END OF GRADE 5

END OF GRADE 5: NH GRADE LEVEL EXPECTATIONS

Numbers and Operations

LEVEL OF EMPHASIS ON NECAP TEST 45%

M(N&O)–5–1 Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 9,999,999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; and positive fractional numbers (proper, mixed number, and improper) (halves, fourths, eighths, thirds, sixths, twelfths, fifths, or powers of ten (10, 100, 1000)), decimals (to thousandths), or benchmark percents (10%, 25%, 50%, 75% or 100%) as a part to whole relationship in area, set, or linear models using models, explanations, or other representations*. CLICK HERE FOR SAMPLE QUESTION. ANOTHER SAMPLE.

M(N&O)–5–2 Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent positive fractional numbers, decimals, or benchmark percents within number formats (fractions to fractions, decimals to decimals, or percents to percents); or integers in context using models or number lines. CLICK HERE FOR SAMPLE QUESTION. ANOTHER SAMPLE.

M(N&O)–5–3 Demonstrates conceptual understanding of mathematical operations by describing or illustrating the meaning of a remainder with respect to division of whole numbers using models, explanations, or solving problems. CLICK HERE FOR SAMPLE QUESTION.

M(N&O)–5–4 Accurately solves problems involving multiple operations on whole numbers or the use of the properties of factors, multiples, prime, or composite numbers; and addition or subtraction of fractions (proper) and decimals to the hundredths place. (Division of whole numbers by up to a two-digit divisor.) (IMPORTANT: Applies the conventions of order of operations with and without parentheses.) CLICK HERE FOR SAMPLE QUESTION. ANOTHER 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.

Geometry and Measurement

LEVEL OF EMPHASIS ON NECAP TEST 25%

M(G&M)–5–1 Uses properties or attributes of angles (right, acute, or obtuse) or sides (number of congruent sides, parallelism, or perpendicularity) to identify, describe, classify, or distinguish among different types of triangles (right, acute, obtuse, equiangular, or equilateral) or quadrilaterals (rectangles, squares, rhombi, trapezoids, or parallelograms).

M(G&M)–5–3 Uses properties or attributes (shape of bases, number of lateral faces, or number of bases) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, spheres, pyramids, or cones).

M(G&M)–5–6 Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles or right triangles through models, manipulatives, or formulas, the area of polygons or irregular figures on grids, and volume of rectangular prisms (cubes) using a variety of models, manipulatives, or formulas. Expresses all measures using appropriate units. CLICK HERE FOR SAMPLE QUESTION.

M(G&M)–5–7 Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands. CLICK HERE FOR SAMPLE QUESTION. ANOTHER SAMPLE.

Algebra and Functions

LEVEL OF EMPHASIS ON NECAP TEST 15%

M(F&A)–5–1 Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, or in problem situations; and writes a rule in words or symbols for finding specific cases of a linear relationship.

M(F&A)–5–3 Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write linear algebraic expressions involving any two of the four operations; or by evaluating linear algebraic expressions using whole numbers.

M(F&A)–5–4 Demonstrates conceptual understanding of equality by showing equivalence between two expressions using models or different representations of the expressions (expressions consistent with the parameters of M(F&A)–5–3), by solving one-step linear equations of the form ax = c, x ± b = c, or x/a = c, where a, b, and c are whole numbers with a ≠ 0; or by determining which values of a replacement set make the equation (multi-step of the form ax ± b = c where a, b, and c are whole numbers with a ≠ 0) a true statement (e.g., 2x + 3 = 11, {x: x = 2, 3, 4, 5}). CLICK HERE FOR SAMPLE QUESTION. ANOTHER SAMPLE.

Data, Statistics and Probability

LEVEL OF EMPHASIS ON NECAP TEST 15%

M(DSP)–5–1 Interprets a given representation (tables, bar graphs, circle graphs, or line graphs) to answer questions related to the data, 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)–5–2.) CLICK HERE FOR SAMPLE QUESTION.

M(DSP)–5–2 Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode) or range to analyze situations, or to solve problems. CLICK HERE FOR SAMPLE QUESTION.

M(DSP)–5–3 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)–5–1. CLICK HERE FOR SAMPLE QUESTION.

M(DSP)–5–5 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 and expresses the result as a fraction.