# Math 8

• Math 8 Information

Math 8 Class Information Letter

### Unit 1:  Rigid Transformations and Congruence

Big Ideas

• Describe and perform translations, rotations, and reflections on a grid
• Determine whether two figures are congruent using rigid transformations
• Use transformations and angle relationships created by a transversal with parallel lines to determine unknown measurements

Required Skills

• Perform rotations, reflections, & translations on a grid and using coordinate rule
• Determine whether a transformation on a given two-dimensional figure results in a congruent figure
• Describe a sequence of rigid transformations that would take one given figure to another
• Understand and use facts about angle sum and exterior angles of triangles, corresponding angles, alternate & same-side interior and exterior angles

### Unit 2 – Dilation, Similarity, and Introducing Slope

Big Ideas

• Describe dilations in terms of their center and scale factor
• Dilate figures on and off coordinate plane
• Identify similar figures and properties of similar figures using transformations
• Explain slope in terms of similar triangles on same line and determine slopes of given lines

Required Skills

• Perform dilations
• Describe the effect of a transformation on a given two-dimensional figure that creates a similar figure
• Describe the sequence of transformations that would take one given figure to another
• Understand and use facts about the angle-angle criterion for similarity of triangles

### Unit 3 – Proportional and Linear Relationships

Big Ideas

• Compare proportional relationships using their equations, tables, and graphs
• Interpret the intercepts and slope of a graph or equation of a linear relationship
• Use the concept that a graph represents all solutions of an equation to solve problems

Required Skills

• Identify and graph linear equations using table of values and using slope and y-intercept
• Interpret rate of change and initial value of a linear relationship in terms of a situation it models
• Describe key elements of a graph (linear vs. nonlinear; increasing, decreasing, or constant intervals)
• Examine rates, ratios, and slope relationships

### Unit 4 – Linear Equations and Linear Systems

Big Ideas

• Write and solve linear equations
• Use graphs and algebraic methods to solve systems of linear equations in two variables

Required Skills

• Review how to perform operations on rational numbers (add, subtract, multiply, & divide)
• Solve multi-step linear equations with rational coefficients
• Identify whether a given linear equation will have one solution, no solution, or infinitely many solutions
• Model situations using linear equations
• Solve linear systems of equation by graphing, substitution, & elimination

### Unit 5 – Functions and Volume

Big Ideas

• Determine whether or not graphs, tables, or rules represent functions
• Create and interpret graphs of functions that represent stories
• Calculate and compare volume of cylinders, cones, and spheres
• Use the relationships between height, radius, and volume to calculate missing dimensions

Required Skills

• Determine whether given relations are functions
• Interpret and compare functions described using different models: verbal descriptions, tables, algebraic expressions/equations, graphs
• Construct functions to model relationship between two quantities
• Use formulas for volumes of cones, cylinders, and spheres to solve problems

### Unit 6 – Exponents and Scientific Notation

Big Ideas

• Identify and create equivalent expressions involving positive, negative, and zero exponents
• Express and perform operations with very large or very small quantities using powers of 10 and scientific notation

Required Skills

• Use rational exponents & rules of exponents to simplify expressions
• Convert numbers between standard form and scientific notation
• Perform operations (add, subtract, multiply, & divide) numbers written in scientific notation

### Unit 7 – The Pythagorean Theorem and Irrational Numbers

Big Ideas

• Understand that square roots and cube roots represent the edge lengths of squares and cubes, and approximate their values
• Use the Pythagorean theorem and its converse to reason about right triangles and find unknown measurements
• Determine fractions and decimal approximations for rational and irrational numbers

Required Skills

• Convert terminating and repeating decimals to fractions and vice-versa
• Identify whether real numbers are rational or irrational, locate on number line, and compare
• Take the square root and cube root of a given number, estimate roots if not perfect
• Solve simple equations involving square roots and cube roots
• Prove the Pythagorean Theorem using visual proof
• Use Pythagorean Theorem to solve problems, such as finding distance between two points and unknown side lengths of a right triangle

### Unit 8 – Association in Data

Big Ideas

• Examine different ways to organize bivariate data (scatter plots & two-way tables)
• Use scatter plots and fitted lines to analyze numerical data and identify associations
• Use two-way tables and bar graphs to identify associations in categorical data

Required Skills

• Construct and interpret scatter plots
• Discuss patterns (clustering, outliers, and association)
• Draw lines of best fit, find their equations, and use to make interpolations/extrapolations
• Construct and investigate patterns of associations that occur in two-way frequency tables