Dear Family,
The next unit in your child's course of study in mathematics class this year is Comparing and Scaling. The unit focuses on the concepts of ratio, proportion, and percent. Students look at problems involving many situations and learn to make comparisons using ratios, fractions, percents, and rates. Some of the questions students explore include making sense of surveys, adapting recipes for different numbers of people, analyzing sales prices, and comparing fuel economy of different cars. By the end of this unit, your child will know several powerful and useful methods for making comparisons.

You can help your child with the ideas in this unit in several ways:

o Ratios, proportions, and percents are found all around us. When you notice such a use in a newspaper or magazine, point it out to your child and discuss with your child what the numbers are telling about the situation.
o If you keep track of your car mileage, you may want to share this with your child. If you use other
modes of transportation, such as a bus or subway, you may want to discuss the cost of the transportation per week, per month, and per year.
o Continue to have your child share his or her mathematics notebook with you. You may want to review the vocabulary section where your child is recording definitions for mathematical words used in this unit. If your child is struggling with any words, together you might look the words up in the dictionary or look through the unit to get a better sense of their meaning.
o Encourage your child's efforts in completing all homework assignments. Look over your child's work, and help your child make sure all questions have been answered and that all explanations are clear.
If you have any questions or concerns about this unit or your child's progress in the class, please feel free to call. We are interested in your child's success in mathematics and want to ensure that this year's mathematics experiences are enjoyable.

Sincerely,

Mr. John Hampshire

Topics:

• Comparing quantitative Information

  • Using ratios, fractions, decimals, rates, unit rates, and percents

• Scale models

• When to use which type of comparisons

Big Ideas:

• Exploring Proportional relationships between quantities

• Using percents to create a common scale for comparison

• Interpreting Fractions as: ratios, rates, or comparisons of a part to a whole

• Scaling ratios up or down

• Comparing quanitities using ratios, rates, or percents

• Estimate population density

Mathematics:

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 different 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?

Tips:

• Be sure to read the Mathematical Highlights on page 4. They give you a preview of the activities and problems.

• As you go through the unit, be thinking about your Unit Project on page 5.

• Get Pages

Games:

http://www.visualfractions.com/

http://regentsprep.org/Regents/math/ratio/PracRatio.htm

http://illuminations.nctm.org/imath/6-8/pooltable/

http://www.mathleague.com/help/ratio/ratio.htm

Additional Resources:

• Centimeter Grid Paper

• Puzzles and Games

• How to succeed in Math

• How to study

• Javascript School Math Toolkit

• Hundreds of virtual interactive tutorials.

• Data analysis and probability games.

• A huge collection of very nice games.

• Many more examples of interactive lessons from the NCTM.

• Integer rod applet

• Basic algebra game for young students.

• Interactive Mathelets.

• Texas Instruments tutorials and links.

• Math tutorials for students of all ages.

• Conversion site, convert just about anything.

• Math flashcards generated by you.

• Tutorials for students.

• Tutorials and lesson ideas.

• Fraction Information