• Module 1: Thinking Proportionally

In this module, students build on their experiences with ratios and proportional relationships from grade 6. They will investigate special ratios to develop and connect formulas for the circumference and area of circles. Students will identify and describe proportional and non-proportional mathematical and real-world situations to understand the characteristics of proportional relationships. They will then use formal strategies to solve proportion and percent problems.

Topic 1: Circles and Ratio

• In this topic, students develop formulas for the circumference and area of circles and use those formulas to solve mathematical and real-world problems.
• MATHia Workspaces (2)
• Investigating Circles
• Calculating Circumference and Area of Circles

Topic 2: Fractional Rates

• In this topic, students review terminology about rates, unit rates, proportions, and strategies to determine equivalent ratios. They extend their work with rates to rates with fractional values.
• MATHia Workspaces (7)
• Fractional Rates
• Determining and Comparing Unit Rates
• Proportional Relationships
• Determining Characteristics of Graphs of Proportional Relationships
• Solving Proportions Using Equivalent Ratios
• Rewriting Proportions as Products
• Solving Proportions Using Means and Extremes

Topic 3: Proportionality

• In this topic, students review the meaning of proportionality and linear relationships and differentiate between proportional and non-proportional relationships, including linear relationships that are not proportional.
• MATHia Workspaces (4)
• Exploring Proportions
• Writing Proportional Relationships with Equations
• Converting Between Forms of Proportional Relationships
• Modeling the Constant of Proportionality

Topic 4: Proportional Relationships

• In this topic, students use their knowledge of proportionality to solve real-world problems about money and scale drawings. They solve a wide variety of multistep ratio and percent problems, including problems about tips, commissions, gratuities, simple interest, taxes, markups and markdowns, and scale factors and drawings.
• MATHia Workspaces (12)
• Fractional Percent Models
• Converting with Fractional Percents
• Using Proportions to Solve Percent Problems
• Solving Simple Percent Problems
• Calculating Percent Change and Final Amounts
• Using Percents and Percent Change
• Calculating Sales Tax or Discounts
• Solving Problems with Both Sales Tax and Discounts
• Analyzing Different Forms of Expressions
• Critical Attributes of Similar Figures
• Using Scale Drawings
• Using Scale Factor