Examples, videos, and solutions to help Grade 7 students learn how to to use equations and graphs to represent proportional relationships arising from ratios and rates involving fractions.
• Students use equations and graphs to represent proportional relationships arising from ratios and rates involving fractions. They interpret what points on the graph of the relationship mean in terms of the situation or context of the problem.
• Proportional relationships can be represented through the use of graphs, tables, equations, diagrams, and verbal
In a proportional relationship arising from ratios and rates involving fractions, the graph gives a visual display of all values of the proportional relationship, especially the quantities that fall between integer values.
Example 1: Mother’s 10K Race
Sam’s mother has entered a 10K race. Sam and his family want to show their support for their mother, but they need to figure out where they should go along the race course. They also need to determine how long it will take her to run the race so that they will know when to meet her at the finish line. Previously, his mother ran a 5K race with a time of 1 ½ hours. Assume Sam’s mother will run the same rate as the previous race in order to complete the chart.
a. What are some specific things you notice about this graph?
b. What is the connection between the table and the graph?
c. What does the point (2, 6 2/3) represent?
Example: Organic Cooking
After taking a cooking class, you decide to try out your new cooking skills by preparing a meal for your family. You have chosen a recipe that uses an organic mushroom mix as the main ingredient. Using the graph below, complete the table of values and answer the following questions.
1. Is this relationship proportional? How do you know from examining the graph?
2. What is the unit rate for cost per pound?
3. Write an equation to model this data.
4. What ordered pair represents the unit rate and what does it mean?
5. What does the ordered pair mean in the context of this problem?
6. If you could spend $10.00 on mushrooms, how many pounds could you buy?
7. What would be the cost of 30 pounds of mushrooms?
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