Jim Dougherty

  • IM / Open Up Grade 6
    • Grade 6: Unit 1 Area and Surface Area
    • Grade 6: Unit 2 Introducing Ratios
    • Grade 6: Unit 3 Unit Rates and Percentages
    • Grade 6: Unit 4 Dividing Fractions
    • Grade 6: Unit 5 Arithmetic in Base Ten
    • Grade 6: Unit 6 Expressions and Equations
    • Grade 6: Unit 7 Rational Numbers
    • Grade 6: Unit 8 Data Sets and Distributions
    • Grade 6: Unit 9  Putting it All Together
  • IM / Open Up Grade 7
    • Grade 7: Unit 1 Scale Drawings
    • Grade 7: Unit 2 Introducing Proportional Relationships
    • Grade 7: Unit 3 Measuring Circles
    • Grade 7: Unit 4 Proportional Relationships and Percentages
    • Grade 7: Unit 5 Rational Number Arithmetic
    • Grade 7: Unit 6 Expressions, Equations and Inequalities
    • Grade 7: Unit 7 Angles, Triangles, and Prisms
    • Grade 7: Unit 8 Probability and Sampling
    • Grade 7: Unit 9 Putting it All Together
  • IM / Open Up Grade 8
    • Grade 8: Unit 1 Rigid Transformations and Congruence
    • Grade 8: Unit 2 Dilations, Similarity, and Introducing Slope
    • Grade 8: Unit 3 Linear Relationships
    • Grade 8: Unit 4 Linear Equations and Linear Systems
    • Grade 8: Unit 5 Functions and Volume
    • Grade 8: Unit 6 Associations in Data
    • Grade 8: Unit 7 Exponents and Scientific Notation
    • Grade 8: Unit 8 – Pythagorean Theorem and Irrational Numbers
    • Grade 8: Unit 9 – Putting It All Together

7.RP.A.2

Recognize and represent proportional relationships between quantities.

  • Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  • Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  • Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
  • Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

7.RP Ratios and Proportional Relationships

7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.