Algebra I Lesson

How Far From Home? Solving Absolute Value Equations

Shared by A STEM Educator

8th or 9th Grade3-act-mathCCSS.MATH.CONTENT.HSA.REI.B.3, CCSS.MATH.CONTENT.HSA.CED.A.150 min

Learning Objective

Students will solve absolute value equations of the form |ax + b| = c by reasoning about two cases and checking solutions in context.

Lesson Overview

Students explore absolute value through the real-world context of a GPS tracker showing distance from a starting point, then solve absolute value equations by reasoning about two possible locations on a number line.

Materials

Printed task sheets (one per student)
Number line posters or printed number lines
Mini whiteboards or scratch paper
Markers
Rulers (optional, for number line work)

Scaffolded Task Progression

1Task 1

Biscuit's GPS shows the dog is exactly 5 blocks from the corner (position 0 on the number line). Mark ALL possible locations on the number line below. How many locations are possible? ```coordgraph {"title":"Biscuit's Possible Locations","xLabel":"Blocks from corner (east = positive)","yLabel":"","xRange":[-8,8],"yRange":[-1,1],"xStep":1,"yStep":1,"polylines":[{"points":[[-8,0],[8,0]],"color":"#374151"}],"points":[{"x":0,"y":0,"label":"Corner (0)"},{"x":5,"y":0,"label":"?"},{"x":-5,"y":0,"label":"?"}]} ```

2Task 2

Write an equation using absolute value that represents 'Biscuit is exactly 5 blocks from the corner.' Use

x

for Biscuit's position. Then list all values of

x

that make your equation true.

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