Algebra 1 Lesson

Investigating Slopes of Parallel and Perpendicular Lines (The Grid Crossings)

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8th or 9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.HSG.GPE.B.5, CCSS.MATH.CONTENT.8.EE.B.660 min

Learning Objective

Students will determine whether two lines are parallel, perpendicular, or neither by comparing slopes, and will write equations of lines parallel or perpendicular to a given line through a specified point.

Lesson Overview

Students use Building Thinking Classrooms pedagogy — standing in random groups at vertical surfaces — to discover the slope relationships for parallel and perpendicular lines through progressive thin-sliced tasks, a Desmos digital investigation, and a leveling consolidation discussion.

Materials

Vertical non-permanent surfaces (whiteboards or chart paper)
Dry-erase markers (one per group)
Index cards (for 90-degree angle verification)
Desmos Classroom activity (teacher-prepared)
Exit ticket slips

Scaffolded Task Progression

1Task 1

Low-Floor Launch (verbal — anchor problem, delivered verbally): 'Draw a coordinate plane on your board. Graph the line

y = \frac{2}{3} x + 1

. Now, draw a brand new line that runs perfectly alongside it like a train track — meaning they will run forever and never intersect. Write down the exact equation of your new line. What did you keep the same? What did you change?'

2Task 2

Slice 1 (verbal): 'A different line has equation

y = - 4 x + 7

. Write the equation of a line parallel to it that passes through the point

(0, - 2)

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