It takes Josephine minutes to complete her homework assignment of problems. If we assume that she works at a constant rate, we can describe the situation using a function. Predict how many problems Josephine can complete in minutes. Answers will vary. Write the two-variable linear equation that represents Josephine’s constant rate of work. Let be the number of problems she can complete in minutes. Use the equation you wrote in part (b) as the formula for the function to complete the table below. Round your answers to the hundredths place. Time taken to complete problems () Number of problems completed () After minutes, Josephine was able to complete problems, which means that she was able to complete problem, then get about halfway through the next problem. Compare your prediction from part (a) to the number you found in the table above. Answers will vary. Use the formula from part (b) to compute the number of problems completed when . Does your answer make sense? Explain. No, the answer does not make sense in terms of the situation. The answer means that Josephine can complete problems in minutes. This obviously does not make sense. For this problem, we assumed that Josephine worked at a constant rate. Do you think that is a reasonable assumption for this situation? Explain. It does not seem reasonable to assume constant rate for this situation. Just because Josephine was able to complete problems in minutes does not necessarily mean she spent the exact same amount of time on each problem. For example, it may have taken her minutes to do problem and then minutes total to finish the remaining problems. Closing (4 minutes) Summarize, or ask students to summarize, the main points from the lesson: We know that a function is a rule or formula that assigns to each input exactly one output. We know that not every function can be expressed by a mathematical rule or formula. The rule or formula can be a description of the assignment.
It takes Josephine minutes to complete her homework assignment of problems. If we assume that she works at a constant rate, we can describe the situation using a function. Predict how many problems Josephine can complete in minutes. Answers will vary. Write the two-variable linear equation that represents Josephine’s constant rate of work. Let be the number of problems she can complete in minutes. Use the equation you wrote in part (b) as the formula for the function to complete the table below. Round your answers to the hundredths place. Time taken to complete problems () Number of problems completed () After minutes, Josephine was able to complete problems, which means that she was able to complete problem, then get about halfway through the next problem. Compare your prediction from part (a) to the number you found in the table above. Answers will vary. Use the formula from part (b) to compute the number of problems completed when . Does your answer make sense? Explain. No, the answer does not make sense in terms of the situation. The answer means that Josephine can complete problems in minutes. This obviously does not make sense. For this problem, we assumed that Josephine worked at a constant rate. Do you think that is a reasonable assumption for this situation? Explain. It does not seem reasonable to assume constant rate for this situation. Just because Josephine was able to complete problems in minutes does not necessarily mean she spent the exact same amount of time on each problem. For example, it may have taken her minutes to do problem and then minutes total to finish the remaining problems. Closing (4 minutes) Summarize, or ask students to summarize, the main points from the lesson: We know that a function is a rule or formula that assigns to each input exactly one output. We know that not every function can be expressed by a mathematical rule or formula. The rule or formula can be a description of the assignment.