Overlay Outlaws

Teacher Facilitation Guide

Justin's Buddy

Learning Objective

Students will identify the solution region of a system of linear inequalities by creating physical overlaps using transparency sheets and analyzing boundary line types.

Materials Checklist

Clear Transparencies (2/student) Blue & Red Dry-Erase Markers Purple Zones Worksheets Spectral Solutions Slides

Pacing Guide

Warm-up 5 MIN

Video Discussion 10 MIN

The Overlay 25 MIN

Closure 5 MIN

"Your graph is your guide."

1 Warm-up: The Voting Booth (5 min)

Display Slide 3. Use physical gestures for high-speed formative assessment:

Solid Line

Students hold arms out straight horizontally.

Dashed Line

Students make "chopping" motions with their hands.

2 Video: The Color Fusion (10 min)

Play the video (Slide 4) from 2:49 - 4:15. This is where Justin explains the "Both" concept.

Look for the Robot Mascot!

"What does the robot say about graphing? (Graphing is the best way to conceptualize infinite solutions.)"

3 Main Activity: The Overlay (25 min)

Step 1: The Blue Print

Students graph \( y \ge -x \) on their first transparency using blue marker. Remind them to check the shading (above) before they start coloring.

Step 2: The Red Zone

Students graph \( y > 3x - 4 \) on the second transparency using red. Critical: This line must be dashed!

Step 3: The Fusion

Students align both transparencies over the worksheet. The purple region is the solution. Have them pick three points from the purple zone and verify them algebraically in the table.

The Boundary Trap (Video 4:35)

Students often struggle with the "Intersection Point." In this activity, point (1, -1) is on the intersection of a solid line and a dashed line.

"Since it doesn't make BOTH true (fails the dashed line), it is NOT a solution to the system."

Extension Idea

Ask: "What would happen if we added a third inequality like \( y \le 5 \)? Create a yellow transparency to find the triple-shaded region."

Differentiation

For students struggling with shading, provide a "test point" checklist on a sticky note to guide their evaluation of (0,0).

Spectral Solutions

Overlay Outlaws Teacher Guide

Spectral Solutions Slides

Purple Zones Worksheet

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