12 of 30 Items .... Type: Open Middle

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It's a well-known formula ... your age divided by two, and add seven. If your date is any younger than that, it's just creepy.

By this calculation, what is the youngest you are allowed to go on a date?

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If the variables represent distinct integers between 20 and 50, what is the largest possible value of the two sides of the equation.

\(\dfrac{a*\dfrac{b}{c}}{\dfrac{d}{e}}=f*\dfrac{g}{h} \)

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Choose the path through the grid that you feel will gather the most points.
You start out at the bottom with 1 point.

While moving from the starting point to the goal, calculate your score by using the "+", "x", and "-" symbols along the way.
Calculate at each step - order of operations is turned OFF for this puzzle.



For example:
N-N-N-N-N-N-E-E-E-E-N would earn 54 points.

You can cross your own path, but you can't take the same route twice, or return along a path you've already taken.

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Using the digits 1-9, complete the number line below.
Each digit can be used only once.
B is halfway between A & C.




Possible solutions?

Food for thought: What is the greatest difference between A & C while still fitting all three parameters?

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There's a neat game you can play with the English language: Place the word "only" anywhere in the sentence. How does it change the meaning?

Only she told him that she loved him.
She only told him that she loved him.
She told only him that she loved him.
She told him only that she loved him.
She told him that only she loved him.
She told him that she only loved him.
She told him that she loved only him.
She told him that she loved him only.

What would it look like if we were trying to create a math problem that worked the same way, except "only" is replaced by the equals sign?

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Can you create a 10-digit number, where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number?

Some hints:

Can it be 0000000000?

Can it be 9000000000?

One answer, slightly obfuscated, is 2³ * 5³ * 7 * 887143

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How many different solutions can we find?

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Here is a list of numbers.



You create the problem ... what hints will you give?
What values of mean, median, mode, range, quartiles?

What are some different statistics that you could give to a classmate (other than the ones below) yet still keep this a solvable problem, with the same answers as the original problem?

Original problem:

mean = 76;
range = 32; IQR = 21

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A Challenge from StandupMath:

Can you arrange the integers 1 to 17 so that each adjacent pair adds to a square number? 

Hey!

What if we didn't put them all in a straight line? What's possible if you do that?

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Start with this:




You know how Open Middle questions work. What questions could you ask?

Here are some thoughts from one class.

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Directions: Using the digits 1 to 9 at most one time each, fill in the empty blanks so that you create a triangle in which \(Cos Θ = \dfrac{\sqrt{2}}{2}\) and which uses the points: (5, 4), (__,__) and (__,__).

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