Traditional
Sequence |
Integrated Sequence |
Performance Expectation |
| Algebra 1 |
Math 1 |
Math 2 |
Math 3 |
|
| A1.1.A |
M1.1A |
A1.1.A |
|
|
|
|
Select and justify functions and equations to model and
solve
problems. |
| A1.1.B |
M1.1B |
A1.1.B |
|
|
|
|
Solve problems that can be represented by linear
functions, equations, and inequalities. |
| A1.1.C |
M1.1C |
A1.1.C |
|
|
|
|
Solve problems that can be represented by a system of
two linear equations or inequalities. |
| A1.1.D |
|
|
M2.1.C |
A1.1.D |
|
|
Solve problems that can be represented by quadratic
functions and equations. (see also A2.1.C) |
| A1.1.E |
M1.1.D |
A1.1.E |
M2.1.D |
A1.1.E |
|
|
Solve problems that can be represented by exp onential
functions and equations. |
| A1.2.A |
M1.6.A |
A1.2.A |
|
|
|
|
Know the relationship between real numbers and the
number line, and compare and order real numbers with and without the
number line |
| A1.2.B |
M1.6.C |
A1.2.B |
|
|
|
|
Recognize the multiple uses of variables, determine all
possible values of variables that satisfy prescribed conditions, and
evaluate algebraic expressions that involve variables. |
| A1.2.C |
M1.7.C |
A1.2.C |
|
|
|
|
Interpret and use integer exponents and square and cube
roots, and apply the laws and properties of exponents to simplify and
evaluate exponential expressions. |
| A1.2.D |
M1.7.B |
A1.2.D |
|
|
|
|
Determine whether approximations or exact values of real
numbers are appropriate, depending on the context, and justify the
selection. |
| A1.2.E |
|
|
M2.5.A |
A1.2.E |
|
|
Use algebraic properties to factor and combine like
terms in polynomials. |
| A1.2.F |
|
|
|
|
M3.6.C |
A1.2.F |
Add, subtract, multiply, and divide polynomials. |
| A1.3.A |
M1.2.A |
A1.3.A |
|
|
|
|
Determine whether a relationship is a function and
identify the domain, range, roots, and independent and dependent
variables. |
| A1.3.B |
M1.2.B |
A1.3.B |
|
|
|
|
Represent a function with a symbolic expression, as a
graph, in a table, and using words, and make connections among these
representations. |
| A1.3.C |
M1.2.C |
A1.3.C |
|
|
|
|
Evaluate f(x) at a (i.e., f(a)) and solve for x in the
equation f(x) = b. |
| A1.4.A |
M1.3.A |
A1.4.A |
|
|
|
|
Write and solve linear equations and inequalities in one
variable. |
| A1.4.B |
M1.3.D |
A1.4.B |
|
|
|
|
Write and graph an equation for a line given the slope
and the y-intercept,
the slope and a point on the line, or two points on the line, and
translate between forms of linear equations. |
| A1.4.C |
M1.3.C |
A1.4.C |
|
|
|
|
Identify and interpret the slope and intercepts of a
linear function,
including equations for parallel and perpendicular lines. |
| A1.4.D |
M1.3.E |
A1.4.D |
|
|
|
|
Write and solve systems of two linear equations and
inequalities in two variables. |
| A1.4.E |
M1.3.B |
A1.4.E |
|
|
|
|
Describe how changes in the parameters of linear
functions and functions containing an absolute value of a linear
expression affect their graphs and the relationships they represent. |
| A1.5.A |
|
|
M2.2.A |
A1.5.A |
|
|
Represent a quadratic function with a symbolic
expression, as a graph, in a table, and with a description, and make
connections among the representations. |
| A1.5.B |
|
|
M2.2.B |
A1.5.B |
|
|
Sketch the graph of a quadratic function, describe the
effects that changes in the parameters have on the graph, and interpret
the x-intercepts as solutions to a quadratic equation. |
| A1.5.C |
|
|
M2.2.D |
A1.5.C |
|
|
Solve quadratic equations that can be factored as (ax +
b)(cx + d) where a, b, c, and d are integers. |
| A1.5.D |
|
|
M2.2.F |
A1.5.D |
|
|
Solve quadratic equations that have real roots by
completing the square and by using the quadratic formula. |
| A1.6.A |
M1.5.A |
A1.6.A |
|
|
|
|
Use and evaluate the accuracy of summary statistics to
describe and compare data sets. |
| A1.6.B |
M1.5.B |
A1.6.B |
|
|
|
|
Make valid inferences and draw conclusions based on
data. |
| A1.6.C |
M1.5.C |
A1.6.C |
|
|
|
|
Describe how linear transformations affect the center
and spread of
univariate data. |
| A1.6.D |
M1.3.F |
A1.6.D |
|
|
|
|
Find the equation of a linear function that best fits
bivariate data that
are linearly related, interpret the slope and y-intercept of the line,
and use the equation to make predictions. |
| A1.6.E |
M1.3.G |
A1.6.E |
|
|
|
|
Describe the correlation of data in scatterplots in
terms of strong or
weak and positive or negative . |
| A1.7.A |
M1.7.A |
A1.7.A |
|
|
|
|
Sketch the graph for an exponential function of the form
y = abn
where n is an integer, describe the effects that changes in the
parameters a and b have on the graph, and answer questions that
arise in situations modeled by exponential functions. |
| A1.7.B |
M1.7.B |
A1.7.B |
|
|
|
|
Find and approximate solutions to exponential equations. |
| A1.7.C |
M1.7.D |
A1.7.C |
|
|
|
|
Express arithmetic and geometric sequences in both
explicit and
recursive forms, translate between the two forms, explain how rate
of change is represented in each form, and use the forms to find
specific terms in the sequence. |
| A1.7.D |
M1.6.D |
A1.7.D |
|
|
|
|
Solve an equation involving several variables by
expressing one
variable in terms of the others. |
| A1.8.A |
M1.8.A |
A1.8.A |
|
|
|
|
Analyze a problem situation and represent it
mathematically. |
| A1.8.B |
M1.8.B |
A1.8.B |
|
|
|
|
Select and apply strategies to solve problems. |
| A1.8.C |
M1.8.C |
A1.8.C |
|
|
|
|
Evaluate a solution for reasonableness, verify its
accuracy, and interpret the solution in the context of the original
problem. |
| A1.8.D |
M1.8.D |
A1.8.D |
|
|
|
|
Generalize a solution strategy for a single problem to a
class of related problems, and apply a strategy for a class of related
problems to solve specific problems. |
| A1.8.E |
M1.8.E |
A1.8.E |
|
|
|
|
Read and interpret diagrams, graphs, and text containing
the symbols, language, and conventions of mathematics. |
| A1.8.F |
M1.8.F |
A1.8.F |
|
|
|
|
Summarize mathematical ideas with precision and
efficiency for a
given audience and purpose. |
| A1.8.G |
M1.8.G |
A1.8.G |
|
|
|
|
Synthesize information to draw conclusions, and evaluate
the
arguments and conclusions of others. |
| A1.8.H |
M1.8.H
(less
algebra
context) |
|
|
|
M3.8.H |
A1.8.H |
Use inductive reasoning about algebra and the properties
of numbers to make conjectures, and use deductive reasoning to prove or
disprove conjectures. |
| Geometry |
Math 1 |
Math 2 |
Math 3 |
|
| G.1.A |
M1.4.A |
G.1.A |
|
|
|
|
Distinguish between inductive and deductive
reasoning. |
| G.1.B |
M1.4.B |
G.1.B |
|
|
|
|
Use inductive reasoning to make conjectures,
to test the plausibility
of a geometric statement, and to help find a counterexample. |
| G.1.C |
M1.4.C |
G.1.C |
M2.3.A |
G.1.C |
|
|
Use deductive reasoning to prove that a
valid geometric statement is true. |
| G.1.D |
|
|
M2.3.C |
G.1.D |
|
|
Write the converse, inverse, and
contrapositive of a valid proposition
and determine their validity. |
| G.1.E |
|
|
M2.3.B |
G.1.E |
|
|
Identify errors or gaps in a mathematical
argument and develop counterexamples to refute invalid statements about
geometric
relationships. |
| G.1.F |
|
|
M2.3.D |
G.1.F |
|
|
Distinguish between definitions and
undefined geometric terms and
explain the role of definitions, undefined terms, postulates (axioms),
and theorems. |
| G.2.A |
M1.4.E |
G.2.A |
|
|
|
|
Know, prove, and apply theorems about
parallel and perpendicular lines. |
| G.2.B |
M1.4.F |
G.2.B |
|
|
|
|
Know, prove, and apply theorems about
angles, including angles that arise from parallel lines intersected by a
transversal. |
| G.2.C |
M1.4.G |
G.2.C |
|
|
|
|
Explain and perform basic compass and
straightedge constructions
related to parallel and perpendicular lines. |
| G.2.D |
|
|
|
|
M3.5.A |
G.2.D |
Describe the intersections of lines in the
plane and in space, of lines
and planes, and of planes in space |
| G.3.A |
|
|
M2.3.E |
G.3.A |
|
|
Know, explain, and apply basic postulates
and theorems about triangles and the special lines, line segments, and
rays associated with a triangle. |
| G.3.B |
M1.4.D |
G.3.B |
M2.3.F |
G.3.B |
|
|
Determine and prove triangle congruence,
triangle similarity, and other properties of triangles. |
| G.3.C |
|
|
M2.3.I |
G.3.C |
|
|
Use the properties of special right
triangles (30°–60°–90° and 45°–
45°–90°) to solve problems. |
| G.3.D |
|
|
M2.3.G |
G.3.D |
|
|
Know, prove, and apply the Pythagorean
Theorem and its converse. |
| G.3.E |
|
|
M2.3.H |
G.3.E |
|
|
Solve problems involving the basic
trigonometric ratios of sine , cosine, and tangent. |
| G.3.F |
|
|
M2.3.J |
G.3.F |
|
|
Know, prove, and apply basic theorems about
parallelograms. |
| G.3.G |
|
|
M2.3.K |
G.3.G |
|
|
Know, prove, and apply theorems about
properties of quadrilaterals
and other polygons. |
| G.3.H |
|
|
|
|
M3.7.A |
G.3.H |
Know, prove, and apply basic theorems
relating circles to tangents ,
chords, radii, secants, and inscribed angles. |
| G.3.I |
|
|
|
|
M3.7.C |
G.3.I |
Explain and perform constructions related to the circle. |
| G.3.J |
|
|
|
|
M3.5.B |
G.3.J |
Describe prisms, pyramids, parallelepipeds, tetrahedra,
and regular
polyhedra in terms of their faces, edges, vertices, and properties. |
| G.3.K |
|
|
|
|
M3.5.C |
G.3.K |
Analyze cross-sections of cubes, prisms, pyramids, and
spheres
and identify the resulting shapes. |
| G.4.A |
M1.3.H |
G.4.A |
|
|
|
|
Determine the equation of a line in the coordinate plane
that is described geometrically, including a line through two given
points, a line through a given point parallel to a given line, and a
line through a given point perpendicular to a given line. |
| G.4.B |
|
|
M2.3.L |
G.4.B |
|
|
Determine the coordinates of a point that is described
geometrically. |
| G.4.C |
|
|
M2.3.M |
G.4.C |
|
|
Verify and apply properties of triangles and
quadrilaterals in the coordinate plane. |
| G.4.D |
|
|
|
|
M3.7.B |
G.4.D |
Determine the equation of a circle that is described
geometrically in
the coordinate plane and, given equations for a circle and a line,
determine the coordinates of their intersection(s). |
| G.5.A |
|
|
|
|
M3.2.A |
G.5.A |
Sketch results of transformations and compositions of
transformations for a given two-dimensional figure on the coordinate
plane, and describe the
rule(s) for performing translations or for performing reflections about
the coordinate axes or the line y = x. |
| G.5.B |
|
|
|
|
M3.2.B |
G.5.B |
Determine and apply properties of transformations. |
| G.5.C |
|
|
|
|
M3.2.C |
G.5.C |
Given two congruent or similar figures in a coordinate
plane, describe a composition of translations, reflections, rotations,
and dilations that
superimposes one figure on the other. |
| G.5.D |
|
|
|
|
M3.2.D |
G.5.D |
Describe the symmetries of two-dimensional figures and
describe
transformations, including reflections across a line and rotations
about a point. |
| G.6.A |
|
|
|
|
M3.7.D |
G.6.A |
Derive and apply formulas for arc length and area of a
sector of a
circle. |
| G.6.B |
|
|
|
|
M3.5.F |
G.6.B |
Analyze distance and angle measures on a sphere and
apply these measurements to the geometry of the earth. |
| G.6.C |
|
|
|
|
M3.5.D |
G.6.C |
Apply formulas for surface area and volume of
three-dimensional
figures to solve problems. |
| G.6.D |
|
|
|
|
M3.5.E |
G.6.D |
Predict and verify the effect that changing one, two, or
three linear
dimensions has on perimeter, area, volume, or surface area of two-and
three-dimensional figures. |
| G.6.E |
|
|
M2.5.B |
G.6.E |
|
|
Use different degrees of precision in measurement,
explain the
reason for using a certain degree of precision, and apply estimation
strategies to obtain reasonable measurements with appropriate
precision for a given purpose. |
| G.6.F |
|
|
M2.5.C |
G.6.F |
|
|
Solve problems involving measurement conversions within
and
between systems, including those involving derived units, and
analyze solutions in terms of reasonableness of solutions and
appropriate units. |
| G.7.A |
|
|
M2.6.A |
G.7.A |
|
|
Analyze a problem situation and represent it
mathematically. |
| G.7.B |
|
|
M2.6.B |
G.7.B |
|
|
Select and apply strategies to solve problems. |
| G.7.C |
|
|
M2.6.C |
G.7.C |
|
|
Evaluate a solution for reasonableness, verify its
accuracy, and interpret the solution in the context of the original
problem. |
| G.7.D |
|
|
M2.6.D |
G.7.D |
|
|
Generalize a solution strategy for a single problem to a
class of
related problems, and apply a strategy for a class of related problems
to solve specific problems. |
| G.7.E |
|
|
M2.6.E |
G.7.E |
|
|
Read and interpret diagrams, graphs, and text containing
the symbols, language, and conventions of mathematics. |
| G.7.F |
|
|
M2.6.F |
G.7.F |
|
|
Summarize mathematical ideas with precision and
efficiency for a
given audience and purpose. |
| G.7.G |
|
|
M2.6.G |
G.7.G |
|
|
Use inductive reasoning to make conjectures, and use
deductive
reasoning to prove or disprove conjectures. |
| G.7.H |
M1.8.H |
G.7.H |
M2.6.H |
G.7.H |
|
|
Synthesize information to draw conclusions and evaluate
the
arguments and conclusions of others. |
| Algebra 2 |
Math 1 |
Math 2 |
Math 3 |
|
| A2.1.A |
|
|
M2.1.A |
A2.1.A |
M3.1.A |
A2.1.A |
Select and justify functions and equations to model and
solve problems. |
| A2.1.B |
|
|
M2.1.B |
A2.1.B |
M3.1.B |
A2.1.B |
Solve problems that can be represented by systems of
equations and inequalities. |
| A2.1.C |
|
|
M2.1.C |
A2.1.C |
M3.1.C |
A2.1.C |
Solve problems that can be represented by quadratic
functions, equations, and inequalities. |
| A2.1.D |
|
|
|
|
M3.1.D |
A2.1.D |
Solve problems that can be represented by exponential
and logarithmic functions and equations. |
| A2.1.E |
|
|
|
|
M3.1.E |
A2.1.E |
Solve problems that can be represented by inverse
variations of the forms
 |
| A2.1.F |
|
|
M2.1.E |
A2.1.F |
|
|
Solve problems involving combinations and permutations. |
| A2.2.A |
|
|
|
|
M3.6.A |
A2.2.A |
Explain how whole, integer, rational, real, and complex
numbers are
related, and identify the number
system(s) within which a given algebraic equation can be solved. |
| A2.2.B |
|
|
|
|
M3.6.B |
A2.2.B |
Use the laws of exponents to simplify and evaluate
numeric and algebraic expressions that contain rational exponents. |
| A2.2.C |
|
|
|
|
M3.6.D |
A2.2.C |
Add, subtract, multiply, divide, and simplify rational
and more
general algebraic expressions. |
| A2.3.A |
|
|
M2.2.C |
A2.3.A |
|
|
Translate between the standard form of a quadratic
function, the
vertex form, and the factored form; graph and interpret the meaning
of each form. |
| A2.3.B |
|
|
M2.2.E |
A2.3.B |
|
|
Determine the number and nature of the roots of a
quadratic function. |
| A2.3.C |
|
|
M2.2.G |
A2.3.C |
|
|
Solve quadratic equations and inequalities, including
equations with
complex roots. |
| A2.4.A |
|
|
|
|
M3.3.A |
A2.4.A |
Know and use basic properties of exponential and
logarithmic
functions and the inverse relationship between them. |
| A2.4.B |
|
|
|
|
M3.3.B |
A2.4.B |
Graph an exponential function of the form f(x) = abx and
its inverse
logarithmic function. |
| A2.4.C |
|
|
|
|
M3.3.C |
A2.4.C |
Solve exponential and logarithmic
equations. |
| A2.5.A |
|
|
|
|
M3.2.E |
A2.5.A |
Construct new functions using the
transformations f(x – h), f(x) + k,
cf(x), and by adding and subtracting functions , and describe the
effect on the original graph(s). |
| A2.5.B |
|
|
|
|
M3.3.D |
A2.5.B |
Plot points, sketch, and describe the
graphs of functions of the form
 and solve related equations. |
| A2.5.C |
M1.2.D |
A2.5.C |
|
|
M3.3.E |
A2.5.C |
Plot points, sketch, and describe the
graphs of functions of the form
and solve related equations. |
| A2.5.D |
|
|
|
|
M3.3.F |
A2.5.D |
Plot points, sketch, and describe the
graphs of cubic polynomial
functions of the form f(x) = ax3 + d as an example of higher
order
polynomials and solve related equations. |
| A2.6.A |
|
|
M2.4.A |
A2.6.A |
|
|
Apply the fundamental counting
principle and the ideas of order and
replacement to calculate probabilities in situations arising from
two-stage
experiments ( compound events ). |
| A2.6.B |
|
|
M2.4.B |
A2.6.B |
|
|
Given a finite sample space
consisting of equally likely outcomes and containing events A and B,
determine whether A and B are independent or dependent, and find the
conditional probability of A
given B. |
| A2.6.C |
|
|
M2.4.C |
A2.6.C |
|
|
Compute permutations and
combinations, and use the results to
calculate probabilities. |
| A2.6.D |
|
|
M2.4.D |
A2.6.D |
|
|
Apply the binomial theorem to solve
problems involving probability. |
| A2.6.E |
|
|
M2.4.H |
A2.6.E |
|
|
Determine if a bivariate data set can
be better modeled with an exponential or a quadratic function and use
the model to make predictions. |
| A2.6.F |
|
|
|
|
M3.4.A |
A2.6.F |
Calculate and interpret measures of
variability and standard deviation and use these measures and the
characteristics of the normal distribution to describe and compare data
sets. |
| A2.6.G |
|
|
|
|
M3.4.B |
A2.6.G |
Calculate and interpret margin of
error and confidence intervals for population proportions. |
| A2.7.A |
|
|
|
|
M3.3.G |
A2.7.A |
Solve systems of three equations with
three variables. |
| A2.7.B |
|
|
M2.5.D |
A2.7.B |
|
|
Find the terms and partial sums of
arithmetic and geometric series
and the infinite sum for geometric series. |
| A2.8.A |
|
|
|
|
M3.8.A |
A2.8.A |
Analyze a problem situation and
represent it mathematically. |
| A2.8.B |
|
|
|
|
M3.8.B |
A2.8.B |
Select and apply strategies to solve
problems. |
| A2.8.C |
|
|
|
|
M3.8.C |
A2.8.C |
Evaluate a solution for
reasonableness, verify its accuracy, and interpret the solution in the
context of the original problem. |
| A2.8.D |
|
|
|
|
M3.8.D |
A2.8.D |
Generalize a solution strategy for a
single problem to a class of related problems and apply a strategy for a
class of related problems to solve specific problems. |
| A2.8.E |
|
|
|
|
M3.8.E |
A2.8.E |
Read and interpret diagrams, graphs,
and text containing the symbols, language, and conventions of
mathematics. |
| A2.8.F |
|
|
|
|
M3.8.F |
A2.8.F |
Summarize mathematical ideas with
precision and efficiency for a given audience and purpose. |
| A2.8.G |
|
|
|
|
M3.8.G |
A2.8.G |
Use inductive reasoning and the
properties of numbers to make conjectures, and use deductive reasoning
to prove or disprove conjectures. |
| A2.8.H |
|
|
|
|
M3.8.H |
A2.8.H |
Synthesize information to draw
conclusions and evaluate the arguments and conclusions of others. |
