Proportional Reasoning

Unit Description:

In this unit, students develop several methods for comparing quantities and use those methods to solve problems. Students learn how to write ratios, percents, fractions, rates and differences. They develop an understanding of when each type of comparison is most appropriate. Students use equivalent ratios and rates to scale comparisons up or down. Unit rates are explored and extended to create rate tables. They use proportions to solve problems. Percent proportions are extended to include markup/discount and computing interest.

Big Ideas:

• It is often necessary to make decisions that involve comparisons of counts or measurements.
• There are many standard ways to make comparisons (i.e., fractions, ratios, rates, differences, and percents)
• Scaling suggests making something bigger or smaller, but similar in key respects to an original.

Essential Questions:

• What quantities should be compared?
• What type of comparison will give the most useful information?
• How can the comparison be expressed in different but useful ways?
• How can given comparison data be used to make predictions about unknown quantities?
• How can you identify and represent proportional relationships?
• How can you use proportional relationships to solve real world percent problems?

Textbook - Glencoe Math Accelerated

• 5-1: Rates
• 5-2: Unit Rates
• 5-4: Converting Rates (Dimensional Analysis for Honors)
• 5-5: Proportional and Non-Proportional Relationships
• 5-6: Graphing Proportional Relationships
• 9-4: Direct Variation
• 5-7: Solving Proportions
• 5-8: Scale Drawings & Models
• 5-9: Similar Figures
• 5-10: Indirect Measurement
• 6-1: Using the Percent Proportion
• 6-3: Using the Percent Equation
• 6-4: Percent of Change
• 6-5: Discount and Markup
• 6-6: Simple and Compound Interest