Download Algebra 2 - Miss Stanley`s Algebra Wiki

Algebra 2
Unit 1, Lesson 2: The Real Number System
Objectives
-
Unit
Skills
Students are able to place any real number in its correct
location on a Venn Diagram of the real number system.
Students can determine if logical statements about real
numbers are true or false, and explain why with reference to
the Venn Diagram.
1-1
Materials and Handouts
Homework
- Answer transparency for hw #1-1
#1-2
- Classification warm-up
Mastering the real
- Sets of cards with numbers
number system
- Transparencies for number system activity
(worksheet)
- Classifying real numbers / understanding real
numbers & answer transparencies
- Homework: Mastering the real number system
Time
Activity
Homework
Check
/
Warm-up
Activity
15 min
- Put the answers to hw #1-1 on the overhead, with 10 questions
circled to grade. Students get one point for each correct,
and write their total at the top of the page.
- When finished checking, they should begin the warm-up:
Classification Warm-Up
- As they are working, circulate to record grades and stamp
homework checkers.
Developing understanding of the number system
40 min
- Give each group a set of cards that each have a single number
on them.
- On the overhead, show the text: “Whole Numbers”. Ask
students to find all their cards that have this kind of
number, and to put them in the middle.
- On the overhead, show the text: “Integers: positive and
negative whole numbers”. Students should identify the cards
that are integers, and put them in the center.
- Now we will begin to develop the number system diagram on the
board. Tell students that we want to organize whole numbers
and integers with a Venn Diagram. As a reminder, show an
overlapping and a subset style Venn Diagram on the overhead.
Ask groups to talk for a minute and decide which one makes
more sense to use in this situation. Clarify why the subset
option is preferable, and draw the first two circles of the
number system on the whiteboard.
- On the overhead, show the text: “Rational Numbers: numbers
that can be expressed as a fraction in the form
-
p
where p and
q
q are both integers, and q ≠ 0.” Clarify what this means.
Ask students to identify their rational number cards and
place them in the middle. Refer back to the numeracy skill
builder if students forget to include whole numbers and
decimals.
Based on this, call on a student to add the rational numbers
circle to the diagram on the board.
-
On the overhead, show the words “Irrational Numbers: numbers
that cannot be expressed as a fraction in the form
20 min
5 min
p
where p
q
and q are both integers, and q ≠ 0.” Ask students to identify
these numbers on their cards. They should realize that it is
all the numbers that they have not already put in the center.
- Based on this, call on a student to put the irrational number
circle on the board. With discussion, the class should
understand that this circle must be mutually exclusive.
- Explain that these numbers together are considered real
numbers; draw in a final circle to complete the diagram.
- Write all the numbers from the cards in the correct location
on the completed Venn Diagram.
- Hand out the Classifying Real Numbers practice sheet. Give
students a few minutes to complete it and then review answers
on the overhead.
Individual Practice
- Students should complete the Understanding Real Numbers
worksheet. Review on the overhead if time permits.
Closure
- Students:
o Write down homework in their logs/planners
o Self-assess on College Habits, filling in their logs
o Report their grades out loud, one by one.
Algebra 2
Unit 1, Lesson 2: Warm-up
Period:
Name:
Classification Warm-Up
Directions:
Use the Venn Diagram to determine if each statement is true or false.
If it
is false, explain why.
Venn Diagram #1:
Overlapping Circles
1) It is possible to be both
Alpha and Omega at the same
time.
Omegas
2) All Omegas are Alphas.
B
Alphas
C
3) If you’re not an Alpha, you
must be an Omega.
A
D
Venn Diagram #2:
4) Some Alphas are not Omegas.
Subsets
Clydes
1) All Clydes are Inkies.
Blinkies
2) All Inkies are Clydes.
Inkies
3) No Blinkies are Inkies.
A
D
B
C
4) If you’re not a Blinky, you’re
a Clyde.
Numeracy Skill Builder:
Write each number as a
fraction.
1) 0.5
2) 3.871
3) 6
4) -2
5) 0.333333...
6) 5¾
Bonus neat-o numeracy trick!
You can write any repeating decimal as a fraction by putting 9’s in
the denominator. Count the number of digits that repeat, and use
that many 9’s in the denominator.
For example:
0.323232...
0.530530...
32
.
99
530
Three digits repeat, so this decimal equals
.
999
Two digits repeat, so this decimal equals
Don’t believe me?
Grab a calculator and try it!
If you want to know why it works, come during lunch and ask!
Algebra 2
Unit 1, Lesson 2: Classwork
Period:
Name:
Classifying Real Numbers
Directions:
Write each number in the correct location on the Venn Diagram of the real
number system.
Each number should be written only once.

3
6,
2.73,
,

7
2,

1
9, 100, 0,  , 1,  ,  3.8, 5.42, 8.293017...
2

Real Numbers
Rational Numbers
Irrational
Numbers
Integers
Whole Numbers
True or false?
If false, explain why.
1) All whole numbers are integers.
are integers.
3) Some rational numbers
2) All integers are whole numbers.
irrational numbers.
4) Some whole numbers are
Understanding Real Numbers
1) List the numbers in the set
 4
 5 , 18, 0,
5,
1
 ,  2.01, 5,
2

 , 2.513, 5.1823159... that are:

Whole numbers
Integers
Rational numbers
Irrational numbers
Real numbers
2) Put a check mark for each set that the number is a part of:
Whole
Number
s
Intege
rs
Ration
al
Number
s
Irrati
onal
Number
s
Real
Number
s
-7
¾
2
5
0.398
3) True or false?
If false, explain why.
a. All integers are rational.
b. If a number is rational, then it must be a whole number.
c. Some irrational numbers are integers.
d. All irrational numbers are real numbers.
e. No whole numbers are integers.
Algebra 2
Homework #1-2
Period:
Name:
Mastering the Real Number
System
1) Write each number in the correct location on the Venn Diagram of the real
number system.
Each number should be written only once.

 3, 2.09824...,
24,
25,
2
,
5
2
2
100,  7,  ,  , 6.5,  3.01, 3 
5
7
Real Numbers
Rational Numbers
Irrational
Numbers
Integers
Whole Numbers
2) List the numbers in the set
are:
Whole numbers
Integers
Rational numbers

 17, 0,
1 5
3,  , , 7.99, 8,
6 7

 , 0.03986..., 0.53 that

Irrational numbers
Real numbers
3) True or false?
If false, explain why.
a. Some irrational numbers are integers.
b. All rational numbers are whole numbers.
c. If a number is not an integer, then it is not a whole number.
d. If a number is not an integer, then it is not a rational number.
e. Some irrational numbers are not real numbers.
f. No rational numbers are integers.
4) Put a check mark for each set that the number is a part of:
Whole
Number
s
Intege
rs
Ration
al
Number
s
0
2.07
-35
7
7
3
5) Write each number in fraction form.
Irrati
onal
Number
s
Real
Number
s
-25
3
5
7
7
0.25
0.002
8
1
9
2.913
0.5555...
0, 1, 2, 3...
Whole
Numbers
Positive and
negative
whole numbers
Integers
Numbers that can be
p
written
in
the
form
q
where p and q are
integers and q ≠ 0
Rationals
Numbers that cannot be
written in the form
where p and q are
integers and q ≠ 0
p
q
Irrationa
ls
7
-5
0.222...
0
-1
0.45
3
4
7.02189...
199 0.5
2
5
9

-32 3.21
11
5
12