4 Converting Degrees Celsius to Degrees Fahrenheit

IMSA 18 June 2004 4

Converting Degrees Celsius to Degrees Fahrenheit

Below are two vertical lines of the same length next to each other. Use one of them as a Celsius temperature scale. Use the other one for a Fahrenheit temperature scale. Mark your Celsius scale in multiples of 10, going from –50 up to +150, using the equal intervals that are marked off on the line. They should be labeled so that the temperatures indicate the same amount of heat at the same level on the scales. To do this, it helps to know that water freezes at 0 °C and at 32 °F; and water boils at 100 °C and at 212 °F. Mark your Fahrenheit scale also in multiples of 10 all the same size (but you will notice that they cannot be the same size as the 10 units on the Celsius scale!). Label all the tick marks on the scales. On the Fahrenheit scale, also mark 32 and 212 which, of course, are not multiples of 10.

Work in groups, but remember to show your group’s work on your own paper so you will have it for review. 9 To convert Celsius degrees to Fahrenheit degrees, you multiply the Celsius temperature by 5 and then add 32.

1. Write a formula for changing Celsius degrees to Fahrenheit degrees using variables. 2. Convert these temperatures in Celsius degrees to Fahrenheit. Use a calculator where helpful. Before you calculate, look at the parallel temperature scales and make an estimate. a. 0 °C b. 53.5 °C 1 ° ° c. 57 3 C d. 100 C e. 156.7 °C f. -10 °C g. -40 °C h. -60 °C 3. Which temperature listed in #2 is coldest? 4. Did you find a temperature that is the same in Celsius as it is in Fahrenheit? If so, what was it? 5. What is the temperature today on St. Thomas or St. Croix (or where you are)? a. ____ °F b. ____ °C

Rosalie A. Dance and James T. Sandefur, 2004

This material is based upon work supported by the National Science Foundation under Grant No. 0087068. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

IMSA 18 June 2004 5

Teaching Guide for Converting Degrees Celsius to Degrees Fahrenheit

Introduction: The mathematics contained in this lesson includes (1) the order of the integers and (2) working with a formula. The lesson provides a visual support for understanding the order of signed numbers.

Students should work in groups of 3 or 4, but each student should complete the assignment her/himself. Observe students’ competence and comfort with calculator use and provide assistance where it is needed.

Answers and teaching suggestions: Be sure that students label the two temperature scales, using multiples of 10 on each. They should use them to estimate the Fahrenheit equivalents in question 2 before they calculate. 9 1. F = C + 32 is a direct translation of the sentence above the question. Of course, any 5 equivalent formula is acceptable. 2. a. 32ºF b. 128.3ºF c. 135.2ºF d. 212ºF e. 314.06ºF f. 14ºF g. -40ºF h. -76ºF 3. The “more negative” the temperature measure is, the colder it is. -60ºC (or -76ºF) is the coldest temperature given. 4. -40ºC is the same as -40ºF. Cold! 5. Some students have never read a thermometer. If you have one students could observe and record every day, the experience would be valuable for many.

When summarizing the lesson, have students note that the colder it is, the lower on the visual scale the temperature appears. Be sure they note that this is true in both Celsius and Fahrenheit. Also have students observe that on their scales, where equivalent temperatures should be on the same level, -40ºC is indeed at the same height as -40ºF. Ask whether students think this will be true of any other number of degrees in both Celsius and Fahrenheit and why. The answer, of course, is no, and it is easy to explain why using algebra, but these students will have only the visual and numerical scales to judge by. Reasons might be expressed by noting that the rate the Fahrenheit degrees increase (or decrease) is much faster than the Celsius degrees change; thus, as we move either up or down from -40 Celsius will never again “catch up” with Fahrenheit.

Rosalie A. Dance and James T. Sandefur, 2004