Grade 3

Grade 6

Mathematics

I. PRE-ALGEBRA

A. PROPERTIES OF THE REAL NUMBERS

·Know and use the associative, commutative, and distributive properties by name and in simplifying expressions involving numbers and variables.

·Understand absolute value and evaluate expressions such as |2x-3| + 3x.

B. LINEAR APPLICATIONS AND PROPORTIONALITY

·Know the concept of slope.

·Translate situations of proportionality into equations of the form y = mx, where m is the constant of proportionality or slope; specifically know and understand d = rt and i = prt.

·Show situations of constant proportionality as a line on the coordinate plane.

·Introduce the concept of a function and determine the equation of a linear function given its slope and intercepts in the form y = mc + b.

·Estimate the values of b and m from a given linear graph.

C. POLYNOMIAL ARITHMETIC

·Add, subtract, multiply, and divide monomials and polynomials (divide polynomials by monomials only).

·Factor binomials that have a common monomial factor.

D. EQUIVALENT EQUATIONS AND INEQUALITIES

·Review equality properties for equations.

·Know that addition or subtraction of the same value from both sides of an inequality maintains the inequality.

·Know that multiplying or dividing both sides on an inequality by a positive number maintains the inequality, but multiplying or dividing by a negative number reverses the inequality; be able to show why using a number line.

·Simplify and solve linear equations in one variable such as 3(2x-5) + 4x = 12(x+5).

·Simplify and graph solution to linear inequalities in one variable such as 3(2x – 5) + 4x ≤ 12(x+5).

E. INTEGER EXPONENTS

·Know and use the associative, commutative, and distributive properties by name and in simplifying expressions involving numbers and variables.

·Understand absolute value and evaluate expressions such as |2x-3| + 3x.

·Know the concept of slope.

·Translate situations of proportionality into equations of the form y = mx, where m is the constant of proportionality or slope; specifically know and understand d = rt and i = prt.

·Show situations of constant proportionality as a line on the coordinate plane.

·Introduce the concept of a function and determine the equation of a linear function given its slope and intercepts in the form y = mc + b.

·Estimate the values of b and m from a given linear graph.

·Add, subtract, multiply, and divide monomials and polynomials (divide polynomials by monomials only).

·Factor binomials that have a common monomial factor.

·Review equality properties for equations.

·Know that addition or subtraction of the same value from both sides of an inequality maintains the inequality.

·Know that multiplying or dividing both sides on an inequality by a positive number maintains the inequality, but multiplying or dividing by a negative number reverses the inequality; be able to show why using a number line.

·Simplify and solve linear equations in one variable such as 3(2x-5) + 4x = 12(x+5).

·Simplify and graph solution to linear inequalities in one variable such as 3(2x – 5) + 4x ≤ 12(x+5).

·Know the meaning of an exponent n when n is positive or negative.

·Know that a non-zero number to the zero power is one.

·Understand why a negative number to an even power is positive and a negative number to odd power is negative.

·Know the multiplication properties of exponents:

Product of powers: (a^m) (aⁿ) = a^(m+n)

Power of a power: (a^m)ⁿ = a^mn

Power of a product: (ab)^m = (a^m)(b^m)

·Convert decimal numbers to and from scientific notation

·Know the proper order of operations with exponents.

·Know and use the associative, commutative, and distributive properties by name and in simplifying expressions involving numbers and variables.

·Understand absolute value and evaluate expressions such as |2x-3| + 3x.

·Know the concept of slope.

·Translate situations of proportionality into equations of the form y = mx, where m is the constant of proportionality or slope; specifically know and understand d = rt and i = prt.

·Show situations of constant proportionality as a line on the coordinate plane.

·Introduce the concept of a function and determine the equation of a linear function given its slope and intercepts in the form y = mc + b.

·Estimate the values of b and m from a given linear graph.

·Add, subtract, multiply, and divide monomials and polynomials (divide polynomials by monomials only).

·Factor binomials that have a common monomial factor.

·Review equality properties for equations.

·Know that addition or subtraction of the same value from both sides of an inequality maintains the inequality.

·Know that multiplying or dividing both sides on an inequality by a positive number maintains the inequality, but multiplying or dividing by a negative number reverses the inequality; be able to show why using a number line.

·Simplify and solve linear equations in one variable such as 3(2x-5) + 4x = 12(x+5).

·Simplify and graph solution to linear inequalities in one variable such as 3(2x – 5) + 4x ≤ 12(x+5).

·Know the meaning of an exponent n when n is positive or negative.

·Know that a non-zero number to the zero power is one.

·Understand why a negative number to an even power is positive and a negative number to odd power is negative.

·Know the multiplication properties of exponents:

Product of powers: (am) (an) = a(m+n)

Power of a power: (am)n = amn

Power of a product: (ab)m = (am)(bm)

·Convert decimal numbers to and from scientific notation

·Know the proper order of operations with exponents.

Product of powers: (a^m) (aⁿ) = a^(m+n)

Power of a power: (a^m)ⁿ = a^mn

Power of a product: (ab)^m = (a^m)(b^m)