algebra I standards
Symbolic reasoning and calculations with symbols are central in algebra. Through
the study of algebra, a student develops an understanding of the symbolic language
of mathematics and the sciences. In addition, algebraic skills and concepts are
developed
and used in a wide variety of problem-solving situations.
- 1.0 Students identify and use the arithmetic
properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four
basic arithmetic operations where applicable:
-
1.1 Students use
properties of numbers to demonstrate whether assertions are true or false.
- 2.0 Students understand and use such
operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and
use the rules of exponents.
- 3.0
Students solve equations and inequalities involving
absolute values.
- 4.0 Students simplify expressions before
solving linear equations and inequalities
in one variable, such as 3(2x-5) + 4(x-2) = 12.
- 5.0 Students solve
multi-step problems,
including word problems, involving linear equations and linear inequalities in one variable and provide justification for
each step.
- 6.0 Students graph
a linear equation and compute the x- and y-intercepts (e.g., graph
2x + 6y
= 4). They are also able to sketch the region defined by linear
inequality (e.g., they sketch the region defined by 2x
+ 6y < 4).
- 7.0 Students verify that a point lies on a
line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
- 8.0 Students understand the concepts of
parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line
perpendicular to a given line that passes through a given
point
- 9.0
Students solve a system of two linear
equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a
system of two linear inequalities in two variables and to sketch the solution sets.
- 10.0 Students add, subtract, multiply, and
divide monomials and polynomials. Students solve multistep problems, including word problems, by using these
techniques.
- 11.0 Students apply basic factoring techniques
to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms
in a polynomial, recognizing the difference of two squares, and recognizing
perfect squares of binomials.
- 12.0 Students simplify fractions with
polynomials in the numerator and denominator
by factoring both and reducing them to the lowest terms.
- 13.0 Students add, subtract, multiply, and
divide rational expressions and functions.
Students solve both computationally and conceptually challenging problems by
using these techniques.
- 14.0
Students solve a quadratic equation by factoring or
completing the square.
- 15.0 Students apply algebraic techniques to
solve rate problems, work problems,
and percent mixture problems.
- 16.0 Students understand the concepts of a
relation and a function, determine whether a given relation defines a function, and give pertinent information about
given relations and functions.
- 17.0 Students determine the domain of
independent variables and the range of de-pendent variables defined by a graph, a set of ordered pairs, or a symbolic
expression.
- 18.0 Students determine whether a relation
defined by a graph, a set of ordered pairs,
or a symbolic expression is a function and justify the conclusion.
- 19.0 Students know the quadratic formula and
are familiar with its proof by
completing the square.
- 20.0 Students use the quadratic formula to
find the roots of a second-degree polynomial and to solve quadratic equations.
- 21.0 Students graph quadratic functions and
know that their roots are the
x-intercepts.
- 22.0 Students use the quadratic formula or
factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one,
or two points.
- 23.0 Students apply quadratic equations to
physical problems, such as the motion of an object under the force of gravity.
- 24.0 Students use
and know simple aspects of a logical argument:
- 24.1 Students
explain the difference between inductive and deductive reasoning and identify and
provide examples of each.
- 24.2 Students
identify the hypothesis and conclusion in logical deduction.
- 24.3 Students use
counterexamples to show that an assertion is false and recognize that a single
counterexample is sufficient to refute an assertion.
-
25.0 Students use properties of the number
system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:
-
25.1 Students use
properties of numbers to construct simple, valid arguments (direct and indirect) for,
or formulate counterexamples to, claimed assertions.
-
25.2 Students judge
the validity of an argument according to whether the properties of the real number
system and the order of operations have been applied correctly at each step.
-
25.3 Given a
specific algebraic statement involving linear, quadratic, or absolute value expressions or
equations or inequalities, students determine whether the statement is true sometimes,
always, or never.
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