Patterns, Sequences, Functions
| Find and extend patterns |
| Recognize and extend a pattern: shape, color and size |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Determine what operation is needed to solve a word problem (addition and subtraction) |
New Vocabulary in this Range: none
New Signs and Symbols: € for answer to equation
Solving Equations, Simplifying Expressions, Order of Operations
| Solve for missing numbers in an addition or subtraction sentence |
| Determine what operation is needed to solve a word problem (any operation) |
New Vocabulary in this Range: none
New Signs and Symbols: ( ) used in equations
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Solve for missing factors in a multiplication or division sentence |
| Evaluate a numerical equation involving more than one operation |
Properties
| Demonstrate the associative, commutative, and zero property of addition |
New Vocabulary in this Range: none
New Signs and Symbols: <, > symbols
Patterns, Sequences, Functions
| Find and extend patterns, both increasing and decreasing |
| Complete a table according to a rule |
| Choose and apply an appropriate problem solving strategy: Find a pattern |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Use inverse operations to find missing equation |
| Write number sentences using addition |
| Identify missing elements in number sentences |
Properties
| Identify the associative, commutative, identity and zero property of multiplication |
Ordered Pairs
| Graph ordered pairs in the first quadrant |
New Vocabulary in this Range: sign
New Signs and Symbols: - used as negative
Patterns, Sequences, Functions
| Count and write by 4’s |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Use symbols of inequality, < and > to write and complete number sentences |
| Solve simple addition problems with "n" as an addend or sum |
| Solve simple multiplication problems with "n" as a multiple or product |
| Solve simple division problems with "n" as a quotient or divisor |
| Identify the base and the exponent of a given numerical expression and calculate its value |
| Evaluate numerical expressions using the order of operations |
| Solve whole number equations with any operation |
New Vocabulary in this Range: if-then, product, sum
New Signs and Symbols: variables, exponents
Patterns, Sequences, Functions
| Use of a function "machine" to determine input and output |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Evaluate an expression involving more than one operation (order of operations) |
| Use the basic properties of multiplication to write an algebraic expression that is equivalent to a given algebraic expression |
| Solve equations involving more than one operation |
| Multiply and divide polynomials |
| Solve equations involving rational numbers (addition and subtraction) |
Properties
| Use strategies to develop computational fluency with multiplication: zero property, property of one, arrays, doubles, nine patterns |
| Use the basic properties of addition to write an algebraic expression equivalent to a given algebraic expression |
| Understand the properties of integers: commutative, associative, identity, zero property of multiplication, distributive property of multiplication over addition, and inverse property of addition |
New Vocabulary in this Range: input, output, table, associative, equation
New Signs and Symbols: £ , ³
Patterns, Sequences, Functions
| Use logic to solve a problem involving a function table |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Solve decimal equations (one step, addition and subtraction) |
| Solve integer equations (one step, multiplication and division) |
| Evaluate expressions using the order of operations (may include parentheses or exponents) |
| Solve quadratic equations |
New Vocabulary in this Range: commutative, solve, square numbers, input, output, number sequence
New Signs and Symbols: none
Patterns, Sequences, Functions
| Complete a function table according to a rule |
| Recognize and continue a number pattern and/or geometric representation (e.g. Fibonacci sequence, triangular numbers) |
| State a rule to explain a number pattern, including arithmetic progression |
| Investigate geometric patterns and relationships and describe them algebraically |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Use boxes or other symbols to stand for any number in expressions or equations |
| Solve whole number equations with one variable (multiplication and division) |
| Solve integer equations (one step, all four operations) |
| Solve equations involving more than one operation |
| Definition and application of absolute value |
| Solve one-step linear equations in one variable using addition, subtraction, multiplication, and division with integer solutions |
| Simplify numeric expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative) |
New Vocabulary in this Range: absolute value, evaluate, quotient
New Signs and Symbols: square root symbol, %, absolute value symbol
Patterns, Sequences, Functions
| Using whole numbers, complete a function table based on a given rule |
| Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is constant |
| Identify linear equation for a straight line |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Write an algebraic expression to model a situation |
| Evaluate an algebraic expression for given values |
| Explore equivalent ratios involving missing variables |
| Use the correct order of operations to evaluate numeric and algebraic expressions |
| Simplify and evaluate expressions that include positive and negative integral components |
| Simplify polynomials by combining like terms |
| Use the rules of exponents to multiply and divide monomials |
| Solve simple linear equations and inequalities over the rational numbers |
New Vocabulary in this Range: inequality, if-then statement, term in sequence, square numbers, negative coefficient
New Signs and Symbols: I = p x r x t
Patterns, Sequences, Functions
| Students analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically |
| Determine whether a relation is defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion |
| Use a function table to determine inverse variation |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Students solve equations and inequalities involving absolute values |
| Understand the concepts of parallel lines and perpendicular lines and how those slopes are related |
| Solve a system of two linear equations in two variables algebraically and interpret the answer graphically |
| Graph a linear function in two variables using the slope-intercept method and identify intercepts |
| Solve a system of two linear inequalities in two variables and identify the solution set |
| Understand and use the rules of exponents, including negative exponents |
| Add, subtract, multiply, and divide monomials and polynomials |
| Apply basic factoring techniques to second- and simple third-degree polynomials, including finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials |
| Add, subtract, multiply, and divide rational expressions and functions |
| Simplify an expression containing imaginary roots |
| Find the difference of two squares |
New Vocabulary in this Range: regression equation, varies inversely as the square, slope of parallel lines, solution to system, factor (used with equations)
New Signs and Symbols: none
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Simplify embedded expressions before solving linear equations and inequalities in one variable |
| Identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers |
| Solve problems that use variables in expressions describing geometric quantities by solving for one variable |
| Solve equations with variables as exponents |
| Use the rules of exponents to multiply polynomials by monomials |
| Derive linear equations by using the point-slope function |
| Find the slope given two points on the line of a given graph |
| Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line |
| Simplify monomials containing integer powers and roots |
| Find the solution set for inequalities that include absolute values |
| Identify the equation of a parabola |
| Simplify expressions containing cube roots |
| Solve expressions containing factorials |
| Find the number of possible solutions for a system of equations |
| Cube a binomial |
Quadratic Formula and Equations
| Solve a quadratic equation by factoring or completing the square |
| Know the quadratic formula and demonstrates its proof by completing the square |
| Identify discriminant and roots |
| Use the quadratic formula to find the roots of a second-degree polynomial and solve quadratic equations |
| Graph quadratic functions and know that their roots are the x-intercepts |
Trigonometry
| Find sin and cosine of a given angle |
| Solve logarithmic functions |
New Vocabulary in this Range: parabola, intercepts, number of solutions, simultaneous equations, counterexample, solution set, sin A, cosine, tangent, discriminant, imaginary solutions, difference of two squares, read solution set from graph, factor completely
New Signs and Symbols:
Patterns, Sequences, Functions
| Determine the domain of independent variables and the range of dependent variables in a relation that is defined by a graph, a set of ordered pairs, or a symbolic expression |
| Analyze properties and relationships of functions (e.g. linear, polynomial, rational) |
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Find the slope of a line parallel to a given line |
| Find the x-intercept of a given equation |
| Solve equations with fractions as exponents |
| Analyze a graph to identify the appropriate system of equations |
| Determine the vertex of a parabola |
| Determine which of several equations can be factored |
| Determine commonalities between three given equations of lines |
Trigonometry
| Use graph to identify trigonometric functions of angles |
| Find cosine, sine, and tangent of any given angle |
| Use law of cosines |
New Vocabulary in this Range: none
New Signs and Symbols: none
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
| Identify the region defined by a linear inequality |
New Vocabulary in this Range: none
New Signs and Symbols