The two quantities being related in this problem are the number of hours (x) and the number of miles (y) Dean can ride on his bike. They are related by the equation y = 13x, which means that for every hour Dean rides, he can travel 13 miles.
Another way Dean could have shown the relationship between the two quantities is by creating a table or a graph. He could have made a table with different values for x (number of hours) and calculated the corresponding values for y (number of miles). This would help him visualize how the miles increase as the hours increase.
Dean demonstrated his ability to reason abstractly and quantitatively by successfully using the equation to calculate how many miles he could ride in 5 hours. He understood the equation and was able to apply it to a specific situation. This shows his ability to think abstractly (using the equation as a general representation of the relationship) and quantitatively (plugging in specific values and calculating a result).
Dean wrote the equation y=13x to show the relationship between the number of hours, x , and the number of miles he can ride on his bike, y . He used his equation to calculate how many miles he could ride his bike in 5 hours: yyy=13x=13×5=65 Dean determined that he could ride 65 miles in 5 hours.What are the two quantities being related in this problem? How are they related? What is another way Dean could have shown the relationship between the two quantities in this problem besides an equation? How did Dean demonstrate his ability to reason abstractly and quantitatively?
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