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NECAP Grade Level Expectations (GLEs) for Math Grade 8
Clicking on a highlighted term will bring up a definition or description of the term, along with examples that help to exemplify it. The examples are not necessarily aligned to the particular grade, but help to clarify the term being defined.
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Web-based Math GLEs |
M(N&O)-8-1 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*. *Specifications for area, set, and linear models for grades 5 - 8: Fractions: The number of parts in the whole are equal to the denominator, a multiple of the denominator, or a factor of the denominator. Percents: The number of parts in the whole is equal to 100, a multiple of 100, or a factor of 100 (for grade 5); the number of parts in the whole is a multiple or a factor of the numeric value representing the whole (for grades 6-8). Decimals (including powers of ten): The number of parts in the whole is equal to the denominator of the fractional equivalent of the decimal, a multiple of the denominator of the fractional equivalent of the decimal, or a factor of the denominator of the fractional equivalent of the decimal. |
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M(N&O)-8-2 Demonstrates
understanding of the relative magnitude of numbers by ordering or
comparing rational numbers, common irrational numbers (e.g.  ,
, ), 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. |
Whole number bases and whole number exponents, and fractional bases with whole number exponents |
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| M(N&O)-8-4 Accurately
solves problems involving proportional reasoning (percent increase
or decrease, interest rates, markups, or rates); multiplication or
division of integers; and squares, cubes, and taking square or cube
roots.
(IMPORTANT: Applies the conventions of order of operations.) |
Whole number bases and whole number exponents, and fractional bases with whole number exponents |
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M(G&M)-8-2 Applies the Pythagorean Theorem to find a missing side of a right triangle, or in problem solving situations. | Pythagorean Theorem | ||
| M(G&M)-8-5 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. | ||||
| M(G&M)-8-6 Demonstrates conceptual understanding of surface area or volume by solving problems involving surface area and volume of rectangular prisms, triangular prisms, cylinders, or pyramids. Expresses all measures using appropriate units. |
Measures and uses units of measure appropriately and consistently Whole number bases and whole number exponents, and fractional bases with whole number exponents |
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Going beyond the K – 8 GLEs: Definitions F&A – 21-24 (function, dependent and independent variables, domain of a function, and range of a function are included in this section to answer the question – “Where does the Functions and Algebra strand go next?” However, the concepts addressed in this section will not be assessed on the K–8 NECAP. | |||
| M(F&A)-8-1 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 (non-recursive explicit equation); generalizes a linear relationship to find a specific case; generalizes a nonlinear relationship using words orsc symbols; or generalizes a common nonlinear relationship to find a specific case. | Patterns
Expresses generalization or rule using words or symbols Pattern Summary Table by grade level Proportional linear relationships (y = kx) Non-proportional linear relationships (y = mx + b) |
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| M(F&A)-8-2 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. |
Proportional linear relationships (y = kx) Non-proportional linear relationships (y = mx + b) Solves problems involving linear relationships Describes the meaning of slope and intercept in concrete situations |
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| M(F&A)-8-3 Demonstrates conceptual understanding of algebraic expressions by evaluating and simplifying algebraic expressions (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 ). |
Whole number bases and whole number exponents, and fractional bases with whole number exponents Evaluating algebraic expressions Simplifying algebraic equations |
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| M(F&A)-8-4 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 multi-step 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. | Equality
Proportional linear relationships (y = kx) Non-proportional linear relationships (y = mx =b) Write equivalent forms of formulas Examples of forms of equations |
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M(DSP)-8-1 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. |
Interprets a given representation Histogram Histogram |
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| M(DSP)-8-2 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 non-random). | Pattern
Evaluates samples from which the statistics were developed (bias) Analyzes
the impact of outliers on the mean, median and mode |
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| M(DSP)-8-3 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 M(DSP)-8-1. (IMPORTANT: Analyzes data consistent with concepts and skills in M(DSP)-8-2.) |
Scatter
plot
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| M(DSP)-8-4 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, orsc others). | Solves
problems using a variety of counting strategies
Fundamental Counting Principle
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