Student Actions

Teacher Actions

• Students will develop accurate and appropriate procedural fluency when solving for a variable in absolute value equations of varying types (one-step, two-step, and multi-step) and manipulating equations by applying mathematical properties learned in pre-algebra.

•  Students will develop a deep and flexible conceptual understanding of the meaning of absolute value as they explore models that demonstrate the multiple possible values of the variable in an absolute value equation and use those models to develop methods for solving various types of absolute value equations.

• Students will develop mathematical reasoning when solving absolute value equations in relation to negative solutions and applying  logical strategies, including checking for reasonableness,  to solve both mathematical and real-world problems

• Use and connect mathematical representations by providing students with models which help the students understand why there are multiple possible values of the variable in an absolute value equation.

• Build procedural fluency from conceptual understanding by working with students to apply mathematical properties learned in pre-algebra  as well as their understanding of the meaning of absolute value to solve absolute value equations.

• Pose purposeful questions as you work alongside students,  assessing their reasoning for solving for a variable in a variety of problems, using these questions to guide them to deeper understanding of both equality and absolute value and to help them check for reasonableness in their solutions.

• Implement tasks that promote reasoning and problem solving by providing real-world applications of absolute value and reminding students to interpret the solution in the original context of the problem and explore various strategies for solving.

• Facilitate meaningful mathematical discourse by encouraging small group and class wide discussion of both solutions in the correct context and different approaches to solving such as using manipulatives, graphing (both coordinate and number line) and more traditional algebraic solutions.  Teachers should also expect students to  use mathematical symbols in the proper context.

   

Key Understandings

Misconceptions

• Accurately solve absolute value equations and determine the number of solutions. 

• Understand that the absolute value is a distance from zero. For example:  |x| = 4 means that the distance from zero is 4 and on a number line it can be represented as two separate points on a number line at 4 and -4.

• Students should be able to use their  mathematical reasoning in problems such as | x - a |  = b and determine that the variable x is b units away from a since the problem of | x | = b is b units from zero.

• Students may struggle with the rules for solving equations when applying them to absolute value.

• Students may solve for the variable when the absolute value is equal to a negative.

• For example: | x + 5 | = -1 is impossible to solve since absolute values cannot equal negative values. Therefore there is NO SOLUTION.

• Students may not solve correctly for the absolute value by simplifying first.

• For example:   -2 |x + 7| = 20

 Before a student separates this into two equations a mistake here is that the student can distribute and results in  -2x - 14 = 20 and -2x - 14 = -20. These two equations are further solved and hence the incorrect solution. One can see here a student forgot to divide by -2 first and the next step will result in no solution since an absolute value cannot equal a negative number.

• Students may fail to find both solutions.