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Therefore I tell you, do not worry about your life, what you will eat or drink; or about your body, what you will wear. Is not life more than food, and the body more than clothes? 26 Look at the birds of the air; they do not sow or reap or store away in barns, and yet your heavenly Father feeds them. Are you not much more valuable than they?
Matthew 6:25-26
Warm up
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85
24
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w
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Today
Warm up
Geometric Series
Finite Differences
Using a formula
Sets
Don’t Forget
Turn in
»
Pick up
» Quiz 2
How many?
1, 10, 102, 103, 104, 105
7
Practice Exercise #6
8
Puzzles
What’s the pattern?
2,5,8,11,...
12, 17, 22, 27, 32, …
94, 91, 88, 85, 82, …
Puzzles
What’s the pattern?
5, 15, 45, 135,...
3, 6, 12, 24, …
40, 20, 10, …
Sequence practice
Arithmetic or geometric? Give the next two
terms in the sequence.
1. 2, 10, 50, 250, …
2. 39, 36, 33, 30, …
3. 1, 3, 32, 33, 34, …
Practice Exercises 2-3
2. Classify each sequence as arithmetic (A), geometric (G), or neither (N): a. 21, 26, 31, 36, … b. 2, 0, -2, 0, 2, … c. 2, 8, 32, 128, … d. 1, 5, 52, 53, … 3. Find the next two terms in each sequence of question 2.
12
What was the purpose of this slide?
37
37
37
a
aa
aa
Remember the Dot Puzzle?
Finite Differences
5,10,15,20,...
20,15,10,5, …
0,1,4,9,16,25, …
0, 3, 24, 81, 192, 375, 648, …
Practice Exercise 4
4. This sequence can be evaluated using the
method of finite differences. Find the next two
terms in the sequence, showing all work in the
space below:
2, 7, 14, 23, 34, 47, …
16
Find the first five terms:
17
64 n
110 1 n
Practice Exercise #7
18
Practice
What comes next?
,,,...
End of section 1-2
20
Do homework §1-2
for next time.
True or False?
All professional football players weigh
more than 300 pounds.
Chapter 2
Not all content included in teacher
competencies (= important knowledge
for teacher)
Content of chapter 2 is important for
» Probability & Statistics
» Teaching all subjects
» Teaching Early childhood counting
» Life
Chapter 2 (continued)
Topics in the book are covered very
briefly;
» Not enough explanation
» Not enough practice problems
Chapter 2 will be split into 9 lessons
Worksheets assigned for each
Book is still a useful reference
Who Cares About Sets?
Sets
You use sets any
time you sort or
organize.
Practical Examples of Sets
Kitchen
Music on iTunes
Videos on Netflix
Dmitri Mendeleev KPCOFGS
Phylogenetic Heirarchy Reflection
Do not be anxious about anything, but in every situation, by prayer and petition, with thanksgiving, present your requests to God.
Philippians 4:6
Warm up
Last time, we described how you use sets
in your kitchen. Describe another
example from real life where you use sets
(probably without thinking about sets).
Write a complete sentence or two.
Today
Warm up
Stumpers
Sets in TEKS
Ways to define a set
Well defined sets
Elements of a set
Cardinality of a set
Subsets
Don’t Forget
Turn in
» HW 1-2
Pick up
» HW 1-1
Homework Stumpers
Darn Kids Practice
21
21
5.21
035.21
0
3
4
53
Are Sets in TEKS?
TEKS 110.16 (Grade 5 ELAR)
(26) Research/Organizing and
Presenting Ideas. Students organize and
present their ideas and information
according to the purpose of the research
and their audience. Students are
expected to synthesize the research into
a written or an oral presentation that:
Examples
Well defined
roster
set builder
cardinality
equality
equivalence
•A is the set of students in
this class who drove a Ford
today.
•B is the set of students in
this class who are smart.
•C is the set of students in
this class who own a pet.
How many ways can you define a set?
Description
Set builder
Roster
Reflection
Who is wise and understanding among you? Let them show it by their good life, by deeds done in the humility that comes from wisdom.
James 3:13
Find the next term
Using the method of finite differences
4, 6, 12, 22, 36, 54
Today
Warm up
Elements of a set
Subsets
Operations on sets
Don’t Forget
Turn in
»
Pick up
» HW 1-2
» Quiz 3
2 factual errors
Essay
If you did not find any “take aways” in the
movie “Gifted Hands”, you may use a
book you have read instead for the essay
assignment. State the book and chapter
you are referring to. (Probably best to get
the book approved ahead of time.)
Gifted Hands Essay
1st Draft (5 points) due 10/1
Final Draft (20 points) due 10/20
300-500 words, double-spaced
Describe the scene or thread you are
referring to
Explain how it will influence you as a
teacher
My example Notation & Terminology
An
Well defined set?
The set of Texas residents who turn 21
on 9/2/2015
The set of UIW students who are tall
The set of UIW students whose height
is greater than 6 feet
The set of horses that have won the
Kentucky Derby
The set of fast horses
Examples
Express in roster form:
The set of odd natural numbers less than 11
The set of high schools in Judson ISD
The set of actors who have played Batman
in a movie
The set of people in this class who have a
pet cat
Find the set’s Cardinal # (cardinality)
A = {1,2,3,…45}
B = {3,6,9,…81}
S is the set of states in the United
States
P is the set of United States Senators
J is the set of United States Supreme
Court Justices
Cardinal or Ordinal?
He is the third idiot who has tried that
line on me tonight.
Annalisa bought drinks for three
different guys tonight.
The Senator has been caught alone
with an intern twenty times.
This is the eleventh time the
Congressman has been indicted on
bribery charges.
Equal, equivalent, both, neither?
A is the set of state governors.
B is the set of states.
A is the set of odd numbers less than 15.
B = {1,3,5,…,13}
A is the set of United States Senators.
B is the set of States in the United States.
Vote with your thumbs:
True
False
True False
5.2 N
6 N
140 N
5 {x|x N and x is between 5 and 11}
5 {x|x N and x is between 5 and 11,
inclusive}
13 {1,2,3,…,16}
Examples of Subsets
Let S be the set of table
spoons in your kitchen.
Let K be the set of butter
knives in your kitchen.
Let R be the set of forks in
your kitchen.
Let V be the set of
silverware in your kitchen.
VS
Which are true?
VS
KR
Examples of Subsets
Let S be the set of table
spoons in your kitchen.
Let K be the set of butter
knives in your kitchen.
Let R be the set of forks in
your kitchen.
Let V be the set of
silverware in your kitchen.
VV
Which are true?
VV
VR
True/False Practice
CD
Tuesday D
C=D
DC
Tuesday C
C={x|x is a day of the week}, D={Monday,Friday}
Practice
AB
p B
A=B
BA
r A
A={p,q,r}, B={q,r,p}
Practice
WB
n G
B and G are equivalent
t W
W
W
G={p,i,n,k}, B={s,t,i,n,k}, W={i,n,k}
The End of Section 2.1A
Finish Worksheet 2.1A
for next time.
How to look enlightened (not ignorant)
cbaa
cbaa
,,
,,
Enlightened
cbaa
cbaa
,,
,,
Ignorant
Reflection
Do not be misled: “Bad company corrupts good character.”
1 Corinthians 15:33
Warm up
A J
A J
J S
A={m,u,l,e}, J={m,u,s,t,a,n,g}, S={k,n,i,g,h,t}
Today
Warm up
Homework Stumpers
Operations on Sets
» Intersection
» Union
» Complement
Venn Diagrams
Don’t Forget
Pick up today
» Blank Venns (2/student)
Turn in today » Wksht 2.1A
Exam 1 on 10/1
Ben and Owen
Use abbreviations, e.g.
Along Came Polly = ap
Quiz 4
Important sets
Nothing
Everything
What is the most important mathematics
topic in Kindergarten?
TEKS 111.2 (b) (K Math)
(2) Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system. The student is expected to:
(A) count forward and backward to at least 20 with and without objects;
Algebras
A Philosophical Question
What is Abstract? Why look at the
world abstractly?
Suppose
2 + 3 =
Warm up
A J
A J
J S
A={m,u,l,e}, J={m,u,s,t,a,n,g}, S={k,n,i,g,h,t}
Reflection
Apply your heart to instruction
and your ears to words of knowledge.
Proverbs 23:12
Warm Up
AB
p B
A=B
BA
r A
A and B are equivalent
A={k,m,n}, B={n,m,k}
Today
Warm up
Shading Venn Diagrams
Power Set
Sets and Addition
Don’t Forget
Pick up today
» Blank Venns (2/student)
Turn in today
»
Exam 1 on 10/1
Gifted Hands Essay
1st Draft (5 points) due 10/8
Final Draft (20 points) due 10/29
300-500 words, double-spaced
Describe the scene or thread you are
referring to
Explain how it will influence you as a
teacher
Rules for Shading Venn Diagrams
One diagram of work for each operation
Order of operations:
» ( )
» ‘ (complement)
» &
Shade each set with contrasting patterns
Perform operation
» overlap
» any shade is good shade
» ‘ photo negative; no shade is good
How much you are able to do in your
head is up to you.
I will teach step-by-step.
Don’t fool yourself! It can get
complicated fast, so go step-by-step at
first.
Venn Diagrams with 2 sets are easier
than Venn Diagrams with 3 sets
Venn Diagrams
BA .4
BA .5
BA .6
A.1
BA.2
BA.3
TEKS 111.2 (Kinder Math)
(3) Number and operations. The student
applies mathematical process standards to
develop an understanding of addition and
subtraction situations in order to solve
problems. The student is expected to:
(A) model the action of joining to represent
addition and the action of separating to
represent subtraction;
5 minute assignment
Write a brief bear story to model an addition problem with sum less than 10. Your story should involve joining (set union) two groups of bears.
Pair up playing teacher/student roles: » “Teacher” directs the “student” to act out your story
using the counting bears
» Make sure “student” counts out each set and final (joined) set
» Write the addition problem just modeled using + sign
» Trade teacher/student roles
Meanings
U is the set of members of the Screen Actors
Guild. (Hollywood actors)
R is the set of actors who have been to rehab.
C is the set of actors who have had cosmetic
surgery.
R.1
CR.2
CR .3
CR .4
Draw a Venn Diagram that satisfies the conditions:
A B =
A B’ =
(C B) A
All my exes live in Texas.
Blessed are they who keep his statutes
and seek him with all their heart.
Psalm 119:2
Warm Up
??? BAn
B A
Today
Warm up
Power set
Surveys
Don’t Forget
Turn in
» ?
Pick up
» Worksheet 2.1C
A Philosophical Question
What can a
set contain?
The Power Set
Let A = {p}
Let B = {p,q}
Let C = {p,q,r}
Let D = {p,q,r,s}
A Puzzle
Redneck Used Autos sells pickups (only
pickups) with the following options: gun
rack, monster tires, spittoon holder,
confederate flag, broken taillights, and
8-track tape player. How many different
ways can you get your pickup at
Redneck Used Autos?
Coffee Shop
At Tarbucks, you can get your coffee with
all, some, or none of the following
ingredients: whipped cream, sugar,
chocolate syrup, mint syrup, blueberry
syrup, hazelnut syrup. How many
different ways can you get your coffee
at Tarbucks?
The End of Section 2.1B
Finish Worksheet 2.1B .
Homework Stumpers Words and Sets
“and”, “but”
“or”
“not” complement
“,” parenthesis use context to figure out where partner parenthesis goes
Meanings
U is the set of UIW students.
D is the set of students who have a dog.
C is the set of students who have a cat.
C D
x y z
w
How many have a cat?
How many have a dog?
How many have neither?
How many have a dog but no
cat?
Meanings
U is the set of UIW students.
D is the set of students who have a dog.
C is the set of students who have a cat.
C D
x y z
w
How many have a dog or a
cat?
How many do not have a
cat?
Do Worksheet Exercise 1 Meanings
U is the set of UIW students.
S is the set of students in a sorority.
T is the set of students who are on a team.
D is the set of students living in a dorm.
T S
g
How many are in a sorority,
on a team, and live in a
dorm?
How many are only on a
team? D
h i
j k m
n p
Meanings
U is the set of UIW students.
S is the set of students in a sorority.
T is the set of students who are on a team.
D is the set of students living in a dorm.
T S
g
How many are in a sorority
and on a team, but don’t live
in a dorm?
D
h i
j k m
n p
Meanings
U is the set of UIW students.
S is the set of students in a sorority.
T is the set of students who on a team.
D is the set of students living in a dorm.
T S
g
How many are in a sorority
OR on a team, but don’t live
in a dorm?
D
h i
j k m
n p
Meanings
U is the set of UIW students.
B is the set of students in the Biology Club.
P is the set of students in the Philosophy Club.
M is the set of students in the Math Club.
P B
g
How many are in exactly one
club?
How many are in exactly two
clubs? M
h i
j k m
n p
Do Worksheet Exercise 2
Surveys
Follow the series of clues to unlock the puzzle
Use a Venn diagram to record the number of elements in each region
Look for a piece of data that can go immediately into a region (Hint: usually work from the bottom up.)
Use known regions and clues to fill in unknown regions
Surveys
Fill in the Venn diagram first.
Then answer the questions.
Surveys
A survey of 50 people found that 20 ate
McDonald’s in the last week, 15 ate
Burger King in the last week, and 10 ate
both.
a. How many ate neither?
b. How many ate only McD?
c. How many ate only BK?
Surveys
A survey of 100 people found that 40
watched Seinfeld, 25 watched General
Hospital, and 50 watched neither.
a. How many watched both?
b. How many watched only Seinfeld?
c. How many watched only GH?
Do Worksheet Exercises 3 & 4 Surveys
100 people had blood tests run, here are the
results:
34 had the A factor (antigen)
35 had the B factor (antigen)
44 had the Rh(+) factor
10 had both the A and B factors (antigens)
17 had the B factor and Rh(+) factor
21 had the A factor and Rh(+) factor
6 had the A and B factors and the Rh(+)
Surveys
100 people were surveyed regarding how
they get their news:
36 watch TV
32 listen to the radio
30 read the newspaper
14 watch TV & listen to radio
12 listen to radio & read the paper
16 watch TV & read the paper
6 use all three sources
Do Worksheet Exercises 5
The End of Section 2.1C
You are finished with 2.1C.
Study Question Stumpers
