CA Super Lotto, 2017
The CA Super Lotto takes is a raffle in California in which people pay a small amount of money to win a great amount a cash. In groups we wanted to calculate the probability of someone anywhere in the states ability to win the lotto.
Process and Solution
Our first shot at the problem consisted mostly of trying to understand what we were being asked to find. In the beginning we divided our understandings of what we already knew about the problem and what questions we still had. What we knew was that we had to multiply the numbers 4347 because those five numbers are the options the person playing the lotto are given (choose five numbers between 147, they cannot repeat!). Doing that gave us a total of 184,072,880. After applying the knowledge we already had, we were left with the Super Number option (choose a number between 127). This is where we ran into difficulties.
My group asked other teams in the classroom how they understood the problem and what they thought the next step would be. Even after that we weren't sure how to go about the second part to the problem, so we asked the teacher.
Myself and my peers asked questions and proposed potential solutions until we came to the most rational solution that went hand in hand with what other groups were doing and was approved by the teacher, which was to multiply 27 by the total we got before.
Myself and my peers asked questions and proposed potential solutions until we came to the most rational solution that went hand in hand with what other groups were doing and was approved by the teacher, which was to multiply 27 by the total we got before.
Problem Evaluation
The CA Super Lotto Problem was not the type of math that I am used to. This problem relies mostly on ones ability to think about numbers and what to do with them vs. plugging it in to a consistent formula. Striving to be able to do this pushed my thinking and my ability to understand probability math problems.
Self Evaluation
The class spent roughly six weeks working with the probability unit that built our understanding of the math in order to finally be able to solve the CA Super Lotto problem. Throughout these weeks I struggled with being able to solve even the simplest problems. Personally, probability is not something that comes to me naturally. Maybe it is because I have a hard time visualizing the quantities or I never heard of the terminology used to solve the problems but essentially I felt that I had to work extra hard to understand what was being presented. I was always the student to ask questions, take notes of everything on the board, and scored a 100% on the unit test after infinite self doubt and uncertainty. For these reasons I feel as though I deserve an A on my effort and work from the past weeks.
Height of the HTHCV Flagpole
For the launch of this math activity we were presented with the following question; HTHCV wants a new flag for the pole outside. It must be as big as possible but there are regulations to how big the flag can be based on the pole. How tall is the flagpole? My initial guess to how tall the pole was 40 ft minimum. After making this guess the class went outside to look at the pole and think of possible ways to measure its' height.
The Shadow Method
We realized that we could use our shadows and the flagpole's shadow to measure the pole's height as long as we took our measurements at the same time during the day for the shapes to come out similar. Similarity means one object equal to another can be obtained by scale even if they are not exactly the same.
My group took a ruler outside and found the necessary measurements to solve the formula. We plugged in the information we found and solved for X (the height of the flagpole). We found that the flagpole is approximately 37 ft tall.

This is what our problem set up looked like. X = the pole's height because that is what we want to solve for. I used cross multiplication to find X.
Setting X/the poles shadow = a persons height/their shadow would make sure the two figures are to scale and solve accurately for X. 
The Mirror Method
Another way of solving for X, or finding the height of the flagpole, was using the mirror method. One student would place a mirror on the ground near the base of the flag pole as long as they could see the top of the pole in the center of the mirror. The student would stand still as other's measure the distance between the base of the pole to the mirror, the student to the mirror, and the height of the student. By using cross multiplication just like in the shadow method and using X/length of pole to mirror = height of student/length of student to mirror we were able to solve for X and find that the approximate height of the pole is 23 ft tall.
The Isosceles Method
The final method to finding the height of the problem is using the isosceles method. An isosceles triangle always has two similar angles and two similar sides. With that rule my group decided that by measuring the distance between the pole and a person you have already found an equal side length to the triangle as long as two angles equaled to 45. We found the degree of the angles by stepping back and holding up a protractor. The approximate height of the pole by using this method is 24 ft.

My final estimation for the flag pole is 28 ft tall. I found this height by finding the average between all my results (adding 24, 23, and 37 and then dividing by 3).
Problem Evaluation
The flagpole problem was very interesting and engaging throughout the solving process. Something I struggled with was understanding the isosceles method and how to use the protractor. I learned how to solve the problem with this method by asking my group and talking about why the solution worked.
Self Evaluation
If I were to grade myself on this similarity unit I would give myself an A. This is because of my participation within my group and how I helped my peers understand questions they didn't and how often my group would work though questions together.
Self Evaluation
If I were to grade myself on this similarity unit I would give myself an A. This is because of my participation within my group and how I helped my peers understand questions they didn't and how often my group would work though questions together.
Edits
For my peer critique feedback I was suggested to add more titles to my writings, for example including "Problem Eval" before my sentences started.