Download MS 104

MS 104
Unit Plan 6
Unit Name:
Looking for Pythagoras
Essential Question:
How do we solve for
missing sides and
angles of triangles?
Grade: 8
Duration: 5 weeks
Big Ideas/Enduring Understandings:
 Find and understand square and cube roots
 Use the Pythagorean Theorem to find missing sides of right triangles
 Use the Pythagorean Theorem to find distance on a coordinate plane
 Explore special right triangles
Common Core Learning Standards:
8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse
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
8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a
coordinate system
8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational
numbers, locate them approximately on a number line diagram
8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the
form x squared = p and x cubed= p where p is a positive rational number. Evaluate square
roots or small perfect squares and cube roots of small perfect cubes.
Student Objectives:
PYTHAGOREAN THEOREM
 Understand and apply the Pythagorean Theorem
 Develop strategies for finding the distance between two points on a coordinate grid
 Explain a proof of the Pythagorean Theorem
 Use the Pythagorean Theorem and its converse to solve a variety of problems
 Use the Pythagorean Theorem to find the equation of a circle with its center located at the origin
REAL NUMBERS
 Understand that the set of real numbers consists of rational and irrational numbers
 Interpret square roots and cube roots of numbers by making use of their related geometric
representations
 Relate the area of a square to the side length of the square
 Estimate the values of square roots
 Estimate the values of cube roots
 Relate the volume of a cube to the edge length of the cube
 Compare numbers that can be represented as fractions (rational numbers) to numbers that cannot be
represented as fractions (irrational numbers) and recognize that the set of real numbers consists of
rational and irrational numbers
 Represent rational numbers as fractions and as terminating decimals or repeating decimals
 Recognize that irrational numbers cannot be represented as fractions and are nonterminating,



nonrepeating decimals
Recognize that the square root of a whole number that is not a square is irrational
Locate irrational numbers on a number line
Use and understand properties of rational and irrational numbers
REGENTS Activities/Tasks
Investigation 2: Squaring Off
Find and estimate square and cube roots, graph square root and cube root equations
Investigation 3: The Pythagorean Theorem
Use the Pythagorean Theorem and its converse
Find Pythagorean Triples
Investigation 4: Using Real Numbers
Explore sets of numbers (whole, integer, rational, irrational)
Approximate irrational numbers
8th Grade Activities/Tasks
Investigation 1: Coordinate Grids
Review of the coordinate plane and finding distance on it (1.1 and 1.2)
Investigation 2: Squaring Off
Find and estimate square and cube roots
Investigation 3: The Pythagorean Theorem
Use the Pythagorean Theorem and its converse
Find distance on the coordinate plane
Investigation 4: Using Real Numbers
Approximate irrational numbers
Explore special triangles
Benchmark 5: Performance Task: Fencing and Grassing
Key Terms/Vocabulary:
Square root Cube root Pythagorean Theorem Converse Hypotenuse Legs Irrational Rational
Resources:
CMP3: Looking for Pythagoras
Glencoe Math
Common Core Mathematics
Big Ideas Math