MATHEMATICS-13
ESSENTIAL UNIT 3 (E03)
(Exponents and Roots)
(July 2013)
Unit Statement: In Unit Three, the student will learn to operate with numbers in
scientific notation, approximate the values of irrational numbers, model the Pythagorean
Theorem, and use the Pythagorean Theorem to solve real life problems. Unit three will
prepare students to evaluate expressions containing exponents in future math courses,
express the magnitude of interstellar distances, and to use right triangle geometry in future
math courses. The student is expected to be familiar with the Key Terms and Concepts
listed below.
Essential Outcomes: (must be assessed for mastery)
Problem solving and higher order thinking components are essential for A level mastery.
Each outcome can contain problem solving and higher order thinking components (as
found in suggested text).
1. The Student Will evaluate expressions with negative exponents and evaluate the zero
exponent. (3-1, p. 92-95)
2. TSW apply the properties of exponents. (3-2, p. 96-99)
3. TSW express large and small numbers in scientific notation and compare two
number written in scientific notation. (3-3, p. 100-104)
4. TSW operate with scientific notation in real-world situations. (3-4, p. 105-108)
5. TSW identify the action taking place in a problem, and decide whether to add, subtract,
multiply, or divide throughout the unit. ( p. 111)
6. TSW find square roots. (3-5, p. 112-115)
7. TSW estimate square roots to a given number of decimal places and solve problems
using square roots. (3-6, p. 116-119)
8. TSW determine if a number is rational or irrational. (3-7, p. 123-126)
9. TSW use the Pythagorean Theorem to solve problems. (3-8, p. 132-135)
10. TSW use the Distance Formula and the Pythagorean Theorem and its converse to solve
problems. (3-9, p. 138-141)
11. TSW use exponents to apply concepts and skills from the unit in a real-world concept.
(p. 143)
Introduced and Practiced Outcomes: (taught not assessed)
1. The Student Will use a graphing calculator to multiply and divide numbers written in
scientific notation. (Technology Lab, p. 109)
2. TSW use a graphing calculator to evaluate expressions that have negative exponents.
(Technology Lab, p. 122)
10
QSI MATHEMATICS-13 E03
Copyright © 1988-2013
3.
TSW classify numbers as rational or irrational and graph them on a number line.
(p. 128-129)
4. TSW use geometry software to explore the converse of the Pythagorean Theorem.
(Technology Lab, p. 136-137)
Key Terms and Concepts:
Hypotenuse
Perfect square
Irrational number
Pythagorean
Theorem
Real number
Scientific notation
Suggested Resources:
Lesson Quiz (HMM TE) after each lesson
Ready To Go On? After lesson 3.4, and 3.9 -assign Ready to Go On? Intervention and
Enrichment worksheets after completion. (HMM “Are you Ready? Intervention and
Enrichment”)
Teacher created assessment (ExamView)
Chapter 3 test (HMM Assessment Resources)
Journal entries (HMM TE)
Suggested Assessment Tools and Strategies:
Attached rubric or teacher generated rubric that assesses ALL essential outcomes (TSWs)
Use base 10 blocks to explore cube roots. (Hands-On Lab, p. 120-121)
Use scissors and paper to explore right triangles. (Hands-On Lab, p. 131)
Additional Resources:
Something Out of Nothing: Marie Curie and the Discovery of Radium
by Carla Killough McClafferty
TE p. 91
Technology Links:
Destiny WebPath Express (located on school’s automated library system)
www.tenmarks.com
This site is free, but requires users to sign up. After opening an account, teachers are able
to generate and track assignments for individual students. This site is a great way to
differentiate instruction in the math classroom.
https://www.khanacademy.org/
Khan Academy provides students with videos of lessons and interactive manipulatives to
enhance student learning. There are also sample problems for a wide variety of topics.
http://phet.colorado.edu/en/simulations/category/math
This website maintained by the University of Colorado offers many simulations, games,
and activities. Many subject areas and topics are covered. This website offers a great
opportunity to develop cross curricular projects.
Suggested rubric on the following page……………………….
11
QSI MATHEMATICS-13 E03
Copyright © 1988-2013
MATHEMATICS-13 SUGGESTED UNIT EVALUATION RUBRIC E03:
Student Name: __________________________
Date: _______________________
 To receive a ‘B’, the student must show ‘B’ level mastery on ALL Essential Outcomes (TSWs).
 To receive an ‘A’, the student must show ‘A’ level mastery in all available ‘A’ level TSW’s and ‘B’ level
mastery on all of the remaining TSW’s.
TSW
1- evaluate expressions
with negative exponents
and evaluate the zero
exponent
2- apply the properties of
exponents
3- express large and small
numbers in scientific
notation and compare two
number written in
scientific notation
4- operate with scientific
notation in real-world
situations
‘A’ LEVEL
‘B’ LEVEL
Example of A level mastery:
The student can give a nonexample (i.e., 53 + 2 3) and
justify why the properties of
exponents would not work.
Example of A level mastery:
The student can create and
solve word problems that
provide real-world
examples of scientific
notation
5- find square roots
The student consistently
demonstrates the ability evaluate
expressions with negative exponents
and evaluate the zero exponent
The student consistently
demonstrates the ability to apply the
properties of exponents.
The student consistently
demonstrates the ability to express
large and small numbers in scientific
notation and compare two numbers
written in scientific notation
The student consistently
demonstrates the ability to operate
with scientific notation in real-world
situations
The student consistently
demonstrates the ability to find
square roots
The student consistently
demonstrates the ability to estimate
square roots to a given number of
decimal places and solve problems
using square roots
6- estimate square roots to
a given number of decimal
places and solve problems
using square roots
7- determine if a number
is rational or irrational
The student consistently
demonstrates the ability to determine
if a number is rational or irrational
8- classify numbers as
rational or irrational and
graph them on a number
line
9- use the Pythagorean
Theorem to solve
problems
The student consistently
demonstrates the ability to classify
numbers as rational or irrational and
graph them on a number line
The student consistently
demonstrates the ability to use the
Pythagorean Theorem to solve
problems
The student consistently
demonstrates the ability to use the
Distance Formula and the
Pythagorean Theorem and its
converse to solve problems
10- use the Distance
Formula and the
Pythagorean Theorem and
its converse to solve
problems
The student is able to
reflect on the problem,
consistently justify the
mathematical concepts used
and explain how the
concepts apply to the
problem
12
QSI MATHEMATICS-13 E03
Copyright © 1988-2013
Notes