You are constructing stairs inside of a house that go up a total of 20 feet. What are the best dimensions (height and length) of each step on the staircase? Draw a diagram of your finished staircase, labeling the height and length of the steps. Explain why your stairs with these dimensions are the most logical. Draw two diagrams of stairs that would NOT be good options. Label the dimensions of these stairs as well. Explain why these stairs would be unreasonable.

You are on a SWAT team in Chicago, and you have come across a bomb that is going to explode in 1 minute. Time is not on your side! The combination to disarm the bomb is equal to the all of the roots of x^3+2x^2-8x in decreasing order. The only tool that you have at your disposal is a graphing calculator, piece of paper, and a pencil. How are you going to stop the bomb from going off without a disarming kit! Brainstorm the different ways that you can crack the code.

In your groups, create a story that can be described from this graph. Make sure you label the x-axis and y-axis and describe your reasoning.

In 3 minutes list everything you can think of that is found in space— besides planets !

You are playing catch with your dog and you throw the ball up into the air. It takes 16 seconds for it to hit the ground. Draw this scenario and list the possible mathematical concepts from our unit that this problem utilizes.

In three minutes, list everything you know about “climate change.”

You have been asked to design a new bumper car ride for the local amusement park. They have asked you to keep cost in mind, as well as what will make for a “fun” bumper car ride. One unit of flooring costs $5 and one unit of railing (used to surround the floor) costs $10. Come up with a design and explain why you think it is the best design for the criteria.

Divide your paper into two columns. For the next 5 minutes, write down everything you know about black holes in one column and everything you know about gravity in the other column.

Say you are playing tetris and this is your board. Where would you place the purple object? Show your moves with arrows, and draw the figure in its new place.Describe the steps you took to get this shape to its final location.

How would you describe the path a car takes traveling from the Engineering Quad to Assembly Hall? Compare it to the path a bird would take. Are there other ways to get to Assembly Hall from the Engineering Quad?

There are a lot of events in everyday life that are affected by chance. For example, some people play the lottery, while others refuse to ride in planes because they are afraid of the chance of a plane crash. Can you think of other situations that are affected by chance? List as many as you can in 3 minutes.

Since we know the shortest distance between two points is a straight line, why do airplanes fly along a curved path when travelling from one city to another?

Say you are riding your bike around the neighborhood. You come to a fork in the road, where one way has a hill with the slope of 4/5, and the other is a hill with a slope of 1/5. Which way would you choose? Explain your answer.

You can choose any 7-digit phone number and you are trying to figure out all the different possibilities. You make two lists. The first list has phone numbers where digits can be repeated. The second list has phone numbers where digits cannot be repeated. What are the differences between the lists? Which one would have more? Why?

Write down all the types of “waves” that you know or have heard of. Then, describe as best as you can what they look like, what they can do. You have 3 minutes to do this.