operations: includes brackets and exponents simplifying (–3/4) ÷ 1/5 + ((–1/3) x (–5/2)) simplifying 1 2 x (4/5)2 – paddle making exponents: includes variable bases 27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128; n4 = n x n x n x n exponent laws (e.g., 60 = 1; m1 = m; n5 x n3 = n8; y7/y3 = y4; (5n)3 = 53 x n3 = 125n3; (m/n)5 = m5/n5; and (32)4 = 38) limited to whole-number exponents and whole-number exponent outcomes when simplified (–3)2 does not equal –32 3x(x 4) = 3x2 12x polynomials: – – variables, degree, number of terms, and coefficients, including the constant term (x2 + 2x 4) + (2x2 3x 4) – – – (5x 7) (2x + 3) • 2n(n + 7) – – (15k2 ÷ (5k) –10k) using algebra tiles two-variable linear relations: two-variable continuous linear relations; includes rational coordinates horizontal and vertical lines graphing relation and analyzing interpolating and extrapolating approximate values spirit canoe journey predictions and daily checks multi-step: includes distribution, variables on both sides of the equation, and collecting like terms includes rational coefficients, constants, and solutions solving and verifying 1 + 2x = 3 2/3(x + 6) – solving symbolically and pictorially MATHEMATICS Content Elaborations Grade 9 –
operations: includes brackets and exponents simplifying (–3/4) ÷ 1/5 + ((–1/3) x (–5/2)) simplifying 1 – 2 x (4/5)2 paddle making exponents: includes variable bases 27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128; n4 = n x n x n x n exponent laws (e.g., 60 = 1; m1 = m; n5 x n3 = n8; y7/y3 = y4; (5n)3 = 53 x n3 = 125n3; (m/n)5 = m5/n5; and (32)4 = 38) limited to whole-number exponents and whole-number exponent outcomes when simplified (–3)2 does not equal –32 3x(x – 4) = 3x2 – 12x polynomials: variables, degree, number of terms, and coefficients, including the constant term (x2 + 2x – 4) + (2x2 – 3x – 4) (5x – 7) – (2x + 3) • 2n(n + 7) (15k2 –10k) ÷ (5k) using algebra tiles two-variable linear relations: two-variable continuous linear relations; includes rational coordinates horizontal and vertical lines graphing relation and analyzing interpolating and extrapolating approximate values spirit canoe journey predictions and daily checks multi-step: includes distribution, variables on both sides of the equation, and collecting like terms includes rational coefficients, constants, and solutions solving and verifying 1 + 2x = 3 – 2/3(x + 6) solving symbolically and pictorially MATHEMATICS Content – Elaborations Grade 9