Florida B.E.S.T. MA.912.AR.4

MA.912.AR.4 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.AR.4.1

  Given a mathematical or real-world context, write and solve one-variable absolute value equations.

• MA.912.AR.4.2

  Given a mathematical or real-world context, write and solve one-variable absolute value inequalities. Represent solutions algebraically or graphically.

• MA.912.AR.4.3

  Given a table, equation or written description of an absolute value function, graph that function and determine its key features.

• MA.912.AR.4.4

  Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine constraints in terms o...

01

What Students Need to Do

Students write absolute value models from distance statements and solve equations and inequalities by splitting them into cases. They graph solutions on number lines and graph V-shaped functions in the coordinate plane. They also graph two-variable inequalities by drawing a boundary and shading the correct region.

02

What Mastery Looks Like

A student can move between a context, an absolute value statement, and its graph. They solve accurately, check solutions, label vertices and intercepts, and use solid or dashed boundaries correctly. They can explain what the solution set means.

03

Common Misconceptions

Students may forget the positive and negative cases when solving equations. They may think absolute value can equal a negative number or reverse graph shifts. They also confuse “and” with “or,” use the wrong boundary line, or shade the wrong region.

04

How to Assess It

Give students y = |x - 2| - 3 and |x - 2| ≤ 3. Ask them to graph both and list the inequality’s solution interval.

1. 01

   Tape a number line on the floor, give students distance inequalities, and have them stand at all possible solution points.

2. 02

   Ask students to explain why |x - 4| = -2 has no solution and why |x - 4| = 2 has two.

3. 03

   Run a card match with absolute value equations, inequalities, solution sets, number-line graphs, and coordinate graphs.

4. 04

   Use a manufacturing tolerance of 0.3 millimeter to write an inequality, find acceptable measurements, and graph the interval.

• MA.912.AR.3

  Write, solve and graph quadratic equations, functions and inequalities in one and two variables.

• MA.912.AR.5

  Write, solve and graph exponential and logarithmic equations and functions in one and two variables.

• MA.7.AR.2

  Write and solve equations and inequalities in one variable.

• MA.912.AR.2

  Write, solve and graph linear equations, functions and inequalities in one and two variables.