CMS Curriculum Guides 2011-2012
8th Grade Math
Unit Title: Looking for Pythagoras
Suggested Time: 14 Days (75 – 90 minute block)
Enduring understanding (Big Idea): Calculating the distance between two points in the plane; Finding areas of figures drawn on a coordinate grid
with whole-number vertices; Understanding square roots as lengths of sides of squares; Understanding the Pythagorean Theorem and how it relates the
areas of the squares on the sides of a right triangle; Using Pythagorean Theorem to solve problems; Investigate rational numbers written as decimals;
Understanding irrational numbers as non-terminating, non-repeating decimals; and Understanding slope relationships of perpendicular and parallel
lines.
Essential Questions: Is it appropriate and useful to use the Pythagorean Theorem in this situation? How do I know this? Do I need to find the distance
between two points? How are irrational numbers and areas of squares related? How can I estimate the square root of a number? How can I find the
length of something without directly measuring it?
?
Unit Plans
Common Core Standards Alignment
Connection to 2003 Standards
Investigation 1
Apply and extend previous understandings of numbers to the system of
rational numbers.
Review 6.NS.6- Understand a rational number as a point on the number line.
Extend number line diagrams and coordinate axes familiar from previous grades
to represent points on the line and in the plane with negative number coordinates
Goal 3.02, 3.03
Expressions and Equations Work with radicals and integer exponents.
8.EE.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.
Goal 3.02
Understand and apply the Pythagorean Theorem
8.EE.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.
Goal 3.01, 3.02
Coordinate Grids
Problems 1.1,1.2, 1.3
Math Reflections
Investigation 2
Squaring Off
Problems 2.1, 2.2, 2.3
Math Reflections
Investigation 3
The Pythagorean Theorem
Problems 3.1, 3.2, 3.3, 3.4
CMS Curriculum Guides 2011-2012
8th Grade Math
Math Reflections
Understand and apply the Pythagorean Theorem
8.G.6- Explain a proof of the Pythagorean Theorem and its converse.
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
8.G.8- Apply the Pythagorean Theorem to find the distance between two points in
a coordinate system.
Solve real-world and mathematical problems involving volume of cylinders,
cones, and spheres.
8.G.9- Know the formulas for the volumes of cones, cylinders, and spheres and
use them to solve real-world and mathematical problems. (ACE Problems)
Investigation 4
Using the Pythagorean
Theorem
Problems 4.1, 4.2, 4.3, 4.4
Math Reflections
Looking Back and Looking
Ahead
Know that there are numbers that are not rational, and approximate them
by rational numbers.
8NS.1- Know that numbers that are not rational are called irrational. Understand
informally that every number has a decimal expansion; for rational numbers show
that the decimal expansion repeats eventually, and convert a decimal expansion
which repeats eventually into a rational number.
8.NS.2.- Use rational approximations of irrational numbers to compare the size of
irrational numbers, locate them approximately on a number line diagram, and
estimate the value of expressions (e.g., π2).
Understand and apply the Pythagorean Theorem
8.EE.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.
Understand and apply the Pythagorean Theorem.
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.
Goal 1.01, 3.02
CMS Curriculum Guides 2011-2012
8th Grade Math
8.G.9 - Know the formulas for the volumes of cones, cylinders, and spheres and
use them to solve real-world and mathematical problems. (ACE problems)
Prior Knowledge: Measuring lengths; working with coordinates; measuring areas of polygons and irregular figures and
surface area of three-dimensional shapes; applying the formula for area of a square; formulating, reading, and interpreting
symbolic rules, solving problems in geometric and algebraic contexts; understanding fractions and decimals; and representing
fractions as decimals and decimals as fractions.
Mathematical Practices Standards for Common Core
1-Make sense of problems and persevere in solving them 2-Reason abstractly and quantitatively 3-Construct viable arguments and
critique the reasoning of others 4-Model with mathematics 5-Use appropriate tools strategically 6-Attend to precision 7-Look for
and make use of structure 8-Look for and express regularity in repeated reasoning
CMS Curriculum Guides 2011-2012
8th Grade Math
Essential Terms Developed in This Unit
Useful Terms Referenced in This Unit
Terms Developed in Previous Unit
Hypotenuse
Conjecture
area
perimeter
Legs
Irrational number
congruent
perpendicular lines
Pythagorean Theorem
Isosceles triangle
coordinate grid
quadrilateral
Real numbers
Rational number
coordinates
ratio
Repeating decimal
equilateral triangle
right angle
Terminating decimal
length
right triangle
parallel lines
square
parallelogram
symmetry
Square roots
CMS Curriculum Guides 2011-2012
8th Grade Math
Resources
Lab-Sheet
Additional Practice/Skills Worksheets
CMP2 Website –online & technology resources
Formal Assessment

Check-Ups

Partner Quiz

Unit Test
Assessment Options

Notebook check

Multiple-Choice

Question Bank

ExamView CD-ROM
Parent Guide-Unit Letters
Spanish Assessment Resources
TeacherExpress CD-ROM
LessonLab Online Courses
Unit Technology Tips