Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 10
Math
Unit 7
8th Grade
Lesson 10 of 16
Jump To
Lesson Notes
There was an error generating your document. Please refresh the page and try again.
Generating your document. This may take a few seconds.
Are you sure you want to delete this note? This action cannot be undone.
Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).
The core standards covered in this lesson
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 10 and 11 engage students in real-world and mathematical problems that can be modeled and solved using the Pythagorean Theorem. In these two lessons, students tackle problems involving a race and speed, and students will see how to apply the Pythagorean Theorem in three dimensions (MP.4). Depending on time, these two lessons can be combined into one lesson for a longer class period, or they can be kept as two separate lessons.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
You have a ladder that is 13 feet long. In order to make it sturdy enough to climb, you place the ladder 5 feet from the wall of a building, as shown in the diagram below.
You need to post a banner on the wall 10 feet above the ground. Is the ladder long enough for you to reach the location you need to post the banner? Explain your answer.
Upgrade to Fishtank Plus to view Sample Response.
Grade 8 Mathematics > Module 2 > Topic D > Lesson 16 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are $${{1\over16}}$$ mile apart and arranged in a square grid. They are both standing at the intersection of 6th Ave and L Street. Doug can run at an average speed of 30 mi/hr through the streets of Salt Lake City, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the intersection of 10th Ave and E Street.
a. Who do you predict will win, and why?
b. Draw the likely paths that Doug and Bert will travel.
c. Who will win the race? Justify your response.
Bird and Dog Race, accessed on March 20, 2017, 12:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Kendrick is interested in purchasing a new television. He has picked out a specific space on a wall on which to mount the television. The wall space is rectangular in shape and measures $$1 \frac{2}{3}$$ feet tall and $$3$$ feet wide.
Sizes of televisions are given in inches and describe the diagonal length from the top corner of the television to the opposite bottom corner.
Can Kendrick fit a 42-inch television on the space that he has picked out? Explain your reasoning.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
Topic A: Irrational Numbers and Square Roots
Define, evaluate, and estimate square roots.
Standards
8.EE.A.2
Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
8.NS.A.18.NS.A.2
Locate irrational values approximately on a number line. Compare values of irrational numbers.
8.NS.A.2
Represent rational numbers as decimal expansions.
8.NS.A.1
Represent decimal expansions as rational numbers in fraction form.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Understanding and Applying the Pythagorean Theorem
Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.
8.G.B.6
Understand a proof of the Pythagorean Theorem.
Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Find missing side lengths involving right triangles and apply to area and perimeter problems.
8.G.B.7
Find the distance between points in the coordinate plane using the Pythagorean Theorem.
8.G.B.8
Topic C: Volume and Cube Roots
Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$ and $${x^3=p}$$.
8.EE.A.28.NS.A.2
Solve real-world and mathematical problems involving the volume of cylinders and cones.
8.G.C.9
Solve real-world and mathematical problems involving the volume of spheres.
Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
We've got you covered with rigorous, relevant, and adaptable math lesson plans for free