Sub Unit 1: Scaled Copies
Use scale factors to create and compare scaled copies.
Describe how scaling affects lengths, angles, and areas in scaled copies.
Sub Unit 2: Scale Drawings
Represent distances in the real world using scale and scale drawings.
Analyze strategies for creating a scale drawing to represnent actual distances and areas.
Sub Unit 1: Proportional Relationships in Tables
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.
Sub Unit 2: Proportional Relationships in Equations
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.
Sub Unit 3: Proportional Relationships in Graphs
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.
Sub Unit 4: Using Proportional Relationships
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.
Sub Unit 1: Circumference of a Circle
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 the pi is the constant of proportionality relating circumference and diameter.
Sub Unit 2: Area of a Circle
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.
Sub Unit 1: Percentages as Proportional Relationships
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.
Sub Unit 2: Applying Percentages
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.
Sub Unit 3: Proportional Relationships with Fractions and Decimals
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.
Sub Unit 1: Adding and Subtracting
Add and subtract positive and negative numbers using a variety of strategies.
Describe strategies for determining the sum or difference of two rational numbers.
Sub Unit 2: Multiplying and Dividing
Perform all four operations with positive and negative numbers using a variety of strategies.
Describe strategies for determing the sum, difference, product, or quotient of two rational numbers.
Sub Unit 3: Applying Operations
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.
Sub Unit 1: Equations and Tape Diagrams
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.
Sub Unit 2: Solving Equations
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.
Sub Unit 3: Inequalities
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 greater than or equal to or less than or equal to symbols.
Analyze descriptions of situations in context to interpret the solution of inequalities.
Sub Unit 1: Angle Relationships
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.
Sub Unit 2: Drawing Triangles
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.
Sub Unit 3: Solid Geometry
Solve real-world and mathematical problems involving the volume and surface area of right prisms.
Compare and contrast cross sections of prisms and pyramids.
Sub Unit 1: Probability
Compare probabilities to the results of repeated experiments.
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.
Sub Unit 2: Sampling
Use measures of center and measures of variability from random samples to draw conclusions about and compare populations.
Explain the purpose of sampling and which methods of obtaining a sample tend to produce representative samples.