Monitoring Water Temperatures

Getting Started

The student is unable to devise an appropriate strategy to solve the problem.

The student attempts to add the numbers in the table and presents this as the final answer.

The student interprets “temperature difference from 22.5” to mean “subtract a number from 22.5.” The student attempts to find the measured temperature for each week by subtracting the number given in the table from 22.5, providing temperatures of 20, 26.6, 23, 21.5, and 25.9 or 20, 18.4, 22, 21.5, and 19.1.

What do the numbers in the table represent?

What is the question asking for?

How do you compute an average?

Assist the student in understanding both what the values in the table represent and the question that is asked in the problem. Review the meaning of the term average and how averages are calculated. While there is more than one way to calculate the average of the five weeks’ temperatures, it might make more sense to the student to first add 22.5 to each value in the table to produce a temperature for each week and to then find the average of these five temperatures. Provide additional practice in calculating averages of rational number data.

Provide additional instruction on adding, subtracting, multiplying, and dividing rational numbers in the form of decimals. Begin with expressions that contain positive decimals and provide focused instruction on any operation with which the student struggles. Review adding, subtracting, multiplying, and dividing signed numbers. Guide the student to use properties of operations to simplify calculations. Then ask the student to evaluate expressions that include both positive and negative decimal numbers.

Review the meaning of the term “difference” as used in this task. Difference is often defined as “the answer to a subtraction problem.” Ask the student to identify the subtraction problems that yield the differences listed in the table. Guide the student to understand that a temperature difference of +2.5 degrees from 22.5 degrees in Week 1 indicates that the measured temperature in Week 1 was 22.5+2.5=25 degrees.

Making Progress

The student is unable to accurately add and subtract positive and negative decimal numbers.

The student understands that five values must be averaged but:

• Is unable to correctly add the five values in the table.
  
  
  
  
• After converting the values in the table to temperatures for each week, is unable to correctly add the five temperature values.
  
  
  
  
• After finding the sum of the temperature differences (-4.5), does not accurately divide by five to find the average difference.
  
  
• After converting the values in the table to temperatures for each week is unable to correctly divide their sum by five.

Can you show me how you added (or divided) these values?

How do you add a negative number to a negative number?

How do you add a negative number to a positive number?

Assist the student in identifying and correcting the calculation error made. Provide additional instruction on adding, subtracting, multiplying, and dividing rational numbers in the form of decimals. Begin with expressions that contain positive decimals and provide focused instruction on any operation with which the student still struggles. Review adding, subtracting, multiplying, and dividing signed numbers. Guide the student to use properties of operations to simplify calculations. Then ask the student to evaluate expressions that include both positive and negative decimal numbers.

Got It

The student provides complete and correct responses to all components of the task.

The student finds the sum of the temperature differences (-4.5), the average of the temperature differences (-0.9), and a final value of 21.6 for the average water temperature during five weeks.



The student uses the temperature differences to find the measured temperatures each week (25, 18.4, 22, 23.5, and 19.1) and averages them by finding their sum, 108, and dividing by five to find an average water temperature of 21.6.

Is there another way you could have solved this problem?

What does the value -4.1 in the table represent?

Ask the student to generate word problems involving the four operations with rational numbers including complex fractions. Allow the student to share the word problems with other instructional groups in the class.

Provide examples of completed problems (similar to the one in this task) that include an error. Ask the student to identify and correct the error.