8th Grade Math (Colorado Academic Standards)

Standard 1: Number and Quantity

• MA.8.NS.A Know that some numbers are irrational and approximate them with rational numbers.
  • 1. Know irrational numbers are not rational; every number has a decimal expansion, and rational decimals repeat; convert repeating decimals to fractions.
  • 2. Use rational approximations to compare and place irrational numbers on a number line and estimate expressions.

Standard 2: Algebra and Functions

• MA.8.EE.A Work with radicals and integer exponents.
  • 1. Use the properties of integer exponents to write equivalent numerical expressions.
  • 2. Use square and cube root symbols for solutions to x² = p and x³ = p; know small perfect squares and cubes and that √2 is irrational.
  • 3. Use one digit times a power of 10 to estimate huge or tiny quantities and say how many times bigger one is.
  • 4. Calculate with numbers in scientific notation, choose suitable units and read technology output.
• MA.8.EE.B Connect proportional relationships, lines and linear equations.
  • 1. Graph proportional relationships with the unit rate as slope and compare relationships shown in different ways.
  • 2. Use similar triangles to explain why slope is constant on a line and derive y = mx and y = mx + b.
• MA.8.EE.C Analyze and solve linear equations and systems of two linear equations.
  • 1. Solve linear equations in one variable.
  • 1.a. Give examples of linear equations with one, infinitely many or no solutions and show which by simplifying.
  • 1.b. Solve linear equations with rational coefficients, including expanding and collecting like terms.
  • 2. Analyze and solve systems of two linear equations.
  • 2.a. Know a system's solutions are the intersection points of the graphs.
  • 2.b. Solve systems of two linear equations algebraically, estimate by graphing and solve simple cases by inspection.
  • 2.c. Solve real-world and math problems that lead to two linear equations in two variables.
• MA.8.F.A Define, evaluate and compare functions.
  • 1. Know a function assigns exactly one output to each input, and its graph is the set of input-output pairs.
  • 2. Compare properties of two functions shown in different ways (equation, graph, table, words).
  • 3. Know y = mx + b defines a linear function with a straight-line graph and give examples of non-linear functions.
• MA.8.F.B Use functions to model relationships between quantities.
  • 1. Build a linear function to model a relationship, find its rate of change and initial value, and interpret them.
  • 2. Describe a relationship from a graph (increasing, decreasing, linear, non-linear) and sketch graphs from descriptions.

Standard 3: Data, Statistics, and Probability

• MA.8.SP.A Investigate patterns of association in two-variable data.
  • 1. Make and interpret scatter plots and describe patterns such as clusters, outliers and positive, negative or non-linear association.
  • 2. Know straight lines model linear associations; fit a line informally and judge the fit.
  • 3. Use a linear model's equation to solve problems, interpreting slope and intercept.
  • 4. Show association in categorical data with two-way tables of frequencies and relative frequencies.

Standard 4: Geometry

• MA.8.G.A Understand congruence and similarity through transformations.
  • 1. Check by experiment the properties of rotations, reflections and translations.
  • 1.a. Lines map to lines and segments to segments of equal length.
  • 1.b. Angles map to angles of equal measure.
  • 1.c. Parallel lines map to parallel lines.
  • 2. Know two figures are congruent if rigid motions (rotations, reflections, translations) map one onto the other, and describe the sequence.
  • 3. Use coordinates to describe what dilations and rigid motions do to 2-D figures.
  • 4. Know similar figures are linked by rigid motions plus dilations, and describe such a sequence.
  • 5. Use informal arguments about triangle angle sums, exterior angles, angles at parallel lines with a transversal, and AA similarity.
• MA.8.G.B Understand and apply the Pythagorean theorem.
  • 1. Explain why the Pythagorean Theorem and its converse are true.
  • 2. Use the Pythagorean Theorem to find unknown sides of right triangles in 2-D and 3-D problems.
  • 3. Use the Pythagorean Theorem to find how far apart two points on a coordinate grid are.
• MA.8.G.C Solve volume problems with cylinders, cones and spheres.
  • 1. Know and use the volume formulas for cones, cylinders and spheres.