Algebraic
Concepts –
includes patterns, functions, solving equations, order of operations,
properties, simplifying expressions and continues up through more difficult
skills in Algebra specific content
Skills and Concepts
RIT score between 151 and 160
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
RIT score between 161 and 170
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
RIT score between 171 and 180
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
RIT score between
181 and 190
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
RIT score between
191 and 200
Patterns, Sequences, Functions
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
RIT scores between
201 and 210
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
RIT scores between
211 and 220
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
RIT scores between
221 and 230
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
RIT scores between
231 and 240
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
RIT scores between
241 and 250
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
RIT scores between
251 and 260
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:
RIT scores between
261 and 270
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
RIT scores between
271 and 280
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: none