Download Number Systems

Table of Contents
Before You Begin
Why and how was this resource developed? .............................................................. i
How does this resource support different teaching styles?....................................... i
How is this resource organized? ................................................................................. i
Problem Solving ........................................................................................................ iv
Math Journals ........................................................................................................... vi
Assessment............................................................................................................... vii
Number Systems .............................................................................................................. 1
Square Roots .................................................................................................................. 28
The Product Law and the Quotient Law ...................................................................... 49
Zero and Negative Exponents ....................................................................................... 67
Powers of Products and Quotients ............................................................................. 83
Putting It All Together .................................................................................................. 107
Scientific Notation ....................................................................................................... 119
Strand Test
Test ......................................................................................................................... 143
Solutions ................................................................................................................ 149
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
G9 • Numbers
Before You Begin
Why and how was this resource developed?
Maximizing Grade 9 Math was developed in 2003–2005 by Alberta teachers to support math
teaching and learning related to the WNCP. A focus group of teachers and department heads
identified a need for a resource that had a 100% fit with the curriculum and that contained
materials to improve achievement of all students including students requiring either
modification or extension of the curriculum.
How does this resource support different teaching styles?
The teaching plans in Maximizing Grade 9 Math are in no way prescriptive – they serve as
models or possible methods by which to teach students. This resource allows for a range of
experience in the teachers who use the resource. Beginning teachers, or teachers new to a
grade level or new to teaching mathematics, will find the strategies helpful and may choose
to use all of the suggestions. Experienced mathematics teachers will adapt the lessons to
suit their individual teaching styles.
How is this resource organized?
The organization of Maximizing Grade 9 Math is based on the strands from the Math 9
curriculum: Number, Patterns and Relations, Shape and Space and Statistics and
Probability. Each strand is individually packaged.
Each lesson is organized in the following manner.
Title page
Sub-strand name
The sub-strand is identified in a box at the top of the page.
Lesson Title
The lesson title is identified next. On all subsequent pages, the lesson title is identified in
the box at the top of the page.
General Outcome
The general outcome, referred to as GO, is identified next. These are taken from the
Mathematics 9 curriculum document.
Specific Outcome
The specific outcome(s) for the teaching plan, referred to as SO, is identified next. Whenever
appropriate, specific outcomes have been grouped together for the teaching plan. These are
taken from the Mathematics 9 curriculum document. Any associated mathematical
processes for each lesson are indicated as follows:
C = Communication, CN = Connections, E = Estimation & Mental Mathematics,
PS = Problem Solving, R = Reasoning, T = Technology and V = Visualization.
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
i
G9 • Numbers
Number Concepts
Number Systems
GO:
Explain and illustrate the structure and the
interrelationship of the set of numbers within the rational
number system.
SO 1: Give examples of numbers that satisfy the conditions of
natural, whole, integral and rational numbers, and show
that these numbers comprise the rational number system.
[C, CN, PS, R]
SO 2: Describe, orally and in writing, whether or not a number is
rational. [C, R]
Essential Background Knowledge
Essential Learnings
Students should be able to:
• explain the difference between a
terminating and a non-terminating
decimal.
Students will be able to:
• classify numbers into their
appropriate number systems
• provide examples of numbers that
belong to more than one number
system
• show how the decimal numbers fit
into both the rational and
irrational number systems
• determine whether or not a
number is rational.
Essential Questions
1.
What is a natural number?
2.
What is a whole number?
3.
What is a rational number?
4.
What is an integer?
5.
What is an irrational number?
6.
What is a real number?
7.
What is the relationship between the number systems?
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
1
G9 • Number Concepts • SO 1-2
Number Systems
Journal Prompts
1.
Describe the difference between terminating and non-terminating decimals.
2.
Explain why a rational number could not be an irrational number.
3.
The natural set of numbers is the first set of numbers to be used in history. What are
some possible reasons for this?
Links to the Texts
• Mathpower
pp. 2–3
• Interactions
pp. 82–83
• Minds on Math
pp. 202–203
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
2
G9 • Number Concepts • SO 3
Number Systems
Warm-up
1.
Use your calculator to convert the following numbers to decimal form.
For example:
2
= 2 ÷ 5 = 0.4
5
a.
1
=
4
b.
3
=
5
c.
6
=
9
d.
2
=
9
e.
8
=
11
f.
4
=
10
g.
1
=
20
h.
4
=
9
i.
23
=
50
j.
2
=
11
k.
8
=
16
l.
5
=
9
m.
2
3
n.
3
8
o.
69
150
2.
Classify these numbers into two groups.
3.
Explain how you created the two groups in question 2.
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
3
G9 • Number Concepts • SO 3
Number Systems
Natural Numbers (N):
“Counting Numbers” N ={1, 2, 3 …}
–3
Whole Numbers (W):
0
1
2
3
–2
–1
0
1
2
3
Positive and negative natural numbers and zero
I = {… -3, -2, -1, 0, 1, 2, 3 …}
–3
Rational Numbers (Q):
–1
Natural Numbers including zero W = {0, 1, 2 …}
–3
Integers (I):
–2
–2
–1
0
1
2
3
Numbers that can be written in the form of a fraction.
a
, where a and b are integers and
b
b cannot be equal to 0. This includes the
following:
Natural Numbers: 6 can be written as 6
1
Whole Numbers: 0 can be written as 0
1
Integers: -8 can be written as –8
1
Terminating Decimals: 0.3 can be written as 3
10
Repeating Decimals: 0.777777…or 0.7 can be
written as 7
9
Decimal numbers that are non-terminating and nonrepeating. Numbers that cannot be written in the
form of a fraction.
For example,
Irrational Numbers (Q):
E.g.,
Real Numbers (R):
3, π,
5 , 67.3591065…
The combination of the rational numbers and the
irrational numbers, which includes all of the above
sets.
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
10
G9 • Number Concepts • SO 3
Number Systems
Guided Practice #2
Give an example of each of the following:
• an integer
• a whole number
• a rational number but not a whole number
• an integer but not a whole number
• a whole number but not a natural number
• a rational number but not an integer
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
11
G9 • Number Concepts • SO 3
Number Systems
Guided Practice #2 and Answers
Give an example of each of the following:
Answers may vary, but some possible answers are:
• an integer
-3, 0, +10
• a whole number
0, 7, 100
• a rational number but not a whole number
5 , 0.83, -16
2
4
• an integer but not a whole number
-10, -7, -1
• a whole number but not a natural number
0 (only one answer)
• a rational number but not an integer
-7 , 5.65, 12
3
5
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
12
G9 • Number Concepts • SO 3
Number Systems
Worksheet 1
1.
2.
3.
4.
Remember,
whole numbers
are 0, 1, 2…
Circle the numbers that are whole numbers.
π
-3.6
3.4444…
11
101
1
3
70
–8
5
-8
0
2000
6.72231879…
Remember, natural
numbers are 1, 2, 3…
Circle the numbers that are natural numbers.
π
-3.6
3.4444…
70
-8
0
11
101
1
3
–8
5
2000
6.72231879…
Remember, rational
numbers can be in a
form of a fraction.
Circle the numbers that are rational numbers.
π
-3.6
11
101
3.4444…
1
3
70
-8
0
–8
5
2000
6.72231879…
Remember,
integers are -3,
-2, -1, 0, 1, 2…
Circle the numbers that are integers.
π
-3.6
3.4444…
11
101
1
3
70
–8
5
-8
0
2000
6.72231879…
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
18
G9 • Number Concepts • SO 1-2
M1
Number Concepts
Number Operations
The Product Law and the Quotient Law
GO:
Develop a number sense of powers with integral exponents
and rational bases.
GO:
Explain how exponents can be used to bring meaning to
large and small numbers, and use calculators or computers
to perform calculations involving these numbers.
SO 4: Illustrate power, bases, coefficient and exponent, using
rational numbers or variables as bases or coefficients. [R, V]
SO 5: Explain and apply the exponent laws for powers with
integral exponents. [PS, R]
SO 7: Document and explain the calculator keying sequences used
to perform calculations involving rational numbers.
[C, PS, T]
Essential Background Knowledge
Essential Learnings
Students should be able to:
• recognize the parts of a power
• represent a power as repeated
multiplication.
Students will be able to:
• use technology to calculate powers
• evaluate expressions with powers
• explain and apply the product law
• explain and apply the quotient
law.
Essential Questions
1.
Draw diagrams to represent and explain the difference between a number
squared and a number cubed.
2.
Explain the product law using both words and symbols.
3.
Explain the quotient law using both words and symbols.
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
49
G9 • Number Concepts • SO 4-5-7
The Product Law and
the Quotient Law
Journal Prompts
1.
Explain why exponents are often used instead of repeated multiplication.
2.
From your previous knowledge of scientific notation, how does scientific notation use
exponential form?
Links to the Texts
• Mathpower
pp. 17–18
p. 21
• Interactions
p. 32
• Minds on Math
pp. 180–181
Copyright © Resource Development Services, Edmonton Public Schools, 2005.
Permission to copy STUDENT MASTERS granted to individual classroom teachers only.
50
G9 • Number Concepts • SO 4-5-7