Math Small Group Hyperdoc

Grade 8 Math

Rigid Transformations and Congruence

  • Objective 1: Perform transformations and determine the coordinates, distances, and angles that result.
  • Objective 2: Describe sequences of transformations that carry one figure onto another.
  • Objective 3 - Solve problems involving angles in triangles.
  • Objective 4 - Recognize the congruent angles formed when parallel lines are cut by a transversal, and solve problems involving them.

Dilations, Similarity, & Introducing Slope

  • Objective 1: Use the definition of congruence and similarity to determine the relationship between two figures.
  • Objective 2: Determine the slope or rate of change from a line or two points.

Linear Relationships

  • Objective 1: Compare proportional relationships represented in different ways.
  • Objective 2: Work fluently between multiple representations of linear relationships.
  • Objective 3: Interpret the slope and y-intercept in a linear relationship.

Linear Equations & Linear Systems

  • Objective 1: Solve one-variable linear equations.
  • Video: Equation with variables on both sides: fractions
  • Video: Equations with parentheses
  • Website:Multi-step equations review
  • Practice: Solving Equations with Fractions
  • Practice: Equations with variables on both sides
  • Practice: Equations with parentheses
  • Check for Understanding: Equations with variables on both sides: decimals & fractions
  • Objective 2: Solve systems of equations by graphing, algebraically, or by inspection.
  • Objective 4 - Identify the number of solutions to a one-variable equation.
  • Objective 5 - Identify the number of solutions to a system of equations.

Functions & Volume

  • Objective 1: Understand that a function is a rule that assigns to each input exactly one output.
  • Objective 2: Analyze graphs of functions and use them to answer questions about a context.
  • Objective 3 - Compare properties of two functions each represented in a different way.
  • Objective 4 - Apply the volume formulas for cylinders, cones, and spheres to solve problems.

Associations in Data

  • Objective 1 - Describe patterns in a scatter plot, such as clustering, outliers, positive or negative association, linear association, or nonlinear association.
  • Objective 2 - Interpret a two-way table summarizing data on two categorical variables.

Exponents & Scientific Notation

  • Objective 1 - Apply the rules and properties of exponents to rewrite expressions.
  • Objective 2 - Extend exponent rules to negative exponents, and rewrite exponential expressions involving negative exponents to use positive exponents instead.
  • Objective 3 - Use scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.
  • Objective 4 - Perform operations with numbers expressed in scientific notation.

Pythagorean Theorem & Irrational Numbers

  • Objective 1 -Solve equations and evaluate expressions involving perfect squares, perfect cubes, square roots, and cube roots.
  • Objective 2 - Apply the Pythagorean Theorem to solve problems on and off the coordinate grid.
  • Objective 3 - Distinguish between numbers that are rational and irrational.
  • Objective 4 - Work fluently between fractions and their decimal expansions.
  • Objective 5 - Estimate the values and number line locations of irrational numbers.

Geometry

MS Geometry Review

  • Objective 1 - Solve problems involving unknown angles.
  • Objective 2 - Perform transformations and determine the coordinates, distances, and angles that result.

Tools of Geometry

  • Objective 1 - Identify transformations
  • Objective 2 - Given a figure and one or more rigid motions, specify the new figure.
  • Objective 3 - Specify a sequence of rigid motions that carries one figure onto another.

Congruence

  • Objective 1 - Use the definition of congruence to specify whether two figures are congruent.
  • Objective 2 - Use known criteria for congruence to specify whether two triangles are congruent.

Similarity

  • Objective 1 - Use the definition of similarity to determine whether two figures are similar.
  • Objective 2 - Use triangle similarity criteria to solve problems.

Trigonometry

  • Introductory Materials
  • Objective 1 - Identify and calculate trigonometric ratios, given a right triangle.
  • Objective 2 - Use sine, cosine, and tangent to find unknown side and angles in right triangles.
  • Objective 3 - Solve word problems involving right triangles.
  • Objective 4 - Use the Laws of Sines to find unknown measurements in triangles.
  • Objective 5 - Use the Laws of Cosines to find unknown measurements in triangles.

Coordinate Geometry

  • Introductory Materials
  • Objective 1 - Find the distance between two points in a coordinate plane.
  • Objective 2 - Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
  • Objective 3 - Use coordinates to prove simple geometric theorems algebraically.
  • Objective 4 - Use the parallel and perpendicular slope criteria to solve geometric problems.
  • Objective 5 - Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Circles and Conic Sections

  • Objective 1 - Work fluently between algebraic and graphical representations of circles.
  • Objective 2 - Identify the conic section given an equation.
  • Objective 3 - Identify and describe the relationships among geometric objects related to circles.
  • Objective 4 - Find arc lengths and areas of sectors of circles.

Algebra I

Patterns and Sequence

  • Objective 1 - Identify the key features of arithmetic and geometric sequences.
  • Objective 2 - Find unknown terms in arithmetic and geometric sequences.
  • Objective 3 - Given only the growth factor, determine whether a sequence is growing or decaying.
  • Objective 4 - Work fluently between sequences and the appropriate recursive and explicit formulas.
  • Objective 5 - Represent and solve problems involving sequences.

Features of Functions

  • Objective 1 - Work fluently between multiple representations of functions, including function notation.
  • Objective 2 - Identify key features of functions.
  • Objective 3 - Understand that a function has two sets (the domain & range) and each element of the domain is assigned exactly one element of the range.
  • Objective 4 - Relate the domain and range of a function to its graph.

Linear and Exponential Functions

  • Introductory Materials
  • Objective 1 - Find the slope or rate of change in linear relationships.        
  • Objective 2 - Work fluently between multiple representations of linear relationships.
  • Objective 3 - Work fluently between multiple representations of exponential functions.

Equations and Inequalities

Quadratic Functions

Quadratic Equations