Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 1
Math
Unit 7
8th Grade
Lesson 1 of 16
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Lesson Notes
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Define, evaluate, and estimate square roots.
The core standards covered in this lesson
8.EE.A.2 — Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
The foundational standards covered in this lesson
6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
7.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Three squares are shown below with their area in square units.
a. What is the side length of each square?
b. Describe the relationship between the side length of a square and its area.
c. Another square has an area of $${{{25}}}$$ square units. Write an equation to show the relationship between the side length, $$s$$, of this square and its area.
d. This equation can be solved by asking, “What number, when squared, equals $${{{25}}}$$?” Another way of saying this is, “What is the square root of $${{{25}}}$$?” Use this information to write two ways to represent the solution to the equation.
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The square below has an area of $$8$$ square units.
a. Estimate the side length of the square. Between what two whole numbers will the side length be? Explain your reasoning.
b. Write an equation to represent the relationship between the side length, $$s$$, of this square and the area.
c. What is the side length of the square?
a. Find the side length of a square with area:
b. What is the side length of a square with area $${50 \space \mathrm{u}^2}$$? Between what two whole numbers is the side length of the square?
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
The square below has an area of $${20}$$ square units.
Taylor writes the equation $$s^2={20}$$ to find the measure of the side length of the square. She reasons that the solution to the equation is $$\sqrt{20}$$ and concludes that the side length of the square is $${10}$$ units.
Do you agree with Taylor? Explain why or why not. If you disagree, include the correct side length of the square.
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.
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Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
Topic A: Irrational Numbers and Square Roots
Standards
8.EE.A.2
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.
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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.
Find missing side lengths involving right triangles and apply to area and perimeter problems.
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.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.
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