NOTE: This is taken from the Teacher's Edition of Comparing and Scaling ©2002

Comparing and Scaling mathematical and problem solving goals:

Comparing and Scaling was created to help students:

Use informal language to ask comparison questions, such as:
“What is the ratio of boys to girls in our class?”
“What fraction of the class is going to the spring picnic?”
“What percent of the girls play basketball?”
“Which model of car has the best fuel economy?”
“Which long-distance telephone company is more popular?”
“What proportion of the delegates should be from rural areas?”

Decide when the most informative comparison is to find the difference between two quantities and when it is to form ratios between pairs of quantities

Develop the ability to make judgments about rounding data to estimate ratio comparisons

Find equivalent ratios to make more accurate and insightful comparisons

Scale a ratio or fraction up or down to make a larger or smaller object or population with the same relative characteristics as the original

Represent data in tables and graphs

Apply proportional reasoning to situations in which capture-tag-recapture methods are appropriate for estimating population counts

Set up and solve proportions that arise in applications

Look for patterns in tables that will allow predictions to be made beyond the tables

Connect unit rates with the rule describing a situation

Begin to recognize that constant growth in a table will give a straight-line graph

Use rates to describe population and traffic density (space per person or car)

The overall goal of the Connected Mathematics curriculum is to help students develop sound mathematical habits. Through their work in this and other number units, students learn important questions to ask themselves about any situation that can be represented and modeled mathematically, such as: When quantities have d~fferent measurements, how can they be compared? When can a comparison be made by subtraction? When can division be used? Why is a ratio a good comparison? How can it be scaled up or down? How does rounding affect the numbers used in a ratio? What is the relationship between ratios and similar figures? Where can ratios be used in daily life to find unknown quantities or inaccessible measurements? How can we connect proportions and graphical techniques for solving problems?