Math 8

  • Math 8 Information

    Math 8 Class Information Letter

    Semester 1 Topics

    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

    Semester 2 Topics

    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

  • Links to Other Web Sites

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    • the California Math CCSS Course 3 on-line textbook
    • i-Ready 

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