MidSchoolMath 1

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.

LESSON: GHOST ISLANDIs the ship on a straight course to hit Isla Fantasma?

Ghost Island

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.

The Math SimulatorTM

ImmersionPlay 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 do we need to know?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

3 ResolutionPlay Ghost Island Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

8.EE.B.6Expressions & Equations

Clicker QuizLaunch the Clicker Quiz, whole-class.

MidSchoolMath 2Ghost Island

8.EE.B.6Expressions & Equations

Gladys: When using similar triangles to discuss slope, be sure to use the vertical side lengths/horizontal side lengths, so that it demonstrates the "rise over run" concept.

Kevin: Help students understand the difference between a proprtional linear relationship (y = mx) and a non-proportional linear relationship (y = mx + b). In a proportional linear relationship, the (x, y) values have a common ratio y/x and a common rate of change between x-values and between y-values. In a non-proportional linear relationship, the (x, y) values do not have a common ratio, but there is still a common rate of change between the x-values and a common rate of change between the y-values.

Megan: Use many graphs and many tables to demonstrate the information above. Shown various examples, ask students to identify proportional linear relationships and non-proportional linear relationships by sight.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #2Standard Math Procedures

Instruction at a Glance

1 Determine the ratio of the side lengths in ∆ADE.

AD = 10 – 2 = 8 = DE 8 – 0 8

AB = 20 – 2 = 18 units

B(0, 20) plus 18 horizontal units will arrive at point C(x, y).

C(0 + 18, 20) C(18, 20)

AB = 1 = 1BC

18 BC

BC = 18

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Determine the length of given side of ∆ABC.

Interpret the results as they relates to coordinate points.

Use rules of similar triangles and corresponding sides to find BC.

== = 1

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GHOST ISLANDIs the ship on course to hit the island?Aboard the ship Isosceles, Captain Mary Read and Sailing Master Bonny Anne are headed to fi nd more treasure.

They have departed Isla Fantasma and have set a course. They hope to arrive at Isla Pinos. It is thought to hold the hidden trea-sure of One-Eyed Whitebeard.

Use the readings on the map to help Bonny Anne determine whether the Isosceles is on course to hit Isla Pinos.

8.EE.B.6

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.

About this standard

Date PeriodName

MidSchoolMath Ghost Island 1 of 2

APPLYING THE STANDARD

Determine the slope, y-intercept and equation of line n and line p.

Slope: _____________ y-intercept:_____________

Equation: ______________________________________

Line n

Slope: _____________ y-intercept:_____________

Equation: ______________________________________

Line p

1)

2) a)

a)

b)

b)

c)

MidSchoolMath Ghost Island 2 of 2

Date PeriodName

How might this standard appear on a test?

Draw this line on the graph and label it line w.y = x - 5

Identify the slope and y-intercept.

Slope: _________ y-intercept: _________

Plot each of these 3 points: (-2, 5) (0, 4) (4, 2)

Draw the line on the graph and label it line z.

Write the equation of the line: ____________

3)

a)

b)

4) Determine the slope (m) for line f and line g.

Line f Line g

m = m =

Solve the above slope equations for y.

Check out my worked example #1, line n

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