Student Actions

Teacher Actions

• Students will develop a deep and flexible conceptual understanding  by examining various models of compound and absolute value  inequalities and discovering relationships between these models.

• Students will develop strategies for problem solving as they explore various models of compound and absolute value inequalities, and then apply those understandings to begin solving problems algebraically.

• Students will develop mathematical reasoning  as they  compare the solutions and constraints in more than one representation, algebraically and graphically, so they can make connections to real-world situations.

• Students will develop a productive mathematical disposition by developing a sense of application and usefulness of solutions with inequalities in real-world situations when solving absolute value and compound inequalities

   

• Use and connect mathematical representations by providing students with many models (verbal, sketches, number lines) of compound and absolute value inequalities.

• Pose purposeful questions while working with individuals, small groups and/or the whole class to guide students’ exploration of a variety of models of inequalities, finding patterns in the models, and connecting them to real-world situations.

• Implement tasks that promote reasoning and problem solving by introducing real-world problems that involve compound and absolute value inequalities, encouraging creative methods for solving (including relying on models), and expecting students to interpret their solutions in the correct context

• Elicit and use evidence of student thinking by assessing understanding, posing questions at specific points of instruction, and adjust accordingly to continue and extend learning for expected outcomes.

   

Key Understandings

Misconceptions

• Students can solve absolute value and compound linear inequalities using properties of inequalities and graph the solutions on a number line.

• Students can identify the the two separate inequalities of absolute value inequalities and determine the outcomes of their graphs.

• Students can use the vocabulary of compound inequalities and determine the number of solutions.

• Given a real-world situation students can write and graph a compound inequality and correctly interpret the solutions in context, understanding that a range of values within certain constraints will be the solution.

Example:

The antifreeze added to your car's cooling system claims that it will protect your car to -35º C and 120º C.  The coolant will remain in a liquid state as long as the temperature in Celsius satisfies the inequality

-35º < C < 120º.  Write this inequality in degrees Fahrenheit.

 Solution:

 Remember

The coolant will remain in a liquid state as long as the temperature in Fahrenheit degrees satisfies the inequality

-31º < F < 248º.

https://slideplayer.com/slide/7600998/

Screenshots of above slides

• Students may not understand the difference between conjunctions and disjunctions, graphically or algebraically.

• Students may think that the inequality symbols in conjunction compound statement indicate the direction of the shading of the number line.

• Students may forget to use the appropriate compound inequality when solving absolute value inequalities.

• Students may arrange the compound solutions of conjunction statements in the wrong order when writing the statements algebraically.

• Students may forget there are two solutions in an absolute value inequality problem.

Example:

| x + 4 | > 3

Case #1:                Case #2:

x + 4 > 3               x + 4 < 3

x > -1                      x < -1