| Academic
Standard |
Student Edition
Lesson(s) |
Standard 1 Operations
with Real Numbers
Students simplify and compare expressions. They use rational exponents,
and simplify square roots. |
| A1.1.1 |
|
Compare real number expressions. |
|
1-1
|
| A1.1.2 |
|
Simplify square roots using factors. |
|
8-5, 8-6 |
| A1.1.3 |
|
Understand and use the distributive, associative,
and
commutative properties. |
|
1-3, 1-4, 1-7
|
| A1.1.4 |
|
Use the laws of exponents for rational exponents. |
|
1-2, 8-1, 8-2, 8-3 |
| A1.1.5 |
|
Use dimensional (unit) analysis to organize
conversions
and computations. |
|
5-1
|
Standard 2 Linear
Equations and Inequalities
Students solve linear equations and inequalities in one variable. They
solve word problems that involve linear equations, inequalities, or formulas. |
| A1.2.1 |
|
Solve linear equations. |
|
3-5, 3-6, 3-7, 4-4, 4-5, 4-6, 4-7, 7-5, 7-6, 7-7 |
| A1.2.2 |
|
Solve equations and formulas for a specified
variable. |
|
1-5, 5-1, 5-2, 5-3, 6-5, 6-6, 8-7
|
| A1.2.3 |
|
Find solution sets of linear inequalities
when possible numbers are given for the variable. |
|
12-1 |
| A1.2.4 |
|
Solve linear inequalities using properties
of order. |
|
12-1, 12-2, 12-3, 12-4, 12-6, 12-7 |
| A1.2.5 |
|
Solve combined linear inequalities. |
|
12-5 |
| A1.2.6 |
|
Solve word problems that involve linear
equations, formulas, and inequalities. |
|
6-5, 6-6, 7-5, 7-6, 7-7, 12-1, 12-3, 12-4, 12-5, 12-6, 12-7, 13-1, 13-2, 13-3, 13-4, 13-5, 13-6, 13-7, 14-5 |
Standard 3 Relations
and Functions
Students sketch and interpret graphs representing given situations. They
understand the concept of a function and analyze the graphs of functions. |
| A1.3.1 |
|
Sketch a reasonable graph for a given relationship. |
|
6-3, 6-4, 6-5, 7-5, 11-1, 11-2, 11-3 |
| A1.3.2 |
|
Interpret a graph representing a given situation. |
|
6-3, 6-4, 6-5, 7-5, 7-6, 11-1, 11-2, 11-3 |
| A1.3.3 |
|
Understand the concept of a function, decide
if a given relation is a function, and link equations to functions.
|
|
6-2, 6-3, 6-4, 6-5 |
| A1.3.4 |
|
Find the domain and range of a relation. |
|
6-1, 6-2, 6-3, 6-4 |
Standard 4 Graphing
Linear Equations and Inequalities
Students graph linear equations and inequalities in two variables. They
write equations of lines and find and use the slope and y intercept of lines.
They use linear equations to model real data. |
| A1.4.1 |
|
Graph a linear equation. |
|
7-5, 7-6 |
| A1.4.2 |
|
Find the slope, x intercept and y intercept
of a line given its graph, its equation, or two points on the line.
|
|
7-2, 7-3, 7-5, 7-6 |
| A1.4.3 |
|
Write the equation of a line in slope intercept
form. Understand how the slope and y intercept of the graph are related
to the equation. |
|
7-3 |
| A1.4.4 |
|
Write the equation of a line given appropriate
information. |
|
7-2, 7-3, 7-7 |
| A1.4.5 |
|
Write the equation of a line that models
a data set and use the equation (or the graph of the equation) to
make predictions. Describe the slope of the line in terms of the data,
recognizing that the slope is the rate of change. |
|
7-4 |
| A1.4.6 |
|
Graph a linear inequality in two variables. |
|
12-7 |
Standard 5 Pairs
of Linear Equations and Inequalities
Students solve pairs of linear equations using graphs and using algebra.
They solve pairs of linear inequalities using graphs. They solve word problems
involving pairs of linear equations. |
| A1.5.1 |
|
Use a graph to estimate the solution of
a pair of linear equations in two variables. |
|
13-1, 13-2 |
| A1.5.2 |
|
Use a graph to find the solution set of
a pair of linear inequalities in two variables. |
|
13-7 |
| A1.5.3 |
|
Understand and use the substitution method
to solve a pair of linear equations in two variables. |
|
13-3 |
| A1.5.4 |
|
Understand and use the addition or subtraction
method to solve a pair of linear equations in two variables. |
|
13-4, 13-5 |
| A1.5.5 |
|
Understand and use multiplication with the
addition or subtraction method to solve a pair of linear equations
in two variables. |
|
13-4, 13-5 |
| A1.5.6 |
|
Use pairs of linear equations to solve word
problems. |
|
13-1, 13-2, 13-3, 13-4, 13-5, 13-6, 13-7
|
Standard 6 Polynomials
Students add, subtract, multiply, and divide polynomials. They factor
quadratics. |
| A1.6.1 |
|
Add and subtract polynomials. |
|
9-2 |
| A1.6.2 |
|
Multiply and divide monomials. |
|
9-3, 15-2 |
| A1.6.3 |
|
Find powers and roots of monomials (only
when the answer has an integer exponent). |
|
14-3 |
| A1.6.4 |
|
Multiply polynomials. |
|
9-3, 9-4, 9-5 |
| A1.6.5 |
|
Divide polynomials by monomials. |
|
15-1, 15-2, 15-3 |
| A1.6.6 |
|
Find a common monomial factor in a polynomial. |
|
10-1, 10-2 |
| A1.6.7 |
|
Factor the difference of two squares and
other quadratics. |
|
10-3, 10-4, 10-5 |
| A1.6.8 |
|
Understand and describe the relationships
among the solutions of an equation, the zeros of a function, the x
intercepts of a graph, and the factors of a polynomial expression. |
|
3-6, 3-7, 4-4, 4-5, 7-3, 7-6, 7-7, 10-1, 10-2, 10-3, 10-4, 10-5, 11-1, 11-2, 11-3, 11-4, 11-5, 11-6, 11-7, 14-5, 15-6 |
Standard 7 Algebraic
Fractions
Students simplify algebraic ratios and solve algebraic proportions. |
| A1.7.1 |
|
Simplify algebraic ratios. |
|
15-1, 15-2, 15-3 |
| A1.7.2 |
|
Solve algebraic proportions. |
|
5-1, 5-2, 5-3, 5-4, 5-5, |
Standard 8 Quadratic,
Cubic, and Radical Equations
Students graph and solve quadratic and radical equations. They graph
cubic equations. |
| A1.8.1 |
|
Graph quadratic, cubic, and radical equations. |
|
11-1, 11-2, 11-3, 11-7, 14-5 |
| A1.8.2 |
|
Solve quadratic equations by factoring. |
|
11-4 |
| A1.8.3 |
|
Solve quadratic equations in which a perfect
square equals a constant. |
|
11-5 |
| A1.8.4 |
|
Complete the square to solve quadratic equations. |
|
11-5 |
| A1.8.5 |
|
Derive the quadratic formula by completing
the square. |
|
11-6 |
| A1.8.6 |
|
Solve quadratic equations by using the quadratic
formula. |
|
11-6 |
| A1.8.7 |
|
Use quadratic equations to solve word problems. |
|
11-3, 11-4, 11-5, 11-6 |
| A1.8.8 |
|
Solve equations that contain radical expressions. |
|
14-5 |
| A1.8.9 |
|
Use graphing technology to find approximate
solutions of quadratic and cubic equations. |
|
11-2, 11-3, 11-4, 11-5, 11-6, 11-7 |
Standard 9 Mathematical
Reasoning and Problem Solving
Students use a variety of strategies to solve problems. |
| A1.9.1 |
|
Use a variety of problem solving strategies,
such as drawing a diagram, making a chart, guess and check, solving
a simpler problem, writing an equation, and working backwards. |
|
1-5, 1-6, 3-5, 3-6, 4-5, 6-2, 6-3, 7-1, 7-2, 11-3, 11-7, 13-7, 14-2 |
| A1.9.2 |
|
Decide whether a solution is reasonable
in the context of the original situation. |
|
1-5, 2-3, 4-4, 4-5, 5-1, 5-4, 6-3, 8-7, 9-1, 9-2, 11-3, 11-4, 11-5, 13-3, 14-5, 15-6 |
Standard 9 Mathematical
Reasoning and Problem Solving
Students develop and evaluate mathematical arguments and proofs. |
| A1.9.3 |
|
Use the properties of the real number system
and the order of operations to justify the steps of simplifying functions
and solving equations. |
|
1-2, 1-3, 1-4, 3-6, 3-7, 4-4, 4-5, 5-1, 5-4, 6-3, 8-7, 9-1, 9-2, 11-3, 11-4, 11-5, 13-3, 14-5, 15-6
|
| A1.9.4 |
|
Understand that the logic of equation solving
begins with the assumption that the variable is a number that satisfies
the equation, and that the steps taken when solving equations create
new equations that have, in most cases, the same solution set as the
original. Understand that similar logic applies to solving systems
of equations simultaneously. |
|
1-2, 1-3, 1-4, 3-6, 3-7, 4-4, 4-5, 5-1, 5-4, 6-3, 8-7, 9-1, 9-2, 11-3, 11-4, 11-5, 13-3, 14-5, 15-6
|
| A1.9.5 |
|
Decide whether a given algebraic statement
is true always, sometimes, or never (statements involving linear or
quadratic expressions, equations, or inequalities). |
|
4-6
|
| A1.9.6 |
|
Distinguish between inductive and deductive
reasoning, identifying and providing examples of each. |
|
|
| A1.9.7 |
|
Identify the hypothesis and conclusion in
a logical deduction. |
|
|
| A1.9.8 |
|
Use counterexamples to show that statements
are false, recognizing that a single counterexample is sufficient
to prove a general statement false. |
|
1-3
|
|
Extra Examples—
