MLS                                                                          Yolanda Volcimus

Harvard                                                                   December 1, 2012

        Relate your understanding of unit rate and proportionality to that of rate of change and slope. How are they similar and how do they differ? How can one use their understanding of unit rate and proportionality to interpret real world rate of change/slope problems presented in graphs.

        A rate, unit rate, proportionality, Rate of Change, and slope all work together to form the understanding of graphs. These relations also have their similarities and differences. We can also use our understanding of unit rate and proportionality to interpret real world Rate of Change/slope problems presented in graphs.   

A rate is a ratio that compares two quantities measured in different units. A rate is similar to a unit rate because a unit rate is a rate whose denominator is 1 when it is written as a fraction. However, a rate can be in any fraction form, whereas, a unit rate has to have a denominator of one. For example, the first chart contains rates only and the second chart has unit rates only. 

                    

Unit Rate

5/1

3/1

9/1

Rates

4/2

7/14

8/5

    

       

      The slope of a line is a measure of its steepness and is a ratio of Rise over Run. There are two types of slopes; a positive slope and a negative slope. A positive slope is when a line in a graph is increasing from left to right.

This picture shows a positive slope. 

However, A negative slope is when the line in a graph is decreasing from left to right when looking at it. This is a picture     of a negative slope.

A Rate of Change is the ratio of two quantities that changes; such as slope. Slope and Rate of Change are similar because the Rate of Change is the ratio for the slope in the simplest form. Without the Rate of Change, the slope wouldn’t be in its simplest form. For instant,

A slope is 6/3. The Rate of Change would be 2 because 6 divided by 3 is 2.

               6 ÷ 3 = 2

               3 ÷ 3 = 1. A slope is different from a Rate of Change because the slope of a line may not necessary be simplified in some situations, however, in a Rate of Change, the ratio is always express in the simplest form.                                                                                                           

         We can use our understanding of unit rate and proportionality to interpret real world Rate of Change/slope problems presented in graphs. For example, some real life examples of slopes are mountains, stairs, and a slide. These things are considered examples of slopes because they are steep which is what slopes measure. If the slope of a stair is 15/5, by using our understanding of using unit rate, we will be able to determine the Rate of Change. We would have to write the slope in the simplest form where the denominator is one. We can do that by dividing both the numerator and the denominator by 5 which gives us an answer of 3.

  15 ÷ 5 = 3

    5 ÷ 5 = 1