For this activity , I choose to open a shoe shop. It is very expensive because it cost $10,000 to open the store and $300 for buy each pair of shoes. My goal is to use math to find out the selling price.I write one equation to see the price if I want to break even and only sell 40% of my shoes. Then, I make an inequalityto show how much I must charge to make a big profit of $500,000. I learn that if I sell many shoes (90% volume), the price can be lower, but if I only sell a few shoes (40% volume), the price must be very, very high like $13,800. I also make some graphs and number lines to show my answers.

During this project, I found out that forming inequality equation was very hard because I have to make sure the equation is usable and make it sound making sense. After listing all the equation I have, I started to work on the poster, the poster is not very easy for me because I had to show all the information that are important but there are too much so I have problem including all the information into the poster, the solution is putting pictures or some shorter/easier word and then during the presenting I can spoke the other information that I can't included in.But this might cause some understanding problems so I want to practise my poster making skills next time, my goal is to make a better poster for the next project.

This assignment is a great connection to the Eco House Project I did last semester. In my project design, I mostly thought about what looked cool and uses sustainable materials, but I didn't really have the math to calculate the budget. This unit taught me the algebra I needed to fill in those gaps, specifically how to use linear equations to find total costs. Now, instead of just guessing how much things cost, I can actually calculate the price of stuff like solar panels and insulation to make a real budget. I use the algebra thing to calculate the cost and equation for my shop to break even, which connects the math from this unit directly to the missing parts of my old project.

For this project, we planned a good adventure package featuring paintball, rock climbing, archery, and a sky walk, all fueled by an all you can eat buffet. To make it work, we used linear equations to model the total cost, setting up a "piecewise function" because the price per student actually drops from $1,110$ to $1,010$ once we hit 15 people which we found out by calculating the rate of change for the group discount. We even graphed our plan against another group’s trip and realized our lines were parallel, meaning our trip stays a constant $3,400$ cheaper no matter how many people join! Working with my team was very smooth since we split up the cost calculations and the graphing, and I’m vert proud of how our sample totals table proved that inviting the 15th student actually makes the whole trip cheaper. The hardest part was definitely making sure the fixed costs and the variable costs didn't get mixed up in the formula, so if I did this again, I’d probably spend more time researching even more activity options to see if we could find a line with an even flatter slope to save us even more cash! 

In this proejct the one thing I want to change is moving away from just "following the steps" and focusing more on "interpreting the graph." During this unit, I realized I was pretty good at the algebra we were learning like moving numbers around to solve for y. but I sometimes struggled to explain what the final line actually meant in a real-world context until the very end of the project. 

I chose this because math is way more useful when I can see that a steeper slope isn't just a bigger number, but represents something like a faster drain on a battery or a higher cost per person. To achieve this, I’m going to start every problem by making a quick prediction sketch before I do any calculations. This specific habit will help me catch "dumb mistakes" faster and help me actually understand what I am doing, and not just memorsing how to do it. This well help me in my future.