Math Write Ups

Notice: What's in the color red means that I edit my mistakes or added something. I fix it by adding or moving an image, correcting grammer, adding a sentance, etc.

Visualizing Numbers

Problem Statement: For this assignment we were put into groups of four and handed a worksheet

identical to the picture on the right. We were then asked to figure out what the 36th shape would

look like. We were given 5 minutes to work alone and the rest of the time to work in our groups.

My First Step: Finding Patterns: As Iobserved each shape I realized that the 1st shape had 1 dot,

the 2nd shape had 2 dots, the 3rd shape had 3 dots and so on. That gave me the clue that the

36th shape would have 36 dots.

But What About All The Patterns With 4's?: As I continued observing I also noticed that all the

dots of every 4th shape were grouped up in 4's and 36 would be a 4th shape. This helped me eliminate the 27 other shapes and keep 8 shapes (numbers 4, 8, 12, 16, 20, 24, 28, 32) to observe. Within those 8 I saw that every 4th shape had the dots grouped of 4 stacked on top of each other to make a square shape.

(I added an image of the shape 32, on the

right, so my audience can visually see what

I am talking about and won't get confused)

32 As A Model For 36: Since 32 had them stacked on top like a square 36 wouldn't and that every 3rd shape was a triangular shape leaving number 36 to be none other than a triangular shape. With all these patterns that I discovered, I concluded that number 36 would like the picture below.

Other People's Process: Many people had different theory's of what number 36 wold look like, but something everyone did in common was try to find patterns. Once different people started finding different patterns, many great theory's arose. One of my classmates named Jose came up with the idea that every shape after the 5th that wasn't a circle had more sets than the actual dots in the sets. As he was explaining to me he used numbers 6 and 10 as examples.

In order to make sure his theory was correct I began to try and find a shape that didn't follow his theory and I quickly realized numbers 8, 10, 12, 18, and 30 didn't work with his idea. After many class discussions we challenged people's thinking and eliminated theory's and shapes that contradicted each other leaving us with two shapes that the number 36 could look like.

Assesment of Problem: Overall I did like this problem because it kept me engaged and it was fairly easy for me to find many patterns which led me to find my solution. It also tied into the video that we saw before tackling this problem which was talking about how seeing something drawn out can sometimes help your brain trigger a solution easier than watching something being done mathematically. This problem helped grow as a collaborator by appreciating other people's ideas and building off of them. I would also push my peers thinking by trying to test their theory and disagreeing with them in a polite manner.

Self Evaluation: If I were to self evaluate myself I would give myself an A. I believe I deserve an A because although I was discouraged at first I still approached the problem with an "I can do it" mindset. I not only pushed my thinking but I would push my classmates thinking by asking for evidence to back up their theory. By doing this I was able take time to really understand what their idea was which is an area that I grew in while working on this problem.

Cost of College 2015

Problem Statement:

PART 1: Our goal was to make a spreadsheet that contained fake student profiles to present the different financial situations people are put through. When finishing the spreadsheet we then presented this to parents and students at senior night so they could estimate their own cost of college.

PART 2: Our goal was to make different calculators in order to show how much students and parents would have to borrow and the amount that will have to be paid montly and in total on the loans.

Part 3: Our goal was to compare two different intersts we would like to follow after high schools and represent which would be the better path to take financially. We then made a presentation including every aspect of the project to have a conversation with our parents.

The Process:

PART 1: In order to produce different financial situations students grouped up in pairs of two and made a fake student profile. My partner Hannah and I then inputed the fake students home income, GPA, and # of family members in a net price calculator for CSU's and UC's to figure out how much our fake student will have to pay for college tuition. After obtaining this information everyone then added the tuition cost to a spreadsheet shared with the whole class.

PART 2: We individually made loan calculators that included the amount of student and parent loans that will be taken out based on the school's tuition and the amount of financial aid that will be provided for you. Once knowing that information it gave us how much the student and parent will have to pay monthly and in total on a 10 year and 25 year loan. We designed the calculator with different "if statements" in order to relate all of the calculator to one number. We designed it this way so we would only have to input the cost of college and the rest of the information would be given to us making it easier and faster.

PART 3: After making all of our calculators we then began to personalize the numbers. We made everything specific to what we were interested in. In doing so we made a graph that compared the yearly salary of at least two different paths we wanted to take after high school. We alo made a presentation that included the colleges we were interested in, the different calculators we made, and the comparison of both paths and which was the better one to take. Once finished we presented all of the information to our parents.

Solution:

PART 1:

Here is a link to the full document above

PART 2:

Here is a link to the loan calculator above

PART 3:

Here is a link to my spreadsheet/graph that compares the 3 different paths I would consider taking after high school

Self Assessment

PART 1: I would give myself an A because I put lots of effort in trying to get the taxes of our fake students as accurate as possible in order to make it relateable for parensts and students at parent night. I would aslo make sure that other classmates double checked what I inputed to make sure the final outcome of the net price calculator was the correct tuition amount.

PART 2: In this portion of the project I would give myself an A+ because I perservered through the difficulties and lead others to success. Although I had a very difficult time making equations for the loan calculator, I continuously asked questions and used the trial and error method to lead me towards the right direction. Once I figured out the 4 most important equations of the calculator I realized it was similar for the rest and was able to accomplish it. Not only did I focus on my work but I also helped my classmates to finish their calculators and helped them through the process instead of just giving them the answers to copy and paste.

PART 3: I would give myself an A+ because I really tried to base it off of what I am passionate about and the different paths that I am interested in not just random careers. I also put lots of effort in making my presentation appealing and added many factors specific to me so that I could have a succesful presentation with my parents. Below our pictures of when I walked my mom through all of the information I got out from this project and the rubric that she needed to fill out based on what I presented.

I would say I have a pretty good communication with my mom and because of this my presentation didn't really spark any conflict since she already knows a bit of what I am interetsed in. She was very pleased with the fact that we were doing more in depth research on loans and for how long we would be in debt for. She also had many clarifying questions on the why behind my paths and what sparked my interst between each. When showing her my graph comparing the three career paths she was confused why I would be more in debt for the CSU instead of the UC and I then explained to her the different apsects that fall within that category such as how UC's are more reliable to give financial aide. Overall I think this was a great way to let my parents know that I am aware of my plan after high school including the financial portion of it.

Shoping Cart Problem

Problem Statement: This problem asked us to look at the picture and information that was given in order to figure out which line is the fastest.

My Process and Solution: Before even starting on the problem as a class we made sure we understood the information that was given to us. We figured out the meaning of ring time, tender time, other time and the importance of it for each customer. As I continued to brainstorm different ways of tackling this problem I decide to break up the information. I learned that from the information given to us the ring time is 21.28 items per minute and with that information I would be able to figure out the number of minutes it takes to ring up any item using the butterfly method. Once figuring out the ring time for each customer you would have to add that time plus the tender time, .58, and the other time, .22, since both those times are always going to be the same for each customer. Doing this would give you the total time of one customer. Once knowing the total time for the four customers in the left lane you add their four times giving you the total time of the lane which ended up being a 3.71 minute wait vs the right lane which was a 1.69 minute wait.

Other People's Process and Solution: As we shared our ideas out loud one of my classmates named Andres had a very similar way of solving the problem that got him to the same answer as mine. Instead of doing the butterfly method to figure out the time for every different number of items as I did, he decided to figure out the amount of time for ONE item; which was .047 minutes. By figuring this out and knowing the tender time and other time he came up with an equation, 0.8 + 0.047x. The 0.8 represents the tender and other time combined which is the same for each customer and the 0.047x is the amount of time for one item multiplied by the amount of items that the customer has. He then plugged in 3, 5, 2, and 1 into the equation getting different total times for each cutomer and then adding all of those numbers to figure out the total wait time for the left lane and plugged in 19 into the equation to figure out the wait time for the right lane. Because he got the exact same answers as me comparing both numbers gives us the answer that the right lane would be the fastest.

Self-Assesment/Problem Assesment: Based on the Superstairs, Circle Square and Shopping Cart problem that we have done so far I would defenitely say that this one has been my favorite. I feel like I really collaborated and tried to get my whole team to understand my thinking without dominating too much the conversation, and made sure to get everyone's thinking and voice into how the problem was solved. I was also able to collaborate with Andres to find a more effiecent way of solving this problem which was coming up with the equation and I used my questioning skills to really push not only my thinking but Andres's thinking to make sure his work made sense and that I understood it completly. I was really able to learn from his way of solving the problem that when Kirby gave us a different scenairo to solve I was able to use Andres's method to solve it quickly.