Using Proportional Relationships Portfolio.
Proportional relationships are a type of relationship in which two quantities are directly related and change at a constant rate. In this portfolio, I will explore different scenarios and contexts that involve proportional relationships and demonstrate my understanding of them through various activities and examples.
Activity 1: Graphing Proportional Relationships
In this activity, I will create graphs to represent different proportional relationships. I will choose a few sets of values and plot them on a graph, making sure that they form a straight line passing through the origin (0, 0). I will then determine the equation of the line and explain what it represents in the given context.
Example 1:
Context: The cost of renting a bike for a certain number of hours.
Values:
Hours Cost (in dollars)
1 10
2 20
3 30
Graph: [insert graph here]
Equation: y = 10x
Explanation: The equation y = 10x represents a proportional relationship between the number of hours (x) and the cost (y) of renting a bike. The cost increases by $10 for every hour rented. The graph is a straight line passing through the origin, indicating that the relationship is proportional.
Activity 2: Word Problems
In this activity, I will solve word problems that involve proportional relationships. I will identify the given information, determine the constant of proportionality, and use it to find the missing values.
Example 2:
Context: A recipe requires 2 cups of sugar to make 24 cookies. How much sugar is needed to make 36 cookies?
Given:
Cups of sugar: 2
Number of cookies: 24
Missing:
Number of cookies: 36
Solution:
Since the relationship between the number of cookies and cups of sugar is proportional, we can set up a proportion to find the missing value:
2/24 = x/36
Cross-multiplying, we get:
24x = 2 * 36
24x = 72
Dividing both sides by 24, we get:
x = 72/24
x = 3
Therefore, 3 cups of sugar are needed to make 36 cookies.
Activity 3: Real-World Application
In this activity, I will find a real-world scenario that involves a proportional relationship and provide a detailed explanation of how it applies.
Example 3:
Context: A car rental company charges $50/day for renting a car. The total cost is directly proportional to the number of days rented.
Explanation: In this scenario, the relationship between the number of days rented and the total cost is proportional. The constant rate of change is $50 per day. This means that for every additional day the car is rented, the total cost will increase by $50. The equation that represents this relationship is y = 50x, where y is the total cost and x is the number of days rented. This proportional relationship allows us to predict the cost of renting a car for any given number of days.
In conclusion, this portfolio demonstrates my understanding of proportional relationships through activities such as graphing, solving word problems, and applying the concept to real-world scenarios. By exploring these different contexts, I have learned how to identify, represent, and use proportional relationships in various situations.