflix subscribers start dropping from the two-screen plans to one-screen plans, this will make them a lot less likely to share their password. No one wants a little offhand altruism to actually affect their viewing habits. That would be bad. If the resulting lack of password-sharers pushes more people to subscribe, then its worth the dollar per subscriber Netflix loses when a user downgrades because of the price increase.
Find the NetFlix subscription numbers to see how the price hike changed things. Was this a good move?