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Date: Tuesday, September 24, 2012
AIM: How do we describe sets of real numbers using interval and/or set notation?
Objectives: SWBAT
- Graph inequalities and compound inequalities
- Describe intersections and unions and complement of multiple sets
- Use set notation and interval notation to describe numbers in a set
Standards:
A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form
A.A.30 Find the complement of a subset of a given set, within a given universe
A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)
Quiz #5: 1. Graph the inequality:  4  x  1 Describe this inequality using interval notation.
2. Given that set A = {-2, 0, 5, 6, 7} and set B = {2, 3, 4, 5, 6}, state the intersection and union of sets A and B.
3. Given the universe is the odd numbers between 0 and 20, set A = {3, 7, 9, 11, 13, 17}. What is the
complement of A in this universe?
Quiz #5R
1. Simplify: 5 ( 8  2) (5)
2. Simplify: 2 27  75 (4)
3. Simplify: 3 90 (3 or less)
An inequality…
Minilesson:
Compares the value of two expressions
Another way to denote these types of number comparisons is to use interval notation.
There are two types of interval notations
( ) – open parenthesis – indicate that the number is not included in the set – an open circle
[ ] – closed brackets – indicate that the number IS included in the set – closed circle
These can be used together to indicate, for example, that the beginning number is included and
the end number is not included in the set.
A set is a group of numbers. We denote a set using { }. Numbers within a set are called
elements.Example: {1, 2, 3}
We can also perform operations with sets:
The union of two sets means that we are combining both sets. Every member of each separate
set is a member of the union.
The intersection of two sets means we are looking for common elements. Only those elements
that are in both sets are in the intersection.
A complement of a set is all the numbers included in one set, but not in another.
Example: The Prospect Heights basketball team uses the following numbers on their jerseys:
{1, 3, 4, 7, 18, 23, 32, 35, 53, 66}. The starters at the opening game are {4, 18, 23, 53, 66}.
Find the complement of this set (i.e. who is on the bench at the beginning of the game). List
this set using set notation.
Example 1: Use interval notation to describe the following inequalities.
Guided
a. x > 9
b. x ≤ -1
c. 3 < x < 5
d. 1 ≤ x ≤ 4
e. -2 < x ≤ 0
Practice
Example 2: What numbers are in each of the following sets?
a. (7, 9)
b. [2, 4]
c. [-1, 0)
Examples:
Given Set A = {1, 2, 3} Find the union and intersection.
Set B = {-1, 0, 1}
Given Set A = {2, 3, 4, 5} Find the union and intersection.
Set B = {1, 2, 3, 4, 5}
Independent Use interval notation to describe the following inequalities and list what numbers are in each
set.
Practice
1) x < 4
2) x ≥ -1
3) 2 < x ≤ 5
4) -2 ≤ x ≤ 1
Summary
What is meant by the terms “union,” “intersection” and “complement?”
MATH MASTER: ____________________________________________________
ALGEBRA
DATE:_____________________________________________________________
PAGE: _______
AIM:_____________________________________________________________________________________
_________________________________________________________________________________________
DO NOW
1. Describe the following symbols:
a. <
b. ≥
c. =
d. >
2. Graph each inequality. Name an example of a solution to each inequality. (For an added challenge, see if you
can name a rational number that is not an integer and an irrational number).
a) x  4
Solutions: _______
b) x  2
c) 5  x
Solutions: _______
d) x  2 or x  1
Solutions: _______
Solutions: _______
e) 0  x  6.5
Solutions: _______
MINI LESSON
An inequality _______________ the value of two expressions.
Interval Notation: Frayer Model
Union, Intersection , Complement: Chart
GUIDED PRACTICE
1. Use interval notation to describe the following inequalities.
a. x > 9
b. x ≤ -1
c. 3 < x < 5
d. 1 ≤ x ≤ 4
e. -2 < x ≤ 0
2. a. List the set of even counting numbers less than 20. Call this set A: ____________________________
b. List the set of multiples of 4, greater than 0 but less than or equal to 28. Call this set B:
___________________________________________________________________________________
c. Find the union of sets A and B: __________________________________
d. Find the intersection of sets A and B: __________________________________
3. The Prospect Heights basketball team uses the following numbers on their jerseys: {1, 3, 4, 7, 18, 23,
32, 35, 53, 66}. The starters at the opening game are {4, 18, 23, 53, 66}. Find the complement of this
set (i.e. who is on the bench at the beginning of the game). List this set using set notation.
THINK, PAIR, SHARE
1. What numbers are in each of the following sets?
a. (7, 9)
b. [2, 4]
c. [-1, 0)
2. Use interval notation to describe the following inequalities and list what numbers are in each set.
a) x < 4
b) x ≥ -1
c) 2 < x ≤ 5
d) -2 ≤ x ≤ 1
_____________
3. Given
_____________
Set A = {2, 3, 4, 5}
Set B = {1, 2, 3, 4, 5}
_____________
_____________
Find the union and intersection.
Union: ___________________
4. Given
Set A = {1, 2, 3}
Set B = {-1, 0, 1}
Intersection: __________________
Find the union and intersection.
Union: ___________________
Intersection: __________________
5. Find the complement of each set if the “universe” is all of the positive integers, less than 24.
a. List the “universe:” ____________________________________________
b. List the even numbers in the universe: __________________________
c. List the complement of the even numbers: __________________________
d. List the prime numbers in the universe: __________________________
e. List the complement of the prime numbers: __________________________
REVIEW OF EVALUATING EXPRESSIONS
Evaluate each expression for the values a = -2, b = 3 and c=4.
bc
1.
2. b a  c
3. c ( a  b)
a
4. a 2  bc
5.
b2  c2
REVIEW OF SIMPLIFYING RADICALS
Simplify.
1. 32
2. 3 8
3. 5 3  3
4.
SUMMARY: What is meant by the terms “union,”
“intersection” and “complement?”
___________________________________________
___________________________________________
___________________________________________
___________________________________________
6 8
5.
8  3 50
6. 4 75  6 27
REFLECTION: WHAT DID YOU LEARN TODAY? On a
scale of 1 to 10, how well do you think you met
today’s objective? What questions do you still have?
___________________________________________
___________________________________________
___________________________________________
TOTAL
POINTS