Math - 2017-18
A.5abc and *A.5ac - Linear Inequalities
A.5 The student will solve multistep linear inequalities in two variables, including
a) solving multistep linear inequalities algebraically and graphically;
b) justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets;
c) solving real-world problems involving inequalities;
A.5 The student will
a) solve multistep linear inequalities in one variable algebraically and represent the solution graphically;
c) solve practical problems involving inequalities;
Bloom's Level: Evaluate
BIG IDEAS
- I can set a freezer
temperature so ice cubes won’t melt, make sure a bridge will hold a loaded
truck, determine how many hours I’d have to work to afford the shoes I want,
avoid receiving a speeding ticket when I can drive, and won’t go over the
allowed number of text messages per month on my cell phone.
- I will apply algebraic properties
and processes to model real-life situations, remembering that the solution will
be a range of possibilities, and absolute value inequalities are used for situations
where margin of error is a concern.
UNDERSTANDING THE STANDARD
- A solution to an inequality is the value or set of values that can be substituted to make the inequality true.
- Real-world problems can be modeled and solved
using linear inequalities.
- Properties of inequality and order can be used
to solve inequalities.
- Set builder notation may be used to represent
solution sets of inequalities.
2016 VDOE Curriculum Framework - AI.5 Understanding
· A solution to an inequality is the value or set of values that can be substituted to make the inequality true.
· The graph of the solutions of a linear inequality is a half-plane bounded by the graph of its related linear equation. Points on the boundary are included unless the inequality contains only < or > (no equality condition).
· Practical problems may be modeled and solved using linear inequalities.
· Solutions and intervals may be expressed in different formats, including set notation or using equations and inequalities.
- Examples may include:
Equation/ Inequality |
Set Notation |
x = 3 |
{3} |
x = 3 or x = 5 |
{3, 5} |
y≥ 3 |
{y: y ≥ 3} |
Empty (null) set ∅ |
{ } |
· Properties of Real Numbers and Properties of Inequality are applied to solve inequalities.
· Properties of Real Numbers:
Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Identity Property of Addition (Additive Identity)
Identity Property of Multiplication (Multiplicative Identity)
Inverse Property of Addition (Additive Inverse)
Inverse Property of Multiplication (Multiplicative Inverse)
Distributive Property
· Properties of Inequality:
Transitive Property of Inequality
Addition Property of Inequality
Subtraction Property of Inequality
Multiplication Property of Inequality
Division Property of Inequality
SubstitutionESSENTIALS
The student will use
problem solving, mathematical communication, mathematical reasoning,
connections, and representations to
A.5a_{1} Solve multi-step linear inequalities in one variable
· A.5a_{1 }Solve multistep linear inequalities in one variable algebraically and represent the solution graphically.
A.5b_{1} Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers
· A.5a_{2 }Apply the properties of real numbers and properties of inequality to solve multistep linear inequalities in one variable algebraically.
A.5c_{1} Solve real-world problems involving inequalities.
· A.5c_{1 }Solve practical problems involving linear inequalities.
· A.5ac_{1 }Determine and verify algebraic solutions using a graphing utility.
KEY VOCABULARY
inequality, axiom, properties of order,
properties of inequality, solution set, systems of linear inequalities set
builder notation