LESSON: THE ROAD LESS TRAVELED · MidSchoolMath The Road Less Traveled Clicker Quiz Launch the...
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MidSchoolMath 1 The Pythagorean Theorem is one of the most useful concepts in mathematics, and it can be applied in many life situations. In The Road Less Traveled, sisters Sonia and Misha are on another one of their road trips, reminiscing about their dad. They are going to back to their hometown to have dinner with their mom and her new friend, Steve. They don’t want to be late, so they are trying to figure out the quickest route from where they are. The data provided is a map image showing the two possible routes the sisters can take (the two routes form a right triangle), as well as the speed limit for each route. LESSON: THE ROAD LESS TRAVELED Which route is faster? The Road Less Traveled Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. The Math Simulator TM Immersion Play The Road Less Traveled Immersion video, whole-class. Restate the question: Which route is faster? Facilitate classroom discussion; ask students: "What do we need to know?" • • • 1 2 Data & Computation Print the Data Artifact 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. • • • • 3 Resolution Play The Road Less Traveled Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction). • • Download the Detailed Lesson Plan Available on the Teacher Dashboard + Simulation Trainer Assign 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. • • • • (Use student headphones.) 8.G.B.7 Geometry
Transcript of LESSON: THE ROAD LESS TRAVELED · MidSchoolMath The Road Less Traveled Clicker Quiz Launch the...
MidSchoolMath 1
The Pythagorean Theorem is one of the most useful concepts in mathematics, and it can be applied in many life situations. In The Road Less Traveled, sisters Sonia and Misha are on another one of their road trips, reminiscing about their dad. They are going to back to their hometown to have dinner with their mom and her new friend, Steve. They don’t want to be late, so they are trying to figure out the quickest route from where they are. The data provided is a map image showing the two possible routes the sisters can take (the two routes form a right triangle), as well as the speed limit for each route.
LESSON: THE ROAD LESS TRAVELEDWhich route is faster?
The Road Less Traveled
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
The Math SimulatorTM
ImmersionPlay The Road Less Traveled Immersion video, whole-class. Restate the question: Which route is faster?Facilitate classroom discussion; ask students: "What do we need to know?"
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2 Data & ComputationPrint the Data Artifact 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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3 ResolutionPlay The Road Less Traveled Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).
••
Download the Detailed Lesson PlanAvailable on the Teacher Dashboard
+ 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.G.B.7Geometry
MidSchoolMath The Road Less Traveled
Clicker QuizLaunch the Clicker Quiz, whole-class.
8.G.B.7Geometry
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Gladys: Be sure students are correctly substituting values into the formula, namely that c should always be the side that is across from the right angle.
Kevin: When calculating square roots that are not perfect, students should know that keeping the radical form (√12) is an exact answer, while the decimal (≈ 3.5) is just an approximation.
Megan: If, when using the formula, students mistakenly multiply values by 2 instead of squaring them, remind them of the proof using actual squares drawn off the sides of the right triangle.
KevinSimpson
GladysGraham
MeganLeBleu
Ex. Clicker Quiz #6Standard Math Procedures
Instruction at a Glance
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Find the length of the base diagonal.
Use the base diagonal and height to find d.
82 + 22 = c2
(√68)2 + 62 = d2
68 = c2
104 = d2
c = √68 (≈8.25)
d = √104 ≈ 10.2 units
64 + 4 = c2
68 + 36 = d2
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THE ROAD LESS TRAVELEDWhich route is faster?Sisters Sonia and Misha love road trips in their van, as they get to be with each other and reminisce about their late father. They are again headed out on the road, their destination being a ghost town they heard about. They signed up for the last tour of the day, so they don’t want to be late.
Help Sonia and Misha decide which route will get them to the ghost town the fastest.
8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
About this standard
Date PeriodName
MidSchoolMath The Road Less Traveled 1 of 2
The fastest route is:
County Roads 45 & 32 County Road 290
APPLYING THE STANDARD
For each triangle, fi nd the length of the missing side. Round to the nearest tenth, if necessary.1)
In ∆XYZ, YW is perpendicular to XZ. The dimensions are shown in centimeters. What is the length, in centimeters, of XZ?Round to the nearest tenth, if necessary.
2)
The area of ∆DEF is 12.3 square units. What is the perimeter?Round to the nearest tenth, if necessary.
6)
How long are the poles for the teepee, assuming an extra 3 feet for the top?Round to the nearest tenth, if necessary.
4) Dixie is laying sod in her yard, shown below. How many square feet of grass sod should she purchase?
5)
What is the perimeter of the triangle?Round to the nearest tenth, if necessary.
3)
Determine the lengths of the legs (a and b) of the right triangle so that the hypotenuse has a length of √13 units.
7)
MidSchoolMath The Road Less Traveled 2 of 2
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How might this standard appear on a test?
a) b) c) d)
a = _________ units
b = _________ units
Check out my worked example #1c
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