#### Math - 2017-18

# A.4b - Justify Expressions

**A.4b** The student will **solve **multistep linear and quadratic equations in two
variables, including

b) ** justifying** steps
used in simplifying expressions and solving equations, using field properties
and axioms of equality that are valid for the set of real numbers and its
subsets;

Graphing
calculators will be used both as a primary tool in solving problems and to
verify algebraic solutions.

**Bloom's Level: ** Evaluate

*Adopted: 2009*

### BIG IDEAS

- I can find how far and how
fast a bus travels, the number and combinations of fruits that can be
purchased, and how long it takes to drain a swimming pool.

- I will be able to write symbolic representations of the
way numbers behave and will know that in order to maintain equality, an
operation performed on one side must also be performed on the other side.

### UNDERSTANDING THE STANDARD

- A solution to an equation is the value or set of
values that can be substituted to make the equation true.
- The solution of an equation in one variable can
be found by graphing the expression on each side of the equation separately and
finding the x-coordinate of the point
of intersection.
- Real-world problems can be interpreted,
represented, and solved using linear and quadratic equations.
- The process of solving linear and quadratic
equations can be modeled in a variety of ways, using concrete, pictorial, and
symbolic representations.
- Properties of real numbers and properties of
equality can be used to justify equation solutions and expression
simplification.
- The zeros or the x-intercepts of the quadratic function are the real root(s) or
solution(s) of the quadratic equation that is formed by setting the given
quadratic expression equal to zero.
- A system of linear equations with exactly one
solution is characterized by the graphs of two lines whose intersection is a
single point, and the coordinates of this point satisfy both equations.
- A system of two linear equations with no
solution is characterized by the graphs of two lines that are parallel.
- A system of two linear equations having infinite
solutions is characterized by two graphs that coincide (the graphs will appear
to be the graph of one line), and the coordinates of all points on the line satisfy both equations.
- Systems of two linear equations can be used to
model two real-world conditions that must be satisfied simultaneously.
- Equations and systems of equations can be used
as mathematical models for real-world situations.
- Set builder notation may be used to represent
solution sets of equations.

### ESSENTIALS

**The student will use
problem solving, mathematical communication, mathematical reasoning,
connections, and representations to**

A.4b_{1} **Simplify **expressions using the field
properties of the real numbers and properties of equality to justify
simplification.

### KEY VOCABULARY

literal equation (formula), expression, equation,
properties of real numbers, properties of equality, quadratic equation,
quadratic function, quadratic expression, roots, zeros, linear equation,
system, substitution, elimination, ordered pair, coordinate, intersection,
intercepts, solution, infinite, parallel, coincide, simultaneous

*Updated: Jun 13, 2017*