END OF GRADE 7

END OF GRADE 7: NH GRADE LEVEL EXPECTATIONS

Numbers and Operations

20% of NECAP QUESTIONS

M(N&O)–7–1 Demonstrates conceptual understanding of rational numbers with respect to percents as a means of comparing the same or different parts of the whole when the wholes vary in magnitude (e.g., 8 girls in a classroom of 16 students compared to 8 girls in a classroom of 20 students, or 20% of 400 compared to 50% of 100); and percents as a way of expressing multiples of a number (e.g., 200% of 50) using models, explanations, or other representations*.

M(N&O)–7–2 Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent rational numbers across number formats, numbers with whole number bases and whole number exponents (e.g., 33, 43), integers, absolute values, or numbers represented in scientific notation using number lines or equality and inequality symbols. Sample NECAP Test Item.

M(N&O)–7–4 Accurately solves problems involving proportional reasoning; percents involving discounts, tax, or tips; and rates. (IMPORTANT: Applies the conventions of order of operations including parentheses, brackets, or exponents.) Sample NECAP Test Item. Additional Sample

*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.

NECAP TESTING VOCABULARY

Geometry and Measurement

25% of NECAP QUESTIONS

M(G&M)–7–1 Uses properties of angle relationships resulting from two or three intersecting lines (adjacent angles, vertical angles, straight angles, or angle relationships formed by two non-parallel lines cut by a transversal), or two parallel lines cut by a transversal to solve problems.

M(G&M)–7–2 Applies theorems or relationships (triangle inequality or sum of the measures of interior angles of regular polygons) to solve problems. Sample NECAP Test Item.

M(G&M)–7–4 Applies the concepts of congruency by solving problems on a coordinate plane involving reflections, translations, or rotations.

M(G&M)–7–5 Applies concepts of similarity by solving problems involving scaling up or down and their impact on angle measures, linear dimensions and areas of polygons, and circles when the linear dimensions are multiplied by a constant factor. Describes effects using models or explanations. Sample NECAP Test Item. Additional Sample

M(G&M)–7–6 Demonstrates conceptual understanding of the area of circles or the area or perimeter of composite figures (quadrilaterals, triangles, or parts of circles), and the surface area of rectangular prisms, or volume of rectangular prisms, triangular prisms, or cylinders using models, formulas, or by solving related problems. Expresses all measures using appropriate units. Sample NECAP Test Item.

NECAP TESTING VOCABULARY

Functions and Algebra

40% of NECAP QUESTIONS

M(F&A)–7–1 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 using words and symbols; generalizes a linear relationship to find a specific case; or writes an expression or equation using words or symbols to express the generalization of a nonlinear relationship. Sample NECAP Test Item. Additional Sample.

M(F&A)–7–2 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, by describing the meaning of slope in concrete situations, or informally determining the slope of a line from a table or graph; and distinguishes between constant and varying rates of change in concrete situations represented in tables or graphs; 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 rates of change. Sample NECAP Test Item.

M(F&A)–7–3 Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write algebraic expressions (including those with whole number exponents or more than one variable); or by evaluating algebraic expressions (including those with whole number exponents or more than one variable); or by evaluating an expression within an equation (e.g., determine the value of y when x = 4 given y = 5x3 – 2). Sample NECAP Test Item. Additional Sample.

M(F&A)–7–4 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 multi-step linear equations of the form ax ± b = c with a ≠ 0, ax ± b = cx ± d with a, c ≠ 0, and (x/a) ± b = c with a ≠ 0, where a, b, c and d are whole numbers; or by translating a problem solving situation into an equation consistent with the parameters of the type of equations being solved for this grade level. Sample NECAP Test Item.

NECAP TESTING VOCABULARY

Data, Statistics and Probability

15% of NECAP QUESTIONS

M(DSP)–7–1 Interprets a given representation (circle graphs, scatter plots that represent discrete linear relationships, or histograms) 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 M(DSP)–7–2.)

M(DSP)–7–2 Analyzes patterns, trends, or distributions in data in a variety of contexts by solving problems using measures of central tendency (mean, median, or mode), dispersion (range or variation), or outliers to analyze situations to determine their effect on mean, median, or mode; and evaluates the sample from which the statistics were developed (bias).

M(DSP)–7–3 Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M(DSP)–7–1.

M(DSP)–7–5 For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event in a problem-solving situation. Sample NECAP Test Item.

NECAP TESTING VOCABULARY