Big Ideas:
Scaled Copies (Lessons 1–5)
Use scale factors to create and compare scaled copies.
Describe how scaling affects lengths, angles, and areas in scaled copies.
Scale Drawings (Lesson 6–11)
Represent distances in the real world using scale and scale drawings.
Analyze strategies for creating a scale drawing to represent actual distances and areas.
Vocabulary
Correspond (Corresponding Parts)
Proportional
Scale
Scale Drawing
Scale Factor
Scaled Copy
Big Ideas:
Proportional Relationships in Tables (Lessons 1–3)
Use tables to recognize proportional relationships.
Determine a constant of proportionality from a table.
Describe the relationship between values in a table using terms such as proportional, non-proportional, and constant of proportionality.
Proportional Relationships in Equations (Lessons 4–7)
Write and use equations to describe proportional relationships.
Determine a constant of proportionality from an equation.
Describe relationships represented with equations using terms such as proportional, non-proportional, and constant of proportionality.
Proportional Relationships in Graphs (Lessons 8–10)
Use graphs to recognize proportional relationships.
Determine a constant of proportionality from a graph.
Describe relationships represented with graphs using terms such as proportional, non-proportional, and constant of proportionality.
Using Proportional Relationships (Lessons 11–13)
Use proportional relationships to solve real-world and mathematical problems.
Interpret different representations of a proportional relationship to make sense of a situation in context.
Vocabulary
Constant of Proportionality
Coordinate Plane
Equivalent Ratios
Origin
Proportional Relationship
Big Ideas:
Circumference of a Circle (Lessons 1-4)
Use the relationships between the radius, diameter, and circumference of a circle to calculate unknown measurements.
Explain that the relationships between the radius, diameter, and circumference of a circle are proportional and that pi is the constant of proportionality relating circumference and diameter.
Area of a Circle (Lessons 5-10)
Calculate the areas of circles and complex shapes composed of fractions of circles.
Describe the relationship between the radius of any circle and its area.
Vocabulary
Circumference
Diameter
Pi
Radius
Big Ideas:
Percentages as Proportional Relationships (Lessons 1–6)
Solve problems involving percent change using representations, such as tape diagrams, double number lines, tables, and equations.
Interpret verbal descriptions and strategies to solve problems about percent change.
Applying Percentages (Lessons 7–10)
Use proportional reasoning to solve problems in real-world situations involving percent increase, percent decrease, and percent error.
Interpret situations involving percent change and apply appropriate representations to solve problems.
Interpret scenarios depicting percent change and percent error.
Proportional Relationships with Fractions and Decimals (Lessons 11-13)
Determine unknown values in proportional relationships involving fractional quantities.
Convert between fraction and decimal representations.
Analyze strategies for solving problems involving proportional relationships with fractional and decimal quantities.
Vocabulary
Percent Decrease
Percent Error
Percent Increase
Repeating Decimal
Terminating Decimal
Big Ideas:
Adding and Subtracting (Lessons 1–5)
Add and subtract positive and negative numbers using a variety of strategies.
Describe strategies for determining the sum or difference of two rational numbers.
Multiplying and Dividing (Lessons 6–10)
Perform all four operations with positive and negative numbers using a variety of strategies.
Describe strategies for determining the sum, difference, product, or quotient of two rational numbers.
Applying Operations (Lessons 11–13)
Apply all four operations with positive and negative numbers to analyze changes in our environment.
Interpret information about real-world situations involving positive and negative numbers.
Vocabulary
Integer
Big Ideas:
Equations and Tape Diagrams (Lessons 1–4)
Use tape diagrams to represent equations and situations in context and to determine unknown values.
Analyze descriptions of situations in context using tape diagrams and equations to interpret the solution.
Solving Equations (Lessons 5–12)
Solve equations of the form px+q=r and p(x+q)=r in real-world and mathematical problems.
Write equivalent expressions by adding, subtracting, expanding, and factoring.
Describe and use strategies for solving equivalent expressions that involve adding, subtracting, factoring, expanding, and reordering terms.
Inequalities (Lessons 13–17)
Solve inequalities of the form 𝑝𝑥 + 𝑞 > 𝑟 and 𝑝𝑥 + 𝑞 < 𝑟 that represent real-world and mathematical problems.
Create graphs that represent solutions to inequalities, including those with ≤ or ≥.
Analyze descriptions of situations in context to interpret the solution of inequalities.
Vocabulary
Expand
Factor
Equivalent Expressions
Greater-than-or-equal-to
Less-than-or-equal-to
Solutions to an Inequality
Big Ideas:
Angle Relationships (Lessons 1–4)
Determine unknown angle measures using facts about complementary, supplementary, and vertical angles.
Write and solve equations for unknown angles in a diagram.
Describe how to determine missing angle measures using reasoning based on angle relationships.
Drawing Triangles (Lessons 5–8)
Construct triangles given three measures of side lengths or angles.
Justify whether a given set of measurements form a unique triangle, more than one triangle, or no triangle.
Solid Geometry (Lessons 9–13)
Solve real-world and mathematical problems involving the volume and surface area of right prisms.
Compare and contrast cross sections of prisms and pyramids.
Vocabulary
Adjacent angles
Complementary Angles
Cross Section
Identical Copy
Supplementary Angles
Vertical Angles
Big Ideas:
Probability (Lessons 1–8)
Compare the results of repeated experiments and the expected probability.
Determine the probability of events by identifying the sample space or designing and using simulations.
Interpret the results from repeated experiments to determine fairness, probability, and the likelihood of events.
Sampling (Lessons 9–15)
Use measures of center and measures of variability from random samples to draw conclusions about and compare populations.
Explain the purpose of sampling which methods of obtaining a sample tend to produce representative samples.
Vocabulary
Compound (Multistep) Event
Event
Experiment
Outcome
Population
Probability
Random
Relative Frequency
Representative Sample
Sample
Sample Space
Simulation
Tree Diagram