Here’s my latest addiction. It’s a game called Planarity. Rearrange the blue vertices so that none of the edges overlap.

So far, I’ve made it to the 16th level with a score of 6611. Take a screenshot of your best score and post it in the comments.

This past Friday, my school had an inservice day for the teachers. I was responsible for a small portion of the day. It was my task to provide a demonstration of the Four Corners differentiated instruction strategy to the rest of the faculty. I decided the best way to accomplish that was to actually go through the activity instead of just telling my colleagues about it. So of course, I based the activity on a mathematical statement. Usually, any discussion of mathematics with the faculty in general is met by moans, groans, and eye-rolling. This time, I was surprised. But I’ll get to that in a minute.Four Corners works like this:

1. Teacher writes a debateable or controversial statement on the board.
2. Students move to the corner of the room where the sign is posted that most closely represents their opinion on the statement.
3. Discussion, questions, and debate are then allowed between the four groups.
4. Next, students are allowed to switch to another corner if they changed their opinion.
5. Students are invited to explain what caused any change of opinion.

The statement I posed to the faculty was this:

There are more integers total (… -3, -2, -1, 0, 1, 2, 3, …) than there are decimal numbers just between 0 and 1.

The four statements that I posted in the four corners were:

I was quite surprised by the amount of discussion that my statement generated. It was very interesting to see how “non-math” people think about mathematics in a purely theoretical setting. The faculty really “dug” the discussion and many of them switched corners as thoughts and arguements were shared.

Ultimately, they ended up fairly evenly divided amongst the four corners. By the end of the activity, they were begging me to tell them which response was actually the correct one (I had told them that one and only one of the responses was indeed correct). I eventually did tell them. But in this post, I’ll leave it to one (or more) of my readers to leave a comment as to which response should be chosen to the above statement.

I’m thinking of a real number. What is it?

You’ve got 20 yes/no questions at your disposal.

Whenever you are ready, ask.

Here’s a quick (maybe) brainteaser from Elias over at Ramblings of an Australian Teacher.

In the multiplication

P Q R
x 3
——
Q Q Q

each of P, Q and R represents a different digit. The sum of P, Q and R is
(A) 16 (B) 14 (C) 13 (D) 12 (E) 10

Think you know the answer and can give a clear explanation? Then email Elias the solution (and post it in a comment here).

The last post contained a fairly easy problem. Now here’s one that is a bit more challenging.

In the figure below, a circle with a center at O and a radius of 4 is inscribed in triangle ABC. Point D is a point of tangency. Segment AD has a length of 8 and segment BD has a length of 6. Find the lengths of the three sides of the triangle — without using trigonometry (sine, cosine, tangent).

[This problem was posed to some mathematics teachers by Victor Katz at the San Antonio national conference of the NCTM.]

Here’s a problem that is a good one to give your Algebra 2 students (or anyone who’s interested).

Find the two distinct numbers whose product, quotient, and difference are all equivalent.

[in layman’s terms] Find two different numbers that, when you multiply them, you get the same thing you do when you subtract them or divide them.

I’ll not give the answer in this post. You give it to me in a comment.