Directions: Using any number between 1 and 6, fill in the boxes to create a true statement. You may only use a number once.

# High School

# Rational Exponents- Open Middle Problem

Directions: Using any number between 1 and 9, fill in the boxes to create a true statement. You may only use a number once.

# Complex Number Operations- Open Middle Problem

Directions: Using the digits 1 to 9, fill in the boxes to make the equality true. You can use each digit only once.

How does changing the signs between the Complex Numbers change the problem?

How does changing the signs between the Real and Imaginary parts of the Complex Number change the problem?

# Properties of Powers- Open Middle Problem

Directions: Using the digits 1 to 9, fill in the boxes to make the equality true. You can only use each digit once.

Can you write this expression in another way?

What is this defining?

# Data and Standard Deviation2- Open Middle Problem

So my local Probability and Statistics guru (@veganmathbeagle) sent me a problem she encountered in a textbook that was very Open Middle-ish. I modified it a bit and here it is…

Directions: Using the numbers 1 to 9, using each only once, create a data set of 4 numbers that fit the following criteria:

The four numbers have the smallest possible standard deviation:

___ , ___ , ___ , ___

The four numbers have the largest possible standard deviation:

___ , ___ , ___ , ___

- Is there more than one data set for either question? If so, what is it?
- How would allowing the use of repeat numbers effect the standard deviation?
- What would your data sets look like if this was allowed?

# Data and Standard Deviation- Open Middle Problem

Directions: Using the numbers 1 to 9, using each only once, create a data set of 5 numbers that fit the following criteria:

Mean = 5

Standard Deviation = 2.6

___ , ___ , ___ , ___ , ___

- Create a data set with the same mean but a smaller standard deviation
- Create a data set with the same mean but a larger standard deviation
- Explain why your standard deviation changes but your mean remains the same
- Explain what changes would happen if this is a sample of the population
- What would happen to your mean and standard deviation if you added 20 to each of your initial data points?

# Creating Probability Area Models

Directions: Using triangles to partition a square with side length of 6, create the following probability area models:

1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9.

- How many triangles are needed to create each?
- If you are unable to create some of the models, explain why.
- What modifications to the problem is needed to create all 9 probability area models?