Course Overview

Big Ideas:

Transformations (Lessons 1–5) 

• Perform translations, rotations, and reflections on and off a grid.

• Use form and informal language to identify and describe translations, rotations, and reflections on and off a grid.

Applying Congruence (Lessons 6–12) 

• Use rigid transformations to determine whether two figures are congruent, discover new angle relationships and determine angle measures.

• Determine unknown angle measures using facts about complementary, supplementary, and vertical angles.

• Justify whether two figures are congruent using language such as rigid transformations, translation, reflection, rotation, pre-image, and image.

• Describe how to determine missing angle measures using reasoning based on angle relationships.

• Analyze the effects of rigid transformations on lines and angles.

Drawing Triangles (Lessons 13-16) 

• Use rigid transformations to determine whether two figures are congruent, discover new angle relationships and determine angle measures.

• Determine unknown angle measures using facts about complementary, supplementary, and vertical angles.

• Justify whether two figures are congruent using language such as rigid transformations, translation, reflection, rotation, pre-image, and image.

• Describe how to determine missing angle measures using reasoning based on angle relationships.

• Analyze the effects of rigid transformations on lines and angles.

Vocabulary

• Adjacent Angles

• Clockwise

• Complementary Angles

• Congruent

• Correspond

• Counterclockwise

• Identical Copy

• Image

• Pre-Image

• Prime Notation

• Reflection

• Rigid Transformation

• Rotation

• Sequence of Transformations

• Supplementary Angles

• Transformation

• Translation

• Transversal

• Vertical Angles

Big Ideas:

Scaled Drawings (Lessons 1–6) 

• Use scale factors to create and compare scaled copies.

• Describe how scaling affects lengths, angles, and areas in scaled copies.

• Represent distances in the real world using scale and scale drawings.

• Analyze strategies for creating a scale drawing to represent actual distances and areas.

Dilations and Similarity (Lessons 7-14) 

• Apply dilations to figures on and off a coordinate grid.

• Use transformations to determine whether two figures are similar.

• Describe dilations precisely using terms such as pre-image, center of dilation, and scale factor.

• Justify whether two figures are similar using terms such as translation, reflection, rotation, dilation, pre-image, and image.

Slope (Lessons 15-16) 

• Make connections between the slope of a line and similar triangles created by that line.

• Determine the slopes of lines.

• Explain how to calculate the slope of a line using vocabulary from this unit.

Vocabulary

• Center of Dilation

• Dilation

• Proprtional

• Scaled Copy

• Scale Factor

• Scale Drawing

• Slope

• Slope Triangle

Big Ideas:

Equations  with Variables on One Side (Lessons 1–11) 

• 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.

• 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.

Equations with Variables on Both Sides (Lessons 12-17) 

• Write and solve equations with variables on both sides of the equal sign.

• Determine the number of solutions to a linear equation.

• Analyze strategies for solving linear equations in one variable.

Inequalities (Lessons 18-22) 

• Solve inequalities of the form px+q=r  and p(x+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

• Greater-Than-Or-Equal-To

• Less-Than-Or-Equal-To

Big Ideas:

Proportional and Linear Relationships (Lessons 1–13) 

• Compare and interpret proportional relationships using multiple representations such as equations, tables, and graphs.

• Calculate and interpret the vertical intercept and slope of a linear relationship in context.

• Analyze strategies for calculating the slope and vertical intercept of a line through two points.

Systems of Linear Equations (Lessons 14–19) 

• Solve systems of linear equations in two variables graphically and algebraically.

• Interpret the intersection point of two linear relationships in context given their graphs or equations.

• Describe strategies for solving systems of linear equations.

Vocabulary

• Horizontal Intercept (X-Intercept)

• Vertical Intercept (Y-Intercept)

• Linear Relationship

• Solution

• Undefined

Big Ideas:

Introduction to Functions (Lessons 1–4) 

• Determine whether graphs, tables, or rules represent functions.

• Describe situations using terms such as function, input, and output.

Representing and Interpreting Functions (Lessons 5–8) 

• Create and compare graphs of functions that represent stories.

• Describe graphs of functions that represent situations.

Vocabulary

• Dependent Variable (Output)

• Independent Variable (Input)

• Function

• Linear Function

• Non-Linear

• Hemisphere

Big Ideas:

Analyzing Data (Lessons 1–9) 

• Compare different ways to organize numerical data with two variables, including scatter plots.

• Compare and contrast various data representations.

• Use scatter plots and linear models to identify associations and make predictions.

• Interpret and describe features of data presented in a scatter plot.

Categorical Data (Lessons 10-11) 

• Use two-way tables and bar graphs to identify associations in categorical data.

• Analyze data presented in two-way tables and bar graphs.

Vocabulary

• Association

• Bivariate Data

• Clusters

• Frequency

• Linear Model (Line of Fit)

• Outlier

• Relative Frequency

• Scatter Plot

• Segmented Bar Graph

• Two-Way Table

• Univariate Data

Big Ideas:

Solid Geometry (Lessons 1-4) 

• Solve real-world and mathematical problems involving the volume and surface area of right prisms.

Volume (Lessons 5-11) 

• Calculate and compare the volumes of cylinders, cones, and spheres.

• Explain the relationship between the volumes of cylinders, cones, and spheres.

Vocabulary

• Adjacent Angles

• Complementary Angles

• Cross Section

• Identical Copy

• Supplementary Angles

• Vertical Angles

Big Ideas :

Exponent Properties (Lessons 1–6) 

• Identify and create equivalent expressions involving positive, negative, and zero exponents.

• Explain and interpret expressions involving exponents and their properties.

Scientific Notation (Lessons 7–14) 

• Express and perform operations with very large or very small quantities using powers of 10 and scientific notation.

• Explain and interpret the meaning of numbers and operations using powers of 10 and scientific notation.

Vocabulary

• Power of Ten

• Scientific Notation

Big Ideas:

Square Roots and Cube Roots (Lessons 1–5)

• Approximate the value of square roots and cube roots.

• Describe the relationship between a square’s side length and area using the term square root, and the relationship between a cube’s edge length and volume using the term cube root.

The Pythagorean Theorem (Lessons 6–14) 

• Use the Pythagorean theorem and its converse to reason about right triangles and calculate unknown measurements.

• Explain a proof of the Pythagorean theorem and its converse.

• Express rational and irrational numbers as fractions and decimal approximations.

• Describe what an irrational number is and give an example.

Vocabulary

• Bar Notation

• Converse

• Cube Root

• Hypotenuse

• Irrational Number

• Legs

• Perfect Cube

• Perfect Square

• Pythagorean Theorem

• Rational Number

• Square Root