Grade 6
2.1.17 Students demonstrate conceptual understanding of rational numbers with respect to ratios (comparison of two whole numbers by division a/b, a : b, and a ÷ b , where b 0); and rates (e.g., a out of b, 25%) using models, explanations, or other representations*. (M(N&O)-6-1)
2.1.18 Students demonstrate understanding of the relative magnitude of numbers by ordering or comparing numbers with whole number bases and whole number exponents (e.g.,33, 43), integers, or rational numbers within and across number formats (fractions, decimals, or whole number percents from 1- 100) using number lines or equality and inequality symbols.
(M(N&O)-6-2)
2.1.19 Students demonstrate conceptual understanding of mathematical operations by describing or illustrating the meaning of a power by representing the relationship between the base (whole number) and the exponent (whole number) (e.g.,33, 43); and the effect on the magnitude of a whole number when multiplying or dividing it by a whole number, decimal, or fraction. (M(N&O)-6-3)
2.1.20 Students accurately solve problems involving single or multiple operations on fractions (proper, improper, and mixed), or decimals; and addition or subtraction of integers; percent of a whole; or problems involving greatest common factor or least common multiple. (IMPORTANT: Applies the conventions of order of operations with and without parentheses.) (M(N&O)-6-4)
Grade 7
2.1.21 Students demonstrate 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)-7-1)
2.1.22 Students demonstrate 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. (M(N&O)-7-2)
2.1.23 Students accurately solve 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.) (M(N&O)-7-4)
*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.
Grades 9-Diploma
2.1.24 Students demonstrate understanding of the relative magnitude of real numbers by solving problems involving ordering or comparing rational numbers, common irrational numbers (e.g.,, ), rational bases with integer exponents, square roots, absolute values, integers, or numbers represented in scientific notation using number lines or equality and inequality symbols. (M(N&O)-10-2)
2.1.25 Students accurately solve problems involving rational numbers within mathematics, across content strands, disciplines or contexts (with emphasis on, but not limited to, proportions, percents, ratios, and rates). (M(N&O)–10–4)
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