Math - 2018-19

A.5bc - Linear Inequalities

A.5  The student will

b)  represent the solution of linear inequalities in two variables graphically;

c)  solve practical problems involving inequalities; 



Adopted: 2016

BIG IDEAS

  • I can master the challenge of a ski slope for snowboarding, determine the gradient of a road, figure the pitch of a roof, and build a handicap accessible ramp to a door.
  • I will understand slope is rate of change where one value changing proportionately effects the other value, and the pattern of this relationship can be represented by a line that facilitates analysis and prediction.


UNDERSTANDING THE STANDARD

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.


ESSENTIALS

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

    ·  A.5bRepresent the solution of a linear inequality in two variables graphically.

    ·  A.5cSolve practical problems involving linear inequalities.

    ·  A.5cDetermine whether a coordinate pair is a solution of a linear inequality or a system of linear inequalities.

    ·  A.5bdDetermine and verify algebraic solutions using a graphing utility.

KEY VOCABULARY

parent function, transformations, slope, intercepts, coordinates, graph, positive slope, negative slope, zero slope, undefined slope, equation of a line, vertical, horizontal, dilations, reflections, translation, rate of change, dependent variable, independent variable, boundary, parallel, perpendicular

2016 Word Wall Cards


Updated: Aug 23, 2018