MA.912.AR.4.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.AR.2.1 
• MA.912.AR.3.1 
• MA.912.F.2.1

Terms from the K-12 Glossary

• Absolute Value

Vertical Alignment

Previous Benchmarks

• MA.6.NSO.1.3  
• MA.6.NSO.1.4 
• MA.7.NSO.2.1

Next Benchmarks

• MA.912.AR.4.4

Purpose and Instructional Strategies

• In grade 6, students solved problems involving absolute value, including context related to distances, temperatures and finances. In grade 7, students solved multi-step order of operations with rational numbers including absolute value. In Algebra I, students write and solve absolute value equations in one variable. In later courses, students will solve and graph real-world problems that are modeled with absolute value functions. 
  • Instruction reinforces the definition of absolute value as a number’s distance from zero (0) on a number line. Distance is expressed as a positive value; example: |3| = 3 and |−3| = 3. The numbers 3 and –3 are each three units away from zero on a number line (MTR.2.1). 
  • Instruction includes asking for solutions of absolute value equation in word form. o For example, the equation |$x$| = 7.1 can be read as “What values of $x$ have absolute value equivalent to 7.1?” 
  • Instruction focuses on recognizing that there are either two solutions, or no solutions to an absolute value equation. 
  • The equation |$x$| = −8 has no solution because the absolute value of a number cannot be negative. 
  • The equation |5$x$ − 2| = 10 has two solutions by the definition of absolute value; one of which satisfies 5$x$ − 2 = 10 and the other satisfies 5$x$ − 2 = −10. 
  • Instruction encourages students to discuss their thinking with their peers (MTR.4.1). Often students will be able to reason out their thinking, but will struggle with representing their thinking mathematically. Encourage this process and ask questions that will help with solving the task (MTR.1.1). Are their multiple ways for students to represent this problem mathematically (MTR.2.1)?

Common Misconceptions or Errors

• Students may forget that absolute value refers to a distance, and is thus a positive number or zero. 
• Students may forget many absolute value equations will produce two solutions. 
• Students may forget some equations have no solutions.

Strategies to Support Tiered Instruction

• Teacher provides a three-column table with equations already sorted into two-, one-, or no-solutions. Teacher asks what is noticed about the equations in each column. Then, students sort additional equations into columns.

• Teacher provides absolute value equations and has students them sort them into a three-column graphic organizer with column headers of: two solutions, one solution and no solution. 

• Teacher models absolute value equations on the number line to show that absolute value is the distance from zero. By the visual representation, students will see how absolute value equations produce two solutions. Manipulatives can be used to represent the constants in each equation. 
  • For example, the absolute value equation |$x$| = 6 can be modeled as shown.

• For example, the absolute value equation |$x$ + 2| = 6 can be modeled as shown.

• For example, the absolute value equation |2$x$ + 2| = 6 can be modeled as shown.

Instructional Tasks

• Determine the solutions of the equation below. |$\frac{\text{1}}{\text{4}}$$x$ − 3| = 10  

• Donna and Kayleigh both go to the same high school. Donna lives 21 miles from the school. Kayleigh lives 6 miles from Donna. 
  • Part A. Write an absolute value equation to represent the location of Kayleigh’s house in relation to the high school. 
  • Part B. How far could Kayleigh live from her school? 

• Jay has money in his wallet, but he doesn’t know the exact amount. When his friend asks him how much he has he says that he has 50 dollars give or take 15. 
  • Part A. Write an absolute value equation to model this situation. 
  • Part B. How much money could Jay have in his wallet? 

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