Grade 8

Unit 1: Rigid Transformations and Congruence
17 Topics
Moving in the Plane
Naming the Moves
Grid Moves
Making the Moves
Coordinate Moves
Describing Transformations
No Bending or Stretching
Rotation Patterns
Moves in Parallel
Composing Figures
What Is the Same?
Congruent Polygons
Congruence
Alternate Interior Angles
Adding the Angles in a Triangle
Parallel Lines and the Angle in a Triangle
Rotate and Tessellate
Unit 2: Dilations, Similarities, and Introducing Slope
12 Topics
Projecting and Scaling
Circular Grid
Dilations with no Grid
Dilations on a Square Grid
More Dilations
Similarity
Similar Polygons
Similar Triangles
Side Length Quotients in Similar Triangles
Meet Slope
Writing Equations of Lines
Using Equations for Lines
Unit 3: Linear Relationships
14 Topics
Understanding Proportional Relationships
Graphs of Proportional Relationships
Representing Proportional Relationships
Comparing Proportional Relationships
Introduction to Linear Relationships
More Linear Relationships
Representations of Linear Relationships
Translating to y = mx + b
Slopes Don’t Have to be Positive
Calculating Slope
Equations of All Kinds of Lines
Solutions to Linear Equations
More Solutions to Linear Equations
Using Linear Relations to Solve Problems
Unit 4: Linear Equations and Linear Systems
16 Topics
Number Puzzles
Keeping the Equation Balanced
Balanced Moves
More Balanced Moves
Solving Any Linear Equation
Strategic Solving
All, Some, or No Solutions
How many Solutions?
When are They the Same?
On or Off the Line?
On Both of the Lines
Systems of Equations
Solving Systems of Equations
Solving More Systems
Writing Systems of Equations
Solving Problems with Systems of Equations
Unit 5: Functions and Volume
19 Topics
Inputs and Outputs
Introduction to Functions
Equations for Functions
Tables, Equations, and Graphs of Functions
More Graphs of Functions
Even More Graphs of Functions
Connecting Representations of Functions
Linear Functions
Linear Models
Piecewise Linear Functions
Filling Containers
How Much Will Fit?
The Volume of a Cylinder
Finding Cylinder Dimensions
The Volume of a Cone
Finding Cone Dimensions
Estimating a Hemisphere
The Volume of a Sphere
Cylinders, Cones, and Spheres
Unit 6: Associations in Data
10 Topics
Organizing Data
Plotting Data
What a Point in a Scatter Plot Means
Fitting a Line to Data
Describing Trends in Scatter Plots
The Slope of a Fitted Line
Observing More Patterns in Scatter Plots
Analyzing Bivariate Data
Looking for Associations
Using Data Displays to Find Associations
Unit 7: Exponents and Scientific Notation
15 Topics
Exponent Review
Multiplying Powers of Ten
Powers of Powers of 10
Dividing Powers of 10
Negative Exponents with Powers of 10
Other Bases
Practice with Rational Bases
Combining Bases
Describing Large and Small Numbers Using Powers of 10
Representing Large Numbers on the Number Line
Representing Small Numbers on the Number Line
Applications of Arithmetic with Powers of 10
Definition of Scientific Notation
Multiplying, Dividing, and Estimating with Scientific Notation
Adding and Subtracting with Scientific Notation
Unit 8: Pythagoras Theorem and Irrational Numbers
15 Topics
The Areas of Squares and Their Side Lengths
Side Lengths and Areas
Rational and Irrational Numbers
Square Roots on the Number Line
Reasoning About Square Roots
Finding Side Lengths of Triangles
A Proof of the Pythagorean Theorem
Finding Unknown Side Lengths
The Converse of Pythagoras Theorem
Applications of the Pythagorean Theorem
Finding Distances in the Coordinate Plane
Edge Lengths and Volumes
Cube Roots
Decimal Representations of Rational Numbers
Infinite Decimal Expansions
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Finding Unknown Side Lengths

Grade 8 Unit 8: Pythagoras Theorem and Irrational Numbers Finding Unknown Side Lengths

Warmup

Activity #1

Calculate Unknown Side Lengths of a Right Triangle.

  • Label all the hypotenuses with c.

  • Find the length of the unknown side.

Activity #2

Calculate Unknown Side Lengths of a Right Triangle.

  • Find the exact value of each variable that represents a side length in a right triangle.

A right triangle has side lengths of a, b, and c units. The longest side has a length of c units.

  • Complete each equation to show three relations among a, b, and c.

Activity #3

Find Length of a Line Segment.

  • Use the tools in the applet below to find the length of the line.

(1.) What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

(2.) What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

(3.) What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

Challenge #1

Find the value of x in the figure.

Challenge #2

The spiral in the figure is made by starting with a right triangle with both legs measuring one unit each. Then a second right triangle is built with one leg measuring one unit, and the other leg being the hypotenuse of the first triangle. A third right triangle is built on the second triangle’s hypotenuse, again with the other leg measuring one unit, and so on.

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