Course Overview

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