1. 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. Students solve equations and inequalities involving
absolute values.
3. Students
simplify expressions before solving linear equations and inequalities in one
variable, such as 3(2x-5) + 4(x-2) = 12.
4. 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).
5. 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.
6. 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.
7. Students add, subtract, multiply,
and divide monomials and polynomials.
Students solve multi-step problems, including word problems, by using
these techniques.
8.
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.
9. Students
solve a quadratic equation by factoring or completing the square.
10. 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.
11. Students
determine the domain of independent variables and the range of dependent
variables defined by a graph, a set of ordered pairs, or a symbolic expression.
12. 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.
13. Students
graph quadratic functions and know that their roots are the x-intercepts.
14. Students
apply quadratic equations to physical problems, such as the motion of an object
under the force of gravity.
15. Students consistently and accurately compute with, apply and convert
the different kinds of forms of rational numbers; begin to work with irrational
numbers, especially P:
15.1 Use the inverse relationship
between raising to a power and root extraction for perfect square integers;
and, for integers which are not square, determine without a calculator, the two
integers between which its square root lies (NS 2.4) 7th
16. Students discover,
describe, and generalize patterns, including linear, exponential, and simple
quadratic relationships and represent them with variables and expressions:
16.1 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections (MG 3.2) 7th
16.2 Know and understand the
Pythagorean theorem and its converse and use it to find the length of the
missing side of a right triangle and the lengths of other line segments and, in
some situations, empirically verify the Pythagorean theorem by direct
measurement (MG 3.3) 7th