8th Grade Math (Maryland MCCRS)

Number and Operation Sense – 8.NOS.A: Irrational numbers

• 8.NOS.A.1 Recognize irrational numbers as decimals that neither end nor repeat and explain why they are not ratios of integers.
• 8.NOS.A.2 Use rational approximations to place irrational numbers on a number line, compare them and estimate expressions.

Number and Operation Sense – 8.NOS.B: Exponents

• 8.NOS.B.3 Apply the properties of integer exponents to write equivalent numerical expressions.
• 8.NOS.B.4 Use square roots and cube roots to represent solutions and describe numbers.
  • a. Use root symbols for solutions of x² = p and x³ = p where p is a positive rational number.
  • b. Evaluate square roots of perfect squares from 1 to 100 and cube roots of perfect cubes from 1 to 125 by inspection.
• 8.NOS.B.5 Use scientific notation to represent and compare very large or very small quantities, and compute with it using technology.
  • a. Write numbers as a single digit times an integer power of 10 to estimate and compare sizes.
  • b. Model and compute real-world quantities in scientific notation, choosing and interpreting units.

Algebraic Thinking – 8.AT.A: Proportional relationships and linear equations

• 8.AT.A.1 Analyze and compare proportional relationships using slope.
  • a. Graph proportional relationships and interpret the unit rate as the slope.
  • b. Compare proportional relationships given as graphs, equations or tables by their slopes.
• 8.AT.A.2 Use proportional reasoning to explain why slope is constant and to write linear equations.
  • a. Use similar ratios to show the slope is the same between any two points on a non-vertical line.
  • b. Write equations for lines through the origin and for lines shifted vertically by b.

Algebraic Thinking – 8.AT.B: Equations, inequalities and systems

• 8.AT.B.3 Solve linear equations in one variable and classify how many solutions they have.
  • a. Give examples with one, infinitely many or no solutions and justify by rewriting the equation.
  • b. Solve equations with rational coefficients, including distributing and combining like terms.
• 8.AT.B.4 Solve linear inequalities in one variable and graph the solutions.
  • a. Solve inequalities, including ones needing distribution and combining like terms.
  • b. Show the solution set on a number line and describe it in context.
• 8.AT.B.5 Analyze and solve systems of two linear equations in two variables.
  • a. Interpret the solution as the point of intersection and check it satisfies both equations.
  • b. Solve by graphing and by substitution, choosing and justifying a method.
  • c. Use structure to tell whether a system has no, one or infinitely many solutions.
  • d. Model and solve real-world problems with two linear equations.

Algebraic Thinking – 8.AT.C: Reason about functions

• 8.AT.C.6 Decide whether a relationship is a function by checking that each input has exactly one output.
  • a. Decide whether tables, mappings or descriptions define a function and explain.
  • b. Read input-output pairs from a graph and decide whether it shows a function.
• 8.AT.C.7 Compare rates of change and intercepts of two linear functions shown in different ways.
• 8.AT.C.8 Classify functions as linear or nonlinear from equations, graphs or input-output pairs and justify.

Algebraic Thinking – 8.AT.D: Model with functions

• 8.AT.D.9 Interpret the graph of a linear function and match equations to graphs.
  • a. Read the slope and y-intercept from a graph.
  • b. Match a linear equation to its graph.
• 8.AT.D.10 Build and interpret a linear function that models how two quantities are related.
  • a. Find the rate of change and initial value from two points, a graph, a table or a description and write the equation.
  • b. Interpret the rate of change and initial value in context.
• 8.AT.D.11 Describe a functional relationship qualitatively from a graph and sketch a graph from a description.

Geometric Reasoning and Measurement – 8.GR.A: Conjecture about and verify geometric relationships

• 8.GR.A.1 Write and solve equations for unknown angles using supplementary, complementary, vertical and adjacent angles.
• 8.GR.A.2 Draw or build triangles from three given measures and decide whether they give one triangle, more than one or none.
• 8.GR.A.3 Argue informally that a triangle's angles sum to 180° and an exterior angle equals the two remote interior angles.

Geometric Reasoning and Measurement – 8.GR.B: The Pythagorean theorem

• 8.GR.B.4 Understand and reason with the Pythagorean theorem and its extensions.
  • a. Explain the theorem and why it holds for every right triangle, using diagrams or informal proof.
  • b. Use the converse to test for right triangles and use Pythagorean inequalities to classify triangles as acute or obtuse.
• 8.GR.B.5 Apply the Pythagorean theorem to solve problems in context.
  • a. Find unknown side lengths in right triangles.
  • b. Find the distance between two points on a coordinate grid.

Reasoning with Data, Statistics and Probability – 8.DS.A: Statistical inquiry

• 8.DS.A.1 Evaluate predictions and conclusions drawn from bivariate data.
  • a. Decide whether associations in sample data justify generalizing to a wider population.
  • b. Spot limits or bias in data collection or in reading trends from scatter plots.

Reasoning with Data, Statistics and Probability – 8.DS.B: Model with bivariate data

• 8.DS.B.2 Make and interpret scatter plots to look for association, describing clusters, outliers and linear or nonlinear patterns.
• 8.DS.B.3 Compare how well different straight-line models fit the same scatter plot.
• 8.DS.B.4 Use a given linear model to predict and interpret its slope and y-intercept in context.

Reasoning with Data, Statistics and Probability – 8.DS.C: Probability

• 8.DS.C.5 Make two-way tables for two categorical variables and calculate and interpret relative frequencies.
• 8.DS.C.6 Find probabilities of compound events by representing or simulating the sample space.
  • a. Represent the sample space and pick out the outcomes that make up an event described in everyday words.
  • b. Find the probability as the fraction of outcomes in the sample space that give the event.