Eighth Grade Math Grade Expectations

M8:1 Demonstrates conceptual understanding of rational numbers

with respect to percents as a way of describing change (percent

increase and decrease) using explanations, models, or other

representations.

M8:2 Demonstrates understanding of the relative magnitude of

numbers by ordering or comparing rational numbers, common

irrational numbers (square root of 2, and p), numbers with whole-number or

fractional bases and whole-number exponents, square roots,

absolute values, integers, or numbers represented in scientific

notation using number lines or equality and inequality symbols.

M8:3 No M8:3 at this grade level

M8:4 Accurately solves problems involving proportional reasoning

(percent increase or decrease, interest rates, markups, or rates);

and squares, cubes and taking square or cube roots.

(IMPORTANT: Applies the conventions of order of operations.)

M8:5 No M8:5 at this grade level

M8:6 No M8:6 at this grade level

M8:7 Estimates and evaluates the reasonableness of solutions

appropriate to grade level.

M8:8 Applies properties of numbers (greatest common factor [GCF],

least common multiple [LCM], prime factorization, divisibility,

inverses, and identities), and commutative, distributive, and

associative properties of operations to solve problems and to

simplify computations.

M8:9 Models situations geometrically. Uses properties and attributes

of lines, angles, and two- and three-dimensional shapes) to

formulate and solve problems.

M8:10 Applies the Pythagorean Theorem to find a missing side of a right

triangle, or in problem-solving situations and solves problems by

applying the Triangle Inequality Theorem to determine if three line

segments with given lengths form a triangle, and the sum of the

angles in a convex polygon of any number of sides.

M8:11 No M8:11 at this grade level

M8:12 No M8:12 at this grade level

M8:13 Applies concepts of similarity to determine the impact of scaling

on the volume or surface area of three-dimensional figures when

linear dimensions are multiplied by a constant factor; to determine

the length of sides of similar triangles, or to solve problems

involving growth and rate and makes scale drawings.

M8:14 Demonstrates conceptual understanding of surface area

or volume by solving problems involving surface area and

volume of rectangular prisms, cylinders, or pyramids. Expresses all

measures using appropriate units.

M8:15 Measures and uses units of measures appropriately and

consistently when solving problems across the content

strands. Makes conversions within or across systems. (See

Appendix B for benchmark units and equivalences for each grade.)

M8:16 No M8:16 at this grade level

M8:17 Sketches a variety of three-dimensional objects using

orthogonal views (projections and isometric views), or constructs1

or accurately represents angle bisector, perpendicular bisector,

congruent segments and regular polygons.

Draws nets of three-dimensional shapes.

M8:18 No M8:18 at this grade level

M8:19 Identifies and extends to specific cases a variety of patterns

(linear and nonlinear) represented in models, tables, sequences,

graphs, or in problem situations; and generalizes a linear

relationship (nonrecursive explicit equation); generalizes a linear

relationship to find a specific case; generalizes a nonlinear

relationship using words or symbols; or generalizes a common

nonlinear relationship to find a specific case.

M8:20 Demonstrates conceptual understanding of linear

relationships ( y = kx; y = mx + b) as a constant rate of change

by solving problems involving the relationship between slope and

rate of change; informally and formally determining slopes and

intercepts represented in graphs, tables, or problem situations;

or describing the meaning of slope and intercept in context; and

distinguishes between linear relationships (constant rates of

change) and nonlinear relationships (varying rates of change)

represented in tables, graphs, equations, or problem situations; or

describes how change in the value of one variable relates to

change in the value of a second variable in problem situations

with constant and varying rates of change.

M8:21 Demonstrates conceptual understanding of algebraic

expressions by evaluating and simplifying (including those with

square roots, whole-number exponents, or rational numbers); or by

evaluating an expression within an equation (e.g., determine the

value of y when x = 4 given y = 7 * square root of x + 2 x).

M8:22 Demonstrates conceptual understanding of equality by showing

equivalence between two expressions (expressions consistent

with the parameters of the left- and right-hand sides of the

equations being solved at this grade level) using models or different

representations of the expressions, solving formulas for a variable

requiring one transformation (e.g., d = rt; d/ r = t); by solving

multistep linear equations with integer coefficients; by showing that

two expressions are or are not equivalent by applying commutative,

associative, or distributive properties, order of operations, or

substitution; and by informally solving problems involving systems of

linear equations in a context.

M8:23 Interprets a given representation (line graphs, scatter plots,

histograms, or box-and-whisker plots) to analyze the data to

formulate or justify conclusions, to make predictions, or to solve

problems.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M8:24.)

M8:24 Analyzes patterns, trends, or distributions in data in a variety

of contexts by determining or using measures of central

tendency (mean, median, or mode), dispersion (range or variation),

outliers, quartile values, or estimated line of best fit to analyze

situations, or to solve problems; and evaluates the sample from

which the statistics were developed (bias, random, or nonrandom).

M8:25 Organizes and displays data using scatter plots to answer

questions related to the data, to analyze the data to formulate

or justify conclusions, to make predictions, or to solve problems;

or identifies representations or elements of representations that

best display a given set of data or situation, consistent with the

representations required in M8: 23.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M8:24.)

M8:26 Uses counting techniques to solve problems in context involving

combinations or permutations using a variety of strategies (e.g.,

organized lists, tables, tree diagrams, models, Fundamental

Counting Principle, or others).

M8:27 For a probability event in which the sample space may or may

not contain equally likely outcomes, determines the possible

outcomes by either sample space (organized list, table, tree

model, area model) or Fundamental Counting Principle and

determines the theoretical probability of that event as a ratio of

favorable outcomes to possible outcomes. Expresses the ratio as a

fraction, decimal, or percent.

M8:28 In response to a teacher- or student-generated question,

makes a hypothesis, collects appropriate data, organizes the data,

appropriately displays/represents numerical and/or categorical

data, analyzes the data to draw conclusions about the questions or

hypothesis being tested, and when appropriate to make predictions,

asks new questions, or makes connection to real-world situations.

(See also GLEs M24, M25 and M29.)

M8:29 Compares and contrasts theoretical and experimental

probabilities of compound events using fractions, decimals, or

percents; and uses theoretical or experimental probabilities to

determine the fairness of a game.

M8:30 Demonstrate understanding of mathematical problem solving2

and communication through:3

• Approach & Reasoning—The reasoning, strategies, and skills

used to solve the problem;

• Connections—Demonstration of observations, applications,

extensions, and generalizations;

• Solution—All of the work that was done to solve the problem,

including the answer;

• Mathematical Language—The use of mathematical language

in communicating the solution;

• Mathematical Representation—The use of mathematical

representation to communicate the solution; and

• Documentation—Presentation of the solution.

2 Problem-solving situations are mathematical problems that reflect the levels of mathematics in the Grade Level Expectations.

3 See Vermont Elementary and Middle Level Mathematics Portfolio Scoring Guide for additional information.

4 See Vermont High School Level Mathematics Portfolio Scoring Guide for additional information.