Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 9
Math
Unit 7
8th Grade
Lesson 9 of 16
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Find missing side lengths involving right triangles and apply to area and perimeter problems.
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 foundational standards covered in this lesson
6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In order to give approximate answers to the tenth of a unit, students may use calculators throughout this lesson. If time allows, students may also practice approximating square roots without calculators as a review of Lesson 2.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Find the missing side length in each right triangle. Give an exact answer and an approximate answer to the nearest tenth of a unit.
a.
b.
Find the area of the isosceles triangle below. Give your answer to the nearest tenth of a square unit.
Find the perimeter of the triangle below. Give your answer to the nearest tenth of a unit.
A set of suggested resources or problem types that teachers can turn into a problem set
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
An isosceles trapezoid is composed of a square and two congruent triangles, as shown below. The area of the square is 16 units squared. Find the area of the trapezoid.
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 8
Lesson 10
Topic A: Irrational Numbers and Square Roots
Define, evaluate, and estimate square roots.
8.EE.A.2
Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
8.NS.A.1 8.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.
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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.
8.G.B.7
Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).
Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
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.2 8.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.
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