8th Grade Standard - 8.EE.B.6
Expressions & Equations
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation
y = mx + b for a line intercepting the vertical axis at b.
LESSON: GHOST ISLAND
Is the ship on a straight course to hit Isla Fantasma?
Connecting geometry to algebra is fascinating, and here we will interpret the slope of a straight line as a series of similar triangles. During Ghost Island, Captain Mary Read and her Sailing Master, Bonny Anne, have departed Isla Verde, headed toward Isla Fantasma. They are working to verify that they are on a direct course to reach Isla Fantasma, which holds the treasure of Calico Jack. The data provided are two maps: one showing the triangle formed by Isla Verde and the ship’s current position, and one showing the triangle formed by Isla Verde and Isla Fantasma.
- Play Ghost Island Immersion video, whole-class.
- Restate the question: Is the ship on a straight course to hit Isla Fantasma?
- Facilitate classroom discussion, ask students: "What are your ideas to help the Professor?"
2. Data & Computation
- Print the Data Artifact, cut into halves, and distribute to students.
- Allow students work time. Then ask students "Does your answer make sense?"
- Consider using a sharing protocol to lead to mathematical insights and/or highlight misconceptions.
- Allow students to revise their work.
- Play Ghost Island Resolution video, whole-class.
- Prepare and give brief lecture (Teacher Instruction).
Answer: The ship is on course for Isla Fantasma. The similar triangles have proportional side lengths; and thus, the line formed by the course of the ship has a constant slope of 2/3.
1. Simulation Trainer
- Have students complete Simulation Trainer.
1. Print and distribute the Practice Printable to your students.
2. Have students complete the Practice Printable. Consider using creative protocols.
1. Have students complete the Practice Printable.
2. Have students complete the Student Reflection Assignment.
1. Have your students go to midschoolmath.com/clicker.
2. Click on Launch Clicker Quiz and note Clicker Quiz code.
3. Have students enter quiz code on their screens.
4. Launch Clicker Quiz.
5. Review Clicker Quiz results and prompt students to make connections to the Math Simulator.