Mathematical Literacy in a Numerate Society
Introduction to the workbook:
Please read first to be successful in this course. To be successful in this course you
must have buy-in from both teacher and student. The goal of the lesson plans is to make
the transition from a traditional style to make the student quantitatively literate. This will
take a different approach. Think of it as going from chalk and talk to transitioning to
teaching through conversation. You’ll still use the chalk, just not so much as with the old
form of the traditional style of lecture.
Constructionist learning style. Have what the student’s knowledge to base future lesson
plans.
One: Number Sense
Lesson One: Numeracy – Enormity of the Geologic Time Scale
Earth’s age of 5 billion years, the formation of life 700 million years ago, the first
appearance of dinosaurs 2000 million years ago, and the Birth of Christ 2000 years ago is
impossible to visualize. But if we reduce the earth’s age to a week, we can visualize the
relative sizes between the numbers.
Lesson Two: Numeracy – Vastness of Space
Issac Newton
The table illustrating the exact size of the planets and the true distances between them is
the same problem for the astronomer as the geologic time scale is to the geologist.
Thousand, millions, billions and trillions of miles is impossible to visualize. Can a
student close their eyes and see the sun, a sphere whose diameter is nearly 865,000 miles
in diameter. Of course not, but if we reduce the scale to 100,000 miles for every inch, we
can provide a visualization as clear as day.
The visualization takes place in two steps.
Step 1: Create a new Scaled back Table, with small objects for the plants and paces you
would take from the sun to place the planets.
Step 2: Create a new table, with the planets size and distance from the sun compared in
relative terms to the size and distance from the sun for earth. In other words, to cement
the size of the solar system in the student’s mind, have them calculate that the Sun has a
volume over a million times that of earth and Pluto is 40 times farther from the Sun than
Earth.
Closure: Have the student re-examine the Table with the real data, and have the students
notice how much better they can comprehend the magnitude of these number. s
compared to
Lesson Three: Set Theory – Introduction to Set Operations
Cantor and Dodgson. The infinite set and set across to the complex number plane
Set operations union, intersection, minus and complement
Cardinality of a set
Goal:
Motivation/ice breakers
Expectations:
Assessments:
Knowledge gained by the student and the teacher success:
Include over heads
a)   
b)   
c)   Q
d)   Q
e) Z  Q
f) Z  Q
g) Q  
h) Q  
and N subset Z, N subset Q, Z subset Q, Q subset R
 Numeracy
 Correlations vs causation
 Coincidence means to coincide, not to cause
 How many ways can something be done? And this has an implication in our
every day lives
 Any two particular events have an extremely high number of associated facts,
events and meanings associated with them. The fact that some of these
occurrences appear to overlap or coincide should not surprise us. It is just a
reflection of the multiplication principle that we wil soon see.
 “you and I were talking about so and so last night
 Two people meet on a plane, they find they have a common acquaintance. So
what.
 Even the bizarre notion of the Kennedy and Lincoln coincidences that seem to
captivate the chat rooms and fill the web pages.
 ? Take any two seemingly unrelated events, ‘google’ the topics on the Internet,
and I assure you, you will get just as many “coincidences” or “what’s the odds of
that’s” as the Kennedy/Lincoln coincidences. You try it.
 spin your own conspiracy theories about two presidents. Write a book, if you
want. I often thought a good book could be written if we employed the same
notion with the vice-presidents. Common thread or little known conspiracies
about those really in charge. From John Adams to Dick Cheney
 December 5th. Boats. Sinking. The result: I found out that on December 5th,
1664, a ship off north Wales with 81 passengers aboard, sank. There was one
survivor. A man named Hugh Williams. On the same date, December 5th, 1785,
a ship sank with 60 passengers aboard. There was one survivor. A man named
Hugh Williams. On December 5th, 1860, a ship with 25 passengers abroad sank.
There was one survivor. A man named Hugh William
 We are compelled to find significance to a string of facts
 Nearly 7000 aumsement park deaths - stands out in a frightening way. But, let’s
examine this number more closely. Roughly 317,000,000 or over 300 million
people visit fixed site amusement parks in a given year. Now, let’s compare this
number to those injured each year in other recreational activities: 82,722 people
are injured on trampolines, 62,812 are injured in swimming pools, 544,561 are
injured on bicycles, 20,000 are injured at music concerts, and 200,000 are injured
in preschool and elementary school playgrounds.
Discuss poverty in this country
 Set Theory
 Counting Theory – Multiplication Principle, Permutations, Combinations
PROJECT
Below is a grid of a city showing three streets that run east-west and three streets that run
north-south. The numbers you see are the number of minutes it usually takes to travel the
segment of the street shown during peek time, which is weekdays from 6:30 to 8:00 am.
The obvious question, you want to get from the “start” to the “end”, which route will
enable you to travel the quickest?
To solve this question, most of us would try to calculate the travel time for each possible
route one at a time and then choose to maneuver through traffic by using the route that
has the smallest number of minutes associated with it. So, let’s examine the travel times
for all possible routes. The natural question arises is ‘how many different routes are
there?’ We don’t want to use a method that would bog us down with too many
calculations.
For notation purposes, so we are not bogged down, let’s use the notation E for east and N
for north. Note, that at any intersection, we would either go east north. So, for the route
ENEN, it would take 3 + 5 + 6 + 4 minutes or 18 minutes. And for the route EENN, it
would take 3 + 7 + 4 + 5 minutes or 19 minutes.
Alright, let’s try to exact the fastest path by hand calculations:
1. ENEN: 18 minutes
2. EENN: 19 minutes
3. ENNE: 13 minutes
4. NEEN: 18 minutes
5. NNEE: 17 minutes
6. NENE: 14 minutes
So, the fastest path would be going east for 2 blocks and then north for two blocks.
We had to try 6 possible paths. Where did the number 6 come from. Well, for each
single block we travel, at each intersection, we have a choice of two directions, either E
or N. And how many blocks do we need to travel along? Four. So, we have 4 in a
group, with 2 choices for each item. Does order matter? Well, we are looking for any list
4! 4(3)(2)(1)
of two E’s and two N’s. So, we have

 6 paths. Note, this is the same
2!2! 2(1)(2)(1)
 4  4(3)
calculation as 4 C2    
6
 2  (2)(1)
Now, let’s zoom our grid out and thus show a larger sector of this city.
Again, we ask, which is the fastest path? Well, first we ask ourselves, would it be just as
easy to try to calculate the time for each possible path again? We need to find the number
of paths possible to know whether or not it would to cumbersome to list each individual
path’s travel time.
Again, there are 2 choices at any intersection, E or N. And we travel a total of 6 blocks.
6! 6(5)(4)(3)(2)(1)
So, we are looking for lists of 3 E’s and 3 N’s. So, we have

 20
3!3! (3)(2)(1)(3)(2)(1)
 6  6(5)(4)
paths. Note, this is the same number as 6 C3    
 20 paths to test.
 3  3(2)(1)
How many different paths would we need to test for each of the following?
or
 8  8(7)(6)(5)
 70 and for the 5 by 5
For the 4 by 4 grid, we would have to try 8 C4    
 4  4(3)(2)(1)
10  10(9)(8)(7)(6)
 252 routes to try.
grid, we would have to try 10 C5    
 5  5(4)(3)(2)(1)
Two: Probability and Statistics
ACTIVITY: Introduction to Permutations and Combinations
Have the class gather in a circle. Count the number of students in the circle. Have the
students shake hands with everyone in the circle.
 How many hands did each person shake?
For ex: if there were 19 people, each person shook 18 hands.
 How many handshakes occurred?
For ex: if there were 19 people in the class, each person shook 18 hands. 19
people shaking 18 hands each is 19(18) = 342 handshakes total. But, each of the
342 handshakes were counted twice, so there were actually ½ of the 342
handshakes, or 171 handshakes.
19(18)
 19 C 2 .
2 *1
 How many hands were shook? 342. Or 19(18)  19 P2
 342 and we divided out the order.
Now, line the students up along the wall. Ask them in how many ways can we elect a
president, vice president and a treasurer to represent the class.
1 person is president, 1 person is vice-president and we have 17 other people standing
that could be treasurer. 19(18)(17) = 5,814 ways the elections could turn out.
Now, say you want to form committees of three. How many committees are possible?
Take groups of three people. Give each person in the first group a card that reads A, B
and C. Have a president line, vice president line and a treasurer line. {ABC, ACB, BAC,
19(18)(17)
 19 C3  969 committees are
BCA, CBA, CAB} or 6 ways to order 6 people.
3 * 2 *1
possible.
Try with a smaller group. A group of five. Give each a name card ALAN, BILLY,
CINDY, DEANN and EVELYN. Want a P, VP and T. Show all ways. Want a
committee of three. Show all 60/6 = 10 ways.
Chapter two
Following is a list of observances typically covered by the Census Bureau's Facts for Features series:
African-American History Month (February)
Back to School (August)
Valentine's Day (Feb. 14)
Labor Day (Sept. 1)
Women's History Month (March)
Grandparents Day (Sept. 7)
St. Patrick's Day (March 17)
Hispanic Heritage Month (Sept. 15Oct. 15)
Asian Pacific American Heritage Month (May)
Halloween (Oct. 31)
Older Americans Month (May)
American Indian/Alaska Native
Heritage Month
Mother's Day (May 11)
(November)
Father's Day (June 15)
Veterans Day (Nov. 11)
The Fourth of July (July 4)
Thanksgiving Day (Nov. 27)
Anniversary of Americans with Disabilities Act (July 26)
The Holiday Season (December)
Editor's note: Some of the preceding data were collected in surveys and, therefore, are subject to sampling
error. Questions or comments should be directed to the Census Bureau's Public Information Office:
telephone:
(301) 763-3030; fax: (301) 457-3670; or e-mail: < pio@census.gov>.
PROJECT: Bayes Formula
Say nothing and just hand out the following poll to your class.
1. Should abortion be legal or illegal if "the woman's life is endangered"
Circle One: Legal Illegal
2. Should abortion be legal or illegal if "the woman's physical health is
endangered"
Circle One: Legal Illegal
3.
Should abortion be legal or illegal if "the pregnancy was caused by rape or
incest"
Circle One: Legal Illegal
4. Should abortion be legal or illegal if "”there is evidence that the baby may be
physically impaired"
Circle One: Legal Illegal
5. Should abortion be legal or illegal if "the woman or family cannot afford to
raise the child"
Circle One: Legal Illegal
6. Which side of the political debate on abortion do you sympathize with more:
the right-to-life movement that believes abortion is the taking of human life
and should be outlawed, OR, the pro-choice movement that believes a woman
has the right to choose what happens to her body, including the right to decide
to have an abortion.
Circle One: Right-to-life Pro Choice
7. Which party most closely reflects your views on most political issues:
Circle One: Democrat
Republican Independent
Collect the poll and ask the class these key Questions:
 Can we draw along party lines on the abortion issue?
 Does the abortion debate transcend party lines, polarizing us in directions we may
not want to admit, as the media would like us to believe?”
Tell the class the first 5 questions were placed on the poll to get you to critically think
about the abortion issue. This is a common practice on may polls. The key questions for
deciphering the question “does abortion transcend party lines?” are the last two question.
Count the results and then runs Baye’s Theorem. Show the class the tree diagram. Then
discuss with the class the results. From your poll, is the abortion issue an issue that
transcends political boundaries? How many arguments can we form from Baye’s
Theorem.
Statistics:
Time: 5 minutes.
Introduce mean, median and mode.
Use the following transparency. Split your class into exactly three groups. This helps
create enough data. Hand out one of the following questions to each of the three groups,
and have the students answer the questions. Then have the students report to the class
their findings.
Range, Mean, Median and Mode
Write the name of each partner in your group.
Find the range, mean, median and mode of for the partners
in your group for each other’s:
Heights, in inches
Range, Mean, Median and Mode
Write the name of each partner in your group.
Find the range, mean, median and mode of for the partners
in your group for each other’s
Distance, in miles, traveled each day to school
Range, Mean, Median and Mode
Write the name of each partner in your
group.
Find the range, mean, median and mode of for the partners in your group for each other’s:
Number of siblings
(brothers and sisters)
Three: Finance
Four: Geometry
Five: Rates of Change and Calculus
Six: Logic, Argument and Proof
Activity: How observant are you? To be done after introducing logic and truth
tables.
After introducing logic and truth tables, run a game of speed math. For the next six
questions, use the following statements.
P: George Washington was the first president of the United States.
Q: Arizona is the only state that has no state capital.
R: 6 + 8 = 100
S: All swans are birds.
Tell your students to study these 4 statements carefully. Tell them to take time to observe
the truth value of each. Then one at a time, write each of the six compound sentences
down. Instruct the students to scream the answer out as quickly as possible. Then have
the students explain what is the fastest way of deciding the truth value of the compound
sentence, that is why they should have been able to answer the question so quickly.
Find the truth value:
1. ~ ( P  R )
2. ~ (Q  P )
3. S  ~ Q
4. ~ P  ~ R
5. R  (~ P  Q )
6. P ~ R
Answers:
1. T It is quick because P and R have opposite truth values, so the conjunction is F, so
the negation of the conjunction is T.
2. F It is quick because Q is F, then the conditional statement is T, so the negation of a
true statement is F.
3. T It is quick because S is T, so the disjunction is T.
4. F It is quick because we are negating P and R, where one is true and one is false, so
the result will have one T and one F statement. Since we have a conjunction, we need
both to be T for the statement to be true.
5. T It is quick because the negation of P is F, so the conditional is true, so the
disjunction is T.
6. T It is quick because P is T ands we have a disjunction.