MI 8th Grade Math Curriculum

MI 8th Grade Math Curriculum

• 8.NS.A.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
  • Rational vs. Irrational numbers
  • Understanding the number systems
• 8.NS.A.2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2).
  • Converting repeating decimals to fractions
  • Determine square roots of rational numbers
  • Estimating square roots
• 8.EE.A.1Know and apply the properties of integer exponents to generate equivalent numerical expressions.
  • Product rule of exponents
  • Quotient rule of exponents
  • Power of a product rule
  • Power of a quotient rule
  • Power of a power rule
  • Using exponents to describe numbers
  • Exponent rules
  • Order of operations with exponents
• 8.EE.A.2Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
  • Cubic and cube roots
  • Square and square roots
  • Converting radicals to mixed radicals
  • Converting radicals to entire radicals
  • Squares and square roots
• 8.EE.A.3Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
  • Scientific notation
• 8.EE.B.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
  • Parallel and perpendicular lines in linear functions
  • Understanding graphs of linear relationships
  • Understanding tables of values of linear relationships
  • Applications of linear relationships
  • Identifying proportional relationships
• 8.EE.B.6Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
  • Slope intercept form: y = mx + b
  • Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
• 8.EE.C.7Solve linear equations in one variable.
  • Introduction to linear equations
  • Model and solve one-step linear equations: ax = b, x/a = b
  • Solving two-step linear equations using addition and subtraction: ax + b = c
  • Solving two-step linear equations using multiplication and division: x/a + b = c
  • Solving two-step linear equations using distributive property: a(x + b) = c
  • Solving literal equations
• 8.EE.C.8Analyze and solve pairs of simultaneous linear equations.
  • Solving systems of linear equations by graphing
  • Determining number of solutions to linear equations
  • Solving systems of linear equations by elimination
  • Solving systems of linear equations by substitution
• 8.F.A.1Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
  • Identifying functions
  • Relationship between two variables
• 8.F.A.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • Function notation
• 8.F.B.4Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
  • Applications of linear relations
• 8.F.B.5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
  • Graphing linear functions using table of values
• 8.G.A.1Verify experimentally the properties of rotations, reflections, and translations.
  • Tessellations using translations and reflections
  • Line symmetry
• 8.G.A.2Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  • Rotational symmetry and transformations
• 8.G.A.3Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  • Tessellations using rotations
  • Enlargements and reductions with scale factors
• 8.G.A.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
  • Similar polygons
• 8.G.A.5Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
  • Similar triangles
• 8.G.B.6Explain a proof of the Pythagorean Theorem and its converse.
  • Pythagorean theorem
• 8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  • Using the pythagorean relationship
• 8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
  • Applications of pythagorean theorem
  • Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
• 8.G.C.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
  • Word problems relating volume of prisms and cylinders
  • Surface area and volume of cones
  • Surface area and volume of spheres
  • Volume of cylinders
• 8.SP.A.1Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • Reading linear relation graphs
  • Box-and-whisker plots and scatter plots
• 8.SP.A.2Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
  • Solving linear equations by graphing