Unit 10 Pythagorean Theorem & Irrational Numbers
Accelerated Lesson
( Note, some activities are marked "OPTIONAL" in the student workbook to meet the accelerated pace.)
Standards
Learning Targets
Additional Resources
1
Addressing:
NC.8.NS.2
NC.8.EE.2
Building Toward:
NC.8.EE.2
NC.8.G.6
NC.8.NS.2
Building On:
NC.6.EE.1
NC.6.G.1
NC.5.G .3
I can find the area of a triangle.
I can find the area of a tilted square on a grid by using methods like “decompose and rearrange” and “surround and subtract.”
I understand the meaning of expressions like √25 and √3.
If I know the area of a square, I can express its side length using square root notation.
I can explain what a square root is.
The Areas of Squares and Their Side Lengths
Digital Manipulative
Khan Academy Videos (Review)
Khan Academy Practice (Review)
Find Base and Height on a Triangle
Finding Missing Length when Given Area of a Triangle
Side Lengths and Areas
Digital Manipulative
2.3: The Sides and Areas of Tilted Squares
Khan Academy Practice
Square Roots of Perfect Squares
Roots of Decimals and Fractions
IXL Math
Square Roots of Perfect Squares
Video Lesson Summary: Side Lengths and Areas of Squares From Illustrative Mathematics
2
Addressing:
NC.8.EE.2
NC.8.NS.1
Building Toward:
NC.8.EE.2
NC.8.NS.2
Building On:
NC.5.NF.4
NC.6.EE.1
I know what an irrational number is and can give an example.
I know what a rational number is and can give an example.
Khan Academy Videos
Intro to Rational and Irrational Numbers
Classifying Numbers: Rational and Irrational
Khan Academy Practice
Classify Numbers: Rational and Irrational
IXL Math
Identify Rational and Irrational Square Roots
Video Lesson Summary: Square Roots on the Number Line From Illustrative Mathematics
3
I can find a decimal approximation for square roots.
I can plot square roots on the number line.
When I have a square root, I can reason about which two whole numbers it is between.
Square Roots on the Number Line
Khan Academy Video
Approximating Square Roots to the Hundredths
Khan Academy Practice
Comparing Irrational Numbers with a Calculator
IXL Math
Estimate Positive Square Roots
Reasoning About Square Roots
Khan Academy Video
Khan Academy Practice
Approximating Square Roots Walk Through
IXL Math
Estimate Positive and Negative Square Roots
Video Lesson Summary: Square Roots on the Number Line From Illustrative Mathematics
4
Addressing:
NC.8.G.6
NC.8.G.7
Building Toward:
NC.8.G.6
Building On:
NC.5.G.3
NC.7.G.2
NC.8.EE.2
I can explain what the Pythagorean Theorem says.
I can explain why the Pythagorean Theorem is true.
Finding Side Lengths of Triangles
Khan Academy Video
Intro to the Pythagorean Theorem
Khan Academy Practice
Use Area of Squares to Visualize Pythagorean Theorem
IXL Math
Pythagorean Theorem: Find the Length of the Hypotenuse
PythagoreanTheorem:Find the Missing Leg Length
A Proof of the Pythagorean Theorem
Digital Manipulative
Khan Academy Video
Bhaskara’s Proof of the Pythagorean Theorem
Video Lesson Summary: The Pythagorean Theorem From Illustrative Mathematics
5
When I have a right triangle, I can identify which side is the hypotenuse and which sides are the legs.
If I know the lengths of two sides, I can find the length of the third side in a right triangle.
6
I can explain why it is true that if the side lengths of a triangle satisfy the equation a2+b2=c2 then it must be a right triangle.
If I know the side lengths of a triangle, I can determine if it is a right triangle or not.
I can use the Pythagorean Theorem to solve problems.
The Converse
Khan Academy Practice
IXL Math
Converse of the Pythagorean Theorem: Is it a Right Triangle?
Applications of the Pythagorean Theorem
Pythagorean Theorem Word Problem: Carpet
Pythagorean Theorem Word Problem: Fishing Boat
Khan Academy Practice
Pythagorean Theorem Word Problems
IXL Math
Pythagorean Theorem: Word Problems
Video Lesson Summary: G8U8V4 Using the Pythagorean Theorem From Illustrative Mathematics
7
I can find the distance between two points in the coordinate plane.
I can find the length of a diagonal line segment in the coordinate plane.
I know what a cube root is.
I understand the meaning of expressions like the cube root of 5.
I can approximate cube roots.
Finding Distances in Coordinate Plane
YouTube Video
How to Find the Distance Between Two Points Using the Pythagorean Theorem
Khan Academy Practice
Use Pythagorean Theorem to Find Perimeter
IXL Math
Find the Distance Between Two Points
Edge Lengths and Volumes
Khan Academy Video
Dimensions of a Cube From Its Volume
Khan Academy Practice
Video Lesson Summary: Using the Pythagorean Theorem From Illustrative Mathematics
Video Lesson Summary: Cube Roots and Decimal Representations From Illustrative Mathematics
8
Addressing:
NC.8.EE.2
NC.8.NS.1
NC.8.NS.2
Building On:
NC.7.NS.2
When I have a cube root, I can reason about which two whole numbers it is between.
I understand that every number has a decimal expansion.
I can write a fraction as a repeating decimal.
Cube Roots
Math is Fun
IXL Math
Decimal Representations of Rational Numbers
Khan Academy Video
Converting a Fraction to a Repeating Decimal
Khan Academy Practice
Writing Fractions as Repeating Decimals
Writing Fractions as Repeating Decimals Review
IXL Math
Write a Repeating Decimals as a Fractions
Video Lesson Summary: Cube Roots and Decimal Representations From Illustrative Mathematics
9
I can write a repeating decimal as a fraction.
I understand that every number has a decimal expansion.
Khan Academy Videos
Converting Repeating Decimals to Fractions (Part 1)
Converting Repeating Decimals to Fractions (Part 2)
Khan Academy Practice
Converting Repeating Decimals to Fractions
Converting Multi-Digit Repeating Decimals to Fractions
Writing Repeating Decimals as Fractions Review
IXL Math
Write a Repeating Decimal as a Fraction
Video Lesson Summary: Cube Roots and Decimal Representations From Illustrative Mathematics