Unit 3:  Pythagorean Theorem & Irrational Numbers

Time Frame:  15 Days

 

 

Math > Grade 8 > Unit 3

 

Unit Description

In this unit, students explore two important new ideas: the Pythagorean Theorem and irrational numbers.  In the process of solving the problems in this unit, students also review and make connections among the concepts of area, distance, slope, and rational numbers.  Students will find the relationships among the side of a square, square roots, and irrational numbers.  They find that the side lengths of some square are irrational numbers.  They discover the Pythagorean relationship through an exploration of squares drawn on the sides of a right triangle.  The coordinate system makes all of these investigations possible.  A coordinate system applied to a rectangular array of dots facilitates locating positions, calculating distances, and finding slopes of lines. 

 

Enduring Understandings

·         We can combine our understanding about mathematical relationships with our knowledge of some mathematical information to help answer questions.

·         The relationship of the sides of right triangles aids in design and construction.

 

 

Essential Questions

·         How are fractions and decimals similar?

·         How can you determine the distance between two points without measuring?

·         What real life situations can be solved using the Pythagorean Theorem?

GLEs: 1, 6, 10, 23, 25, 27, 28, 29, 31

 

Students will know…

·         Coordinate grids (coordinate plane with four quadrants).

·         Slope (ratio of the change in dependent to the independent variables in lines).

·         Perpendicular and parallel lines (study of slope properties).

·         Rational number (number that can be expressed as the ratio of two integers, e.g., 4 = 8/2 is a rational number).

·         Pythagorean Theorem (relationship between the legs and hypotenuse of a right triangle)

·         Square root (the length of the side of a square that has the root as its area).

·         Repeating decimal (a non-ending decimal number that repeats a set of numbers).

·         Terminating decimal (e.g., a decimal number that does not repeat and has a finite number of digits).

 

Students will be able to…

·         Locating points, giving directions, finding distances on the coordinate plane.

·         Identifying, interpreting, calculating change in “rise/run? In lines (i.e., slope).

·         Identifying irrational numbers with geometric representations (i.e., squares).

·         Using geometric representations to derive mathematical relationships (e.g., Pythagorean Theorem).

·         Applying the Pythagorean Theorem in multiple situations.

·         Finding fractional representations of repeating and terminating decimal numbers.

·         Applying algebraic rules to solve equations and explore mathematical relationships.

Assessments

·       Performance Task

·       Performance Task Rubric

·       Performance Task Notes

·       Teacher Ref. – Field Diagram

·       Pythagoras Project

·       Unit Review

·       Section 1-2 Test Form A

·       Section 1-2 Test Form B

·       Section 1-2 Test Form C

·       Section 1-3 Test

·       Section 1-3 Retest

·       Section 4-5 Test

·       Section 4-5 Retest

·       Unit Test Form A

·       Unit Test Form B

·       Unit Test Form C

 

 

 

·       Reflection 1

·       Section 1 Quiz

·       Reflection 2

·       Section 2 Quiz

·       Inv. 1-2 Review PPT

·       3.1 Quiz

·       Reflection 3

·       Section 3 Review

·       Section 3 Quiz

·       Section 1-3 Quiz

·       Section 4 Quiz

·       Section 3-4 Review

·       Section 3-4 Quiz

·       Reflection 5

·       Section 5 Quiz

·       Inv. 3-5 Review PPT

·       Section 4.2-6.2 Quiz Form A

·       Section 4.2-6.2 Quiz Form B