Using proportional relationships portfolio worksheet
Portfolio Worksheet
Name: [Your Name]
Instructions:
1. Choose a proportional relationship to explore.
2. Write the equation for the proportional relationship.
3. Create a table of values for the relationship.
4. Graph the relationship on a coordinate plane.
5. Write an equation for the relationship in slope-intercept form.
6. Write a brief explanation of the meaning of the slope and y-intercept in the context of the relationship.
7. Solve a problem using the proportional relationship.
Proportional Relationship: The relationship between the number of hours worked and the amount of money earned.
1. Equation for the Proportional Relationship:
Let's assume that for every hour worked, $10 is earned. The equation for the relationship can be written as:
Earnings = 10 * Hours
2. Table of Values:
Hours (x) | Earnings (y)
-----------------------------
0 | 0
1 | 10
2 | 20
3 | 30
4 | 40
3. Graph of the Relationship:
(Please imagine a coordinate plane with hours on the x-axis and earnings on the y-axis. Plot the points (0, 0), (1, 10), (2, 20), (3, 30), and (4, 40) to create the graph.)
4. Equation in Slope-Intercept Form:
The equation for the proportion in slope-intercept form can be derived from the proportional equation as:
Earnings = 10 * Hours
Rearranging the equation, we have:
Earnings = 10 * Hours + 0
This can be simplified to:
Earnings = 10 * Hours + 0
Therefore, the equation in slope-intercept form is:
y = 10x
5. Meaning of the Slope and Y-Intercept:
In this context, the slope of the line (10) represents the rate at which earnings increase per hour worked. For every additional hour worked, the earnings increase by $10. The y-intercept (0) represents the initial earnings when no hours are worked.
6. Problem:
John works at a part-time job where he earns $10 per hour. Given that he worked for 5 hours, how much money did he earn?
Solution:
Using the proportional relationship, we can substitute the value of 5 hours into the equation:
Earnings = 10 * 5
Earnings = $50
Therefore, John earned $50 for working 5 hours.
(Note: You can choose any other proportional relationship and repeat the same steps to complete your portfolio worksheet.)
To use a proportional relationships portfolio worksheet, follow these steps:
1. Understand the concept of proportional relationships: Before starting the worksheet, make sure you understand what a proportional relationship is. In a proportional relationship, the ratio between two quantities remains constant.
2. Read the instructions: Begin by carefully reading the instructions provided on the worksheet. Pay attention to any specific requirements or prompts given.
3. Identify the given information: Look for the given information in the problem. This could include values, measurements, or any other relevant data.
4. Determine the variables: Identify the variables involved in the proportional relationship and assign them appropriate letters or symbols.
5. Set up the ratio: Use the given information and variables to set up a ratio or a proportion. For example, if the problem states that "for every 2 apples, there are 3 oranges," you would set up the ratio as 2:3 or as a fraction 2/3.
6. Solve the problem: Use cross-multiplication or any other method to solve the proportion and find the missing value. Make sure to show your work and write down all the steps taken.
7. Check your answer: After obtaining the solution, double-check your answer to ensure it makes sense within the context of the problem. You can also verify proportionality by checking if all the other ratios in the problem also hold true.
8. Record your solution: Write down the solution neatly in the provided spaces on the worksheet. Include units if necessary.
9. Reflect and analyze: Take a moment to think about the problem and analyze your solution. Consider whether it aligns with the given information and the concept of proportional relationships.
10. Repeat for additional problems: If the worksheet contains multiple problems, repeat the above steps for each problem, ensuring to read and follow the new set of instructions for each one.
Remember, the purpose of a portfolio worksheet is to practice and demonstrate your understanding of proportional relationships. Make sure to show your work, explain your reasoning, and provide complete solutions for each problem.