Problem Statement: (Restate the problem using words, pictures, and/or a diagram)
Dr. Drew is building a new patio with tiles. Some of the tiles need to be stronger than others because they are on a diagonal line that people are more likely to walk on. He wants his patio size to be 60 tiles by 90 tiles. He wants to know how many extra strong tiles he needs to buy for that's size. Dr. Drew kept changing his mind and wants to know the formula that way it's easier in the long run.
Process Description: (How did you try to solve the problem? You may also consider how others in your group tried)
Unfortunately the way I did it did not help me find the formula. I did it the long and hard way. I got six sheets of graph paper, taped and stapled them together, then drew out 60 by 90. I drew the best diagonal line straight across and got the answer of 95 tiles. Not knowing that this is on point correct but I’m 99.9% sure it is.
Extensions: Invent some extensions or variations to the problem; that is, write down some related problems.They can be easier, harder, or about the same level of difficulty as the original problem. (You don't have to solve these additional problems.)
1.A)
Mathew is building a pool for him and his friends to skate in. There is a invisible diagonal line through the pool that is skated on more than other parts of the pool making them wear down quicker. Mathew wants to know how many extra strong tiles he needs to buy in order for them not to wear down as quickly. The dimensions of the pool are 60 by 90 tiles. How many extra strong tiles does Mathew need to buy for his new pool.
1.B)
After talking to a pool specialist Mathew kept changing his mind on the size of the pool, He wants the Formula for how to find the amount of extra pool tiles he needs. Can you find the Formula and give it to him?
Solution: (The end result, wrong or right, it doesn’t matter! Include one or many solutions as long as they make sense to you!)
The one solution I used was the drawing out of a 60 by 90 patio on 6 pieces of graph paper.
I drew the diagonal line and shaded the squares that that the line went through. It came out to around 95 extra strong squares.
Self-Assessment: Reflect on two Habits of a Mathematician you used when solving this problem
The two habits of a mathematician were staying organized and being systematic. Having six pieces of graph paper that are connected is a space taker, I taped them together that way it could be organized and not take up space.