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Unit 1: Algebraic Expressions & Equations
In Unit 1, I learned about algebraic expressions and equations, including how to simplify expressions, combine like terms, solve one-step and knowing the special terms. I also learned how to use variables to represent unknown values and how to check my answers by substituting the value back into the equation.
For example, I solved the equation 3x + 5 = 20. The first step, I minus 5 from both sides to get 3x = 15 (20-5), then I divided by 3 to find x = 5. This example shows that I understand how to solve the variable step by step. I also improved in organizing my work clearly and showing all steps, which helped me make fewer mistakes. Overall, I became more confident in solving equations and understanding how algebra works.
Mini-Project 1: Algebra in Real Life
For my mini-project, I created a real-life situation about tutoring students to earn money. I used a variable (x) to represent the number of hours I work. I earn $20 per hour, and I have costs, including $5 per hour for renting a classroom and a fixed cost of $60 for materials.
To find the break-even point, I used an equation: 20x = 60 + 5x
This means my revenue equals my total cost. I solved the equation step by step by subtracting 5x from both sides, which gave me 15x = 60. Then I divided by 15 and got x = 4. This shows that I need to work 4 hours to break even and cover all my costs.
Next, I used an inequality to find how many hours I need to earn at least $1440 profit: 20x − (60 + 5x) ≥ 1440
I simplified it to 15x − 60 ≥ 1440, then added 60 to both sides to get 15x ≥ 1500. Finally, I divided by 15 and got x ≥ 100. This means I need to tutor at least 100 hours to reach my profit goal. 😭😭😭😭 I think it's impossible.
This project helped me understand how to use algebra in real life, especially for money and planning. One challenge was making sure I set up the equation and inequality correctly from the situation. I was surprised that math can be used to solve real-world problems like business. If I did this project again, I would explain my steps more clearly and improve my graph to make it easier to understand.
Unit 2: Relations
In Unit 2, we learned about different types of relations and how math can be used to model real-life situations. We solved problems involving graphing lines, rate of change, inverse variation, transformations, and piecewise functions. One important thing I learned was how equations and graphs can represent situations in everyday life, such as the total cost of a trip depending on the number of students attending. I also learned how to identify patterns and explain relationships between variables using graphs and equations. At first, some topics like piecewise functions were confusing, but after practicing more problems, I started understanding how different equations can work together in one graph.
Example 1
Example 1
I included my “Plan a Trip” poster because it shows how I used piecewise functions and cost equations in a real-life situation. Our group planned a class trip and calculated the total cost depending on the number of students attending. This project helped me understand how algebra can be used for budgeting and decision-making. I am proud that our graph and equations matched our pricing model correctly. If I could change something, I would make the graph larger and easier to read.
Example 2
Example 2
I also included my Week 9 notes and slides about piecewise functions because this topic was one of the most challenging parts of the unit for me. These notes show how I practiced graphing different equations with different conditions. At first, I mixed up when to switch equations, but after more practice, I improved a lot. This work shows my progress in understanding more advanced graphing skills. If I could redo it, I would organize my notes more clearly and add more examples.
Mini-Project 2: Plan a Trip!
For Mini-Project 2, my group planned a trip to Century Empire and created a full budget for 19 students. We included activities like rope rappelling, paintball, rock climbing, and a BBQ meal set. We used algebra and piecewise functions to model the total trip cost depending on the number of people attending, and then graphed the relationship between students and total cost. Working with my team was fun because everyone contributed ideas and helped with different parts of the project. I am most proud of our final poster because it looked organized and connected math to a realistic situation. One challenge was making sure all the calculations matched correctly in the graph and equations. If I did this project again, I would spend more time improving the graph design and double-checking every calculation earlier.
Area of Growth:
One thing I want to improve as a math learner is checking my work more carefully before turning assignments in. Sometimes I understand the concept, but I make small mistakes in calculations or graphs because I work too quickly. I also want to show my steps more clearly so it is easier to follow my thinking. To improve this, I will slow down during quizzes and homework, review my answers before submitting them, and organize my notes better. I think this will help me become more confident and accurate in math.
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