*if the angle at B and the angle at D are 90°? Because that sure would make it easier to find x.*

**KNOW**180 Days of Ideas for Discussion in Math Class. (as of 9July2014, we're in overtime!)

If we are told that we have a quadrilateral inscribed in a circle with diameter 10, do we **KNOW **if the angle at B and the angle at D are 90°? Because that sure would make it easier to find x.

This question is from the NY Regents test, and discussed by Patrick Honner in his long-running series, "Are These Tests Any Good?".

Can your students find what is wrong with it?

How would they fix it?

source.

Can your students find what is wrong with it?

How would they fix it?

source.

These questions are from the NY Regents test, and discussed by Patrick Honner in his long-running series, "Are These Tests Any Good?".

Can your students find what is wrong with them?

and

source.

Can your students find what is wrong with them?

and

source.

So ... I've seen a couple of YouTube videos that feature songs about the Quadratic Formula. I often see it written like this:

and it occurs to me that I've always written it this way:

Which one is better?

$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

and it occurs to me that I've always written it this way:

$x = \dfrac{-b}{2a} \pm \dfrac{\sqrt{b^2-4ac}}{2a}$

Which one is better?

Everyone older than ten knows that there is a way to play tic-tac-toe so that you can never lose. Any game that can be played to a draw unless someone makes a newbie's mistake, is boring once you know the secret.

Let's look at this one and see if you can find a strategy for it:

**Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.**

Is there a guaranteed winning strategy for Player 1?

Is there a guaranteed winning strategy for Player 2?

source:

Let's look at this one and see if you can find a strategy for it:

Is there a guaranteed winning strategy for Player 1?

Is there a guaranteed winning strategy for Player 2?

source:

```
Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.
— Chris Lusto (@Lustomatical) July 16, 2015
```

How does his later comment help? "It’s equivalent to tic-tac-toe since any row/col/diagonal in a 3x3 magic square sums to 15, but more mathematically interesting."
Everyone older than ten knows that there is a way to play tic-tac-toe so
that you can never lose. Any game that can be played to a draw unless
someone makes a newbie's mistake, is boring once you know the secret.

Let's look at this one and see if you can find a strategy for it:

There are thirteen pins and the two players take turns bowling.When bowling, you can knock down any pin or two adjacent pins (but not two that are separated by a space) that you like. The loser knocks over the last pin.

The gnome has bowled first, knocking down #2. How do you best play this game so that you are guaranteed to win?

If you go first, what is your best play?

source: Loyd's Encyclopedia, 1914.

Let's look at this one and see if you can find a strategy for it:

There are thirteen pins and the two players take turns bowling.When bowling, you can knock down any pin or two adjacent pins (but not two that are separated by a space) that you like. The loser knocks over the last pin.

The gnome has bowled first, knocking down #2. How do you best play this game so that you are guaranteed to win?

If you go first, what is your best play?

source: Loyd's Encyclopedia, 1914.

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