Download Topic/ Theme/ Duration Pythagorean Theorem

Unit Plan
Mathematics
Unit: 6
Grade: 8
Solve one‐variable linear equations, including cases with infinitely many solutions or no solutions
Solve problems involving volumes of cones, cylinders, and spheres together with previous geometry work, proportional reasoning and multi‐
step problem solving in grade 7
Pythagorean Theorem
Topic/ Theme/
6 weeks
Duration
How do we solve for missing sides and angles of triangles?
Essential
Question(s)
 Find and understand square and cube roots
Key Student
the Pythagorean Theorem to find missing sides of right triangles
Learning Objectives  Use
Use the Pythagorean Theorem to find distance on a coordinate plane
Standard
 Explore special right triangles
Skills
8.G.6( ). Explain a proof of the
Pythagorean Theorem and its converse.
Explain a proof of the Pythagorean
Theorem and its converse.
Resources
CMP Looking for Pythagoras
Glencoe Chapter 5: Lesson 5, Inquiry Lab
Tell whether a triangle is a right
triangle
8.G.7( ). Apply the Pythagorean
Theorem to determine unknown side
lengths in right triangles in real-world
and mathematical problems in two and
three dimensions.
Use the Pythagorean Theorem to
find missing side lengths
8.G.8( ). Apply the Pythagorean
Use the Pythagorean Theorem to
Common Core Mathematics
CC 8-9, 3.2, 3,3
Big Ideas Math: 7.3, 7.5
CMP Looking for Pythagoras
Glencoe Chapter 5: Lesson 6
Apply the Pythagorean Theorem to
real-world and word problems
Common Core Mathematics
3.3
Big Ideas Math: 7.3, 7.5
CMP Looking for Pythagoras
Theorem to find the distance between
two points in a coordinate system.
find distance between points on a
coordinate plane and in real world
problems
Glencoe Chapter 5: Lesson 7
Common Core Mathematics
3.4
8.NS.2: Use rational approximations of
irrational numbers to compare the size
of irrational numbers; locate then
approximately on a number line
diagram.
8.EE.2: Use square root and cube
root symbols to represent solutions
to equations of the form x 2 = 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.
Vocabulary
Sequence of Key Learning
Activities
Big Ideas Math: 7.3, 7.5
CMP Looking for Pythagoras
Glencoe
Common Core Mathematics
3.4
Big Ideas Math: 7.4
CMP Looking for Pythagoras
Glencoe
Common Core Mathematics
3.4
Big Ideas Math: 7.1, 7.2, 7.3, 7.4, 7.5
right triangle, leg, hypotenuse, right angle, Pythagorean Theorem, square root, squared,
formula, proof
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
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Activities/Tasks
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
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
Assessments
Note: Standards in bold are identified as major standards. Standards with checkmarks are standards recommended for greater
emphasis
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