Benne So - Volume 2
The Genius Academy
1
African Mathematical Genius
Benne So - Volume 2
Dr. Freya A. Rivers
LaMailede Moore
Ed. D. Vanderbilt University
B. S. Mathematics, Michigan State University
Dr. Abdulalim Shabazz
Shariba Rivers
Ph. D. Cornell University
Ed. S. Louisiana State University
Julian Brooks
B. S. Louisiana State University
2
Sankofa Publishing Company
Copyright
August 25, 1999
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or
transmitted, in any form or by any means, without prior written permission of
Sankofa Publishing Company. Printed in Baton Rouge, LA, USA.
Sankofa Publishing Company
3863 Waverly Hills Rd
Lansing, MI 48917
517-484-0428
[email protected]
isbn # 0-9667215-2-7
AMG2
3
Table Of Contents
Challenging the Genius Mathematics Curriculum
Message from Dr. Shabazz
Introduction
4
5
8
Book Two
Theme 4: Time
Theme 5: Change
Theme 6: Seasons
9
58
98
4
CHALLENGING THE GENIUS MATHEMATICAL CURRICULUM
AFRICAN MATHEMATICAL GENIUS BENNE SO
MISSION
The mission of the curriculum is to center, educate and nurture all students to achieve their maximum potential while developing future
world leaders.
PHILOSOPHY
The philosophy is that all children can and will learn to their maximum potential and that their dreams should be their only boundaries.
IDEALS
The ideal is to provide a holistic program that will produce students who are :

Academically competent

Behaviorally confident

Socially conscious

Culturally aware
ACADEMIC FOCUS
The academic focus is an experiential mathematics curriculum with strong emphasis in individualization and critical thinking. “Learning
by doing” is the primary teaching strategy because people remember ninety percent of what they see and do and only ten percent of what
they read.
DISCIPLINE
The discipline approach is taught using ethical principles of truth, justice, righteousness, order, balance, harmony and reciprocity. There are
only three rules: Respect self, Respect others and Respect the environment.
GENIUS
Dr. Abdulalim A. Shabazz of Clark Atlanta University earned his Bachelor’s degree from Lincoln University, Master’s from Massachusetts
Institute of Technology (MIT) and Doctorate from Cornell University. He has directly and indirectly produced more than half of the current
Black mathematicians (at the Ph.D. level) in the United States. He is African Mathematical Genius at its finest.
Thanks
Special thanks and recognition is extended to the Marcus Garvey Academy and their director, Anyim Palmer for providing the role model
that inspired us to undertake this process. Thanks to the Roots Academy for providing an African centered curriculum prototype. Sankofa
Publishing Company wishes to thank Dr. Shabazz for agreeing to edit African Mathematical Genius with our staff. We are truly honored
to have his contributions and his validation of our work.
5
Message from Dr. Shabazz
Studies paint a dismal picture of underachievement and underrepresentation of Africans, Native
Americans and Hispanics in the mathematical sciences, engineering and technology. In terms of
historical time this is a recent phenomenon.
From the beginning of humans until the fall of
Granada in Spain in 1492, Africans, Native Americans, Hispanics and their ancestors were the
leaders of all intellectual pursuits including the arts, sciences and mathematics.
We seek to maximize each student’s motivation and raise self-esteem while producing excellence in
mathematics. Experience teaches the best ways to change these misconceptions are: (a) to show
students how they, through their ancestors, have contributed to the growth and development of the
mathematical sciences through the ages; (b) to provide them with role models in their own images
and with many examples of successful students just like themselves; and (c) to create a favorable
humanistic learning and teaching environment in which they can mature and develop to a high degree
rapidly.
The basic assumptions are:
 all students can excel in mathematics
 a high level of success depends upon the students’ perception of their ability and upon their
hard work
 students come to school to learn.
Such assumptions and an understanding thereof are necessary if all students are to have hope of
achieving educational success.
To effectively teach all students, teachers must take them as they come to the classroom. As Dr.
Clarence H. Stephen, professor emeritus of mathematics of the Potsdam College of the State
University of New York, so eloquently says, “We teach the students we have, not the students we
wish we had”. Lack of knowledge or background should not be used against students.
Not having a
rounded mathematical background is not a real barrier to mathematical development. What is
missing should be supplied; what is broken should be fixed, and should be done as quickly as
possible. Certainly, students in the beginning should be given problems and challenges which they
can handle, but given in a humane way, never seeking to injure or lower self-esteem. Indeed, this
is in accordance with proceeding from the known to the unknown.
6
With this background teachers must have the:
 knowledge of the subject to be taught
 will to teach all students
 belief that all students can learn
 historical facts so that all students can learn the part they have played in the creation and
development of mathematical knowledge
 willingness to accept students as they are and take them where they should go
 motivation to inspire students to work harder
 desire to publicize their students’ success in mathematics.
Other areas to consider are:
ATTITUDE
1. Consistently show students the role they have played in the development of mathematics
through historical and current facts
2. Have students write reports on multi-cultural mathematicians--ancient and modern
3. Allow students frequent experiences of success by having them to solve exercises of low
difficulty then solving those of higher complexity
4. Allow students to experiment with concepts and develop rules and methods on their own,
while the teacher facilitates the process
5. Allow students to compare and debate their concepts and methods with others
6. Allow students to prove or disprove mathematical assumptions, written and oral
7. Allow students to teach the class about a topic that they enjoy
CONCEPTUALIZATION
There are three common ways to perceive a mathematical concept or idea:
1. Physical model (geometric representation, 1-3 dimensions)
2. Algebraic model (formulas, equations, inequalities, “analytical form”)
3. Mental model (written or verbal representation that best describes concept or idea)
COMMUNICATION
Since spoken/written language is first used by the student to convey his/her thoughts and
concepts, it is natural to engage the student in using the language with which he/she is already
familiar to express and define “mathematical” language.
1. Have students translate written/spoken language into mathematical symbols and expressions
2. Have students check the reasonableness of statements and results
3. Have students check the validity of statements
PROCESS
Natural learning takes place first by physical activity or processes that convey an idea or
concept. Next is learning by verbal communication, which conveys an idea or concept through the
spoken word. Last is learning by written or symbolic communication, which conveys an idea or
concept through symbols such as alphabets and/or numbers, etc.
7
1. Conception-Object, Idea, Concept
2. General familiarization-Superficial introduction of object, concept or idea
3. Experimentation-Contact and close observation of object’s, concept’s and idea’s properties
and qualities
4. Assumptions/Theorems/Rules-Develop rules and definitions based on experimentation
5. Application-Perform tasks based on rules and theorems
INTRINSIC MERIT
Experimentation with mathematical concepts and properties is the scientific activity that
naturally stimulates the student to think clearly, logically, and constructively. Comfort in
experimentation gives the student intellectual freedom causing that student to reach within to
create unique concepts.
Logical training causes the student to constructively access, arrange and use facts to
successfully produce a desired outcome. Early exposure of the student to mathematical concepts
and methods naturally causes the student to be more “friendly” with mathematics in later years.
RELEVANCE
The learning and practice of mathematics by the student will train that student to logically
create strategies and solutions relevant to the needs of home or community life. Further the
practice of mathematics will train the student in efficient production of self-determined
objectives and goals.
In-depth mathematics training at the early years increases the likelihood of mathematics and
scientific success in the middle and high school ages. The Challenging the Genius Mathematics Curriculum prepares children for their future leadership.
8
I
ntroduction
The Challenging the Genius Mathematical Curriculum is organized into four books. The
first book is Potential Genius our preschool curriculum. The next books are African Mathematical Genius Giri So, Benne So and Bolo So. The African Mathematical Genius books are divided
into three themes in each book for a total of nine themes. The themes are infused across the
curriculum with goals and objectives for math, language arts, science, social studies/history/
geography and health with sample lessons in art, PE and music. The math theme is fully developed
with class introductions of topic, vocabulary, exercise and activities.
The basic strategies and techniques utilized in a holistic program include repetition and drill
while recognizing the concept of patterning. The drills used encompass a multi-sensory approach
for culturally relevant learning. This enables students to transfer these experiences for
implementation.
HOW TO USE THIS BOOK
This book should be regarded as a guide for educational creativity. It is not a recipe.
Each
theme is accompanied by an introduction explaining the African history of mathematics. These
introductions are followed by goals and objectives with page numbers referring to suggested
activities. The language of mathematics is included, as is a collection of worksheets for
practice and reinforcement. Mental math and review exercises are included in each theme to check
mastery. Games and activities are included, and can be used during instruction or for additional
enhancement. Each theme ends with goals that offer suggestions to extend the lessons across the
curriculum.
This book can facilitate instruction. It is filled with suggestions that we have found sound and
useful. Be creative! Develop your African Mathematical Genius.
9
10
K
Mathematics - Time
emet is where we find the earliest documentation of measuring time. Tony Browder, in Nile Valley Contributions to
Civilization, shows a shadow clock which is more than 3,400
years old. It casts shadows on a bar marking off the hours as a
crossbar turns toward the east. There were many timekeeping devices
in Kemet, including stone sundials and the tekhnu (obelisk) which
was used to measure the equinox. Today, the clock is used to measure
time by the second, minute and hour. The first clock made in the
United States was created by Benjamin Banneker, who also wrote an
almanac and designed the street plan of Washington, DC. The
ancestors of KEMET and Banneker operated on Imani (faith) as they
considered tasks that were beyond their time.
Success as a form of justice was their reward.
11
Theme 4: Time
MATHEMATICS: CLOCKS AND SCHEDULES
Goal: To develop an understanding of time and an introduction to Geometry.
Objectives:
1. Explain all parts of the clock
2. Identify and articulate times on clock
3. Identify angles made by hands on clocks
4. Orally define and give examples of geometric lines and figures
5. Identify shapes
6. Explain angles of geometry
7. Describe the angles on a clock and their corresponding time
8. Select congruent figures
9. Create lines of symmetry
10. Identify solid figures
11. Define and identify tessellations
12. Create a cube and pyramid
13. Create a schedule of chores by day and time
14. Graph time on schedule
15. Practice addition and subtraction
12
Vocabulary
Time—A certain point in the past, present, or future, as shown on a clock or calendar.
Clock— A device used to tell time.
Second—A unit of time equal to 1/60th of a minute.
Minute—A unit of time equal to 60 seconds or 1/60th of an hour.
Hour—A unit of time equal to 60 minutes or 3600 seconds or 1/24th of a day.
Day— The time of light between sunrise and sunset; twenty-four hours; the time it takes the earth to make a complete
rotation on it’s axis.
Week—A unit of time equal to seven days.
Month—One of the 12 divisions of a year as defined by the Gregorian calendar. A period of approximately four weeks or
30 days.
Year—The period in time where the earth makes one complete revolution around the sun; 365 1/4 days.
Decade—A unit of time equal to ten years.
Score—A unit of time equal to twenty years.
Century—A unit of time equal to one hundred years.
Millennium—A unit of time equal to one thousand years.
13
Vocabulary
Geometry—The study of measurements of points, lines, and shapes.
Angle—A figure formed by two lines diverging from a common point.
Tessellation—A pattern formed by polygons with no crevices.
Fractal— A geometric shape which is:
a. Self - similar and
b. has fractional (fractal) dimensions.
Bisect - To divide into two equal parts
14
Historical Look
Mexico City, Mexico, North America
The Aztecs, an indigenous people of Tenochtitlan or present day Mexico City, began making their calendar in
1427 and completed it in 1479. They used pictographs to represent the information. The circle has twenty
squares representing each day of the Aztec month. They are called the Ring of Solar Archetypes. The Aztec
year consisted of eighteen months. This amounted to three hundred sixty days. Additionally five days were
added called Nemontemi (unlucky days) which were sacrificial days. The stone was used not only as a calendar but also as a sundial.
Egypt
The worlds first calendar was the ancient Egyptian calendar. It dates back as far as 4236 B.C.E. This calendar was based on the moon’s
cycles and was regulated by the stars. The lunar month was determined by the interval between successive full moons, which is precisely 29
days, 12 hours, 44 minutes, and 2.7 seconds. The word month is derived from the mona, which means “moon”. Additionally, the astronomers of KMT or Egypt developed stellar and solar calendars. The solar calendar provided a more accurate measurement.
Asia
The Islamic calendar begins with Muhammad’s flight from Mecca to Medina in 622 A.C.E. This is also a lunar calendar.
The Chinese calendar is rooted in their philosophy and astrology. It is greatly influenced by Lao Tzu and Confucius, the founders of Taoism
and Confucianism, respectively. There are twelve signs in Chinese astrology that corresponds to one year. In this zodiac calendar there are
twelve animals that represent each year. Each person is born in one of the twelve zodiac animals. The animals are as follows: The Boar, the
Rat, the Ox, the Tiger, the Rabbit, the Dragon, the Snake, the Horse, the Ram, the Monkey, the Rooster, and the Dog. The Chinese New Year,
called Nian, is also different from the Western new year because it is lunar instead of solar.
Europe
In parts of Scandinavia above the Arctic Circle the sun does not set for parts of the summer and during parts of the
winter the sun does not rise. Because of this the Scandinavians divided each sun-cycle into eight sections. A place
on the horizon that lay in the center of these eight marks is called a “daymark”. Time is identified by noting when
the Sun stood over one of these daymark-points on the horizon.
15
Reading The Clock
second hand
long hand
(minute hand)
short hand
(hour hand)
THE FACE OF A CLOCK
Clocks have three hands (when equipped with a second hand) that are used to tell time. The
short hand on the clock points to the hour. The long hand points to the minute.
All of the parts together make up the face.
There are 24 hours in 1 day.
Each hour has 60 minutes which equals one revolution of the minute hand.
Each minute has 60 seconds, one revolution of the second hand (each mark on the clock represents either one second or one minute).
16
Telling Time
The time is 1:00
The time is 2:00
The time is 3:00
The time is 4:00
The time is 5:00
The time is 6:00
because the short
because the short
because the short
because the short
because the short
because the short
hand is pointing hand is pointing hand is pointing hand is pointing hand is pointing hand is pointing
to the 1 and the
to the 2 and the
to the 3 and the
to the 4 and the
to the 5 and the
to the 6 and the
long hand is
long hand is
long hand is
long hand is
long hand is
long hand is
pointing to the 12. pointing to the 12. pointing to the 12. pointing to the 12. pointing to the 12. pointing to the 12.
The time is 7:00
The time is 8:00
The time is 9:00
The time is 10:00 The time is 11:00 The time is 12:00
because the short
because the short
because the short
because the short
because the short
because the short
hand is pointing hand is pointing hand is pointing hand is pointing hand is pointing hand is pointing
to the 7 and the
to the 8 and the
to the 9 and the
to the 10 and the
to the 11 and the
to the 12 and the
long hand is
long hand is
long hand is
long hand is
long hand is
long hand is
pointing to the 12. pointing to the 12. pointing to the 12. pointing to the 12. pointing to the 12. pointing to the 12.
17
Reading The Clock
short hand
(hour hand)
long hand
(minute hand)
THE FACE OF A CLOCK
The short hand tells you the hour. On the clock above the time is 3:00. This is because the short hand is on the three
and the long hand is on the twelve.
The long hand tells you the minute counting by ones. For every numeral displayed on the clock from 1 - 12 you count
by fives.
If the short hand is between two numbers, pick the lesser of the two numbers for the hour.
The time here is 5:09.
18
Working With Time
Write the correct time under the clock
XII
19
Units of Time
Your eyes blink about every second.
II
Most popular songs last about 3-4 minutes.
It takes about 1 hour to travel from Lansing to Detroit by car
and about 4 hours from Detroit to Chicago.
1 day passes between the end of school on Tuesday and the end of
school on Wednesday.
There is one week between this Sunday and next Sunday.
There is one month between December 1st and January 1st.
A year will pass between your 5th birthday and your 6th.
What will be the best unit of time to use to measure each activity?
1. Being in school for a day
2. This Kwanzaa to next Kwanzaa
3. Singing your ABC’s
4. Writing your name
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Units of Time

There are 60 seconds in 1 minute.

There are 60 minutes in 1 hour.

There are 24 hours in 1 day.

There are 7 days in 1 week.

There are approximately 30 days in a month.

There are 12 months in each year.

There are 10 years in a decade.

There are 20 years in a score.

There are 100 years in a century.

There are 1,000 years in a millennium.
1. How many years are in two decades?
2. How many days are in three weeks?
3. How many months are in a half of a score?
4. How many hours are in two days?
5. How many minutes are in a half hour?
21
More with Time
When working with standard time (dividing the day into two twelve hour blocks), the same hour can be used to mean in
the morning or evening. You use the abbreviation ‘a.m.’ to tell morning time and the abbreviation ‘p.m.’ to tell evening
time. The abbreviations are Latin and mean ante meridiem(before noon) and post meridiem(after noon). For instance
9:00 a.m. means 9 in the morning, while 9:00 p.m. means 9 in the evening.
Scientists use a 24-hour clock to avoid such confusion. Beginning at midnight (the beginning of a new day), the
hours are numbered from 0 to 24. We call this method of telling time military time. When using military time, you
say the time in a different way. For instance, 9:00a.m. is not “nine o’ clock in the morning,” but “nine hundred hours.”
Standard Time
Military Time
12:01 midnight
0001 hours
1:00 am
0100 hours
2:00 am
0200 hours
3:00 am
0300 hours
4:00 am
0400 hours
5:00 am
0500 hours
6:00 am
0600 hours
7:00 am
0700 hours
8:00 am
0800 hours
9:00 am
0900 hours
10:00 am
1000 hours
11:00 am
1100 hours
12:00 noon
1200 hours
1:00 pm
1300 hours
2:00 pm
1400 hours
3:00 pm
1500 hours
4:00 pm
1600 hours
5:00 pm
1700 hours
6:00 pm
1800 hours
7:00 pm
1900 hours
8:00 pm
2000 hours
9:00 pm
2100 hours
10:00 pm
2200 hours
11:00 pm
2300 hours
12:00 midnight
2400 hours
1. If it is 10:30a.m. now, what time will
it be in 10 minutes?
2. How would you say/write 8:40 a.m.
in military time?
3. If there are 7 days in one week, how
many days are in two weeks?
4. Five minutes from now it will be 9:45p.m. What time is it now?
5. How would you say/write 6:30p.m. in military time?
22
Daily Organizer - List what you do on a daily basis at specific times
4:30pm 5:00pm 5:30pm 6:00pm 6:30pm 7:00pm 7:30pm 8:00pm 8:30pm 9:00pm 9:30pm
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
23
Geometry
A line is a straight path that
extends in both directions
without ending.
Point A
Point B
A line segment is part of a
Points have no size or
line. It has two endpoints.
dimension. They are used to
tell position of lines and
objects. Points are named
A ray is a part of a line that
with capital letters.
extends in one direction to
infinity(never ending).
When two lines or line
When two lines or line
segments intersect, they meet segments never cross
and cross at a point.
(intersect), they are parallel
lines.
A
B
)
A
B
C
90°
When two lines or line
segments intersect, they
When two lines or line
form angles.
segments cross (intersect) or
ABC
(Angle ABC)
join to form a 90° angle, they
are perpendicular. The sign The point where lines
intersect to form angles is
used to show that lines are
called a vertex (point B).
perpendicular is .
Figures that have the same
size and shape are
congruent.
Figures that have the same
shape but are not the same
size are similar.
vertex
24
C
A plane is made up of an
infinite set of points.
Together these points make a
flat surface. A plane
extends infinitely in all
directions. Planes do not
have thickness.
Working with Geometry
1. Draw a line segment.
2. Circle the ray.
a.
b.
3. A plane is a flat surface with a limited amount of points.
4. Are these two figures congruent?
5. Locate the angle and vertex of these two intersecting lines.
6. Are these figures similar?
7. Draw a set of perpendicular lines.
8. Draw a set of parallel lines.
25
Circle:
c.
True
or
False
Geometry - Polygons
4
5
7
5
7
5
6
4
5
3
10
3
8
3
Polygons are flat, twodimensional shapes.
Polygons are closed figures
that have at least three
straight sides and angles or
vertexes.
Regular polygons are
polygons that have sides of
equal length and angles of
equal measure.
Irregular polygons are
polygons with sides of
unequal length and angles
of unequal measure.
11
9
9
5
A triangle is a polygon that
has three sides and
vertexes.
11
7
9
11
6
An isosceles triangle is a
triangle with exactly two
equal sides.
A scalene triangle is a
An equilateral triangle is a A right triangle is a triangle
triangle with no equal sides. triangle with all equal sides. with a 90° angle(right angle).
26
Working with Geometry - Polygons
1. Color the regular polygons red and color the irregular polygons blue.
a.
b.
c.
d.
e.
f.
2. Place an X on the shapes that are not polygons.
a.
b.
c.
3. Locate the angles and vertexes on this triangle.
d.
A
B
C
4. Draw a line of symmetry on the isosceles triangle.
a.
b.
c.
27
d.
e.
f.
Geometry - Polygons
Quadrilaterals are polygons
that have four sides, four
vertexes, and four angles.
Parallelograms are
Trapezoids are quadrilaterals Squares are quadrilaterals
quadrilaterals that have
that have one pair of parallel with all equal sides. A
parallel line segments in both sides.
square has 4 right angles.
pairs of opposite sides.
Rectangles are
parallelograms with 2 long
sides and 2 short sides. A
rectangle has 4 right angles.
A Rhombus is a
parallelogram with 4 equal
sides. It looks like a square
that is slanted or leaning.
28
A Pentagon is a polygon with A Hexagon is a polygon with
5 sides, 5 vertexes and 5
6 sides, 6 vertexes and 6
angles.
angles.
Working with Geometry - Polygons
1. A quadrilateral has ____________ sides.
a. 6
b. 0
c. 4
d. 9
2. A square has 2 long sides and 2 short sides.
Circle:
True
or
False
3. Circle the Rhombus.
a.
b.
4. A triangle has ___________ sides.
a. 4
b. 3
c. 2
c.
d.
d. 0
5. Draw a pentagon.
6. Is a trapezoid considered a parallelogram?
7. A ___________ has 4 right angles, 2 long sides and 2 short sides.
a. square
b. hexagon
c. rectangle
d. triangle
8. A triangle is a quadrilateral.
Circle:
True
29
or
False
Geometry and Addition
90
90
60
90
90
90
3cm
3cm
3cm
3cm
30
The sum of all the angles of a The sum of all angles of a
triangle is 180°.
polygon with 4 sides
(quadrilateral) is equal to
360°.
The sum of all angles of a
circle is equal to 360°.
To find the perimeter of a
polygon, you add all the
sides:
3cm + 3cm + 3cm +3cm= 12cm
The perimeter of this polygon is equal
to 12cm.
2 cm
4cm
4cm
5cm
1cm
3cm
To find the perimeter of a
square you add all the sides.
Remember all 4 sides are
equal:
2cm + 2cm + 2cm + 2cm =
8cm
To find the perimeter of a
rectangle you add all the
sides. Remember the 2 short
sides are equal and the 2
long sides are equal:
1cm + 1cm + 4cm + 4cm= 10cm
30
3cm
6cm
To find the perimeter of a
To find the total length of
triangle you add all three
these two lines you add them
sides:
together:
4cm + 3cm + 5cm = 12cm
3cm + 6cm = 9cm
The total length of this line is
9cm.
Geometry
Is this figure a polygon?
Is this figure a polygon?
If yes, tell why:
If yes, tell why:
If each side of this polygon
measures six inches, what is
the perimeter? Explain your
answer.
8
Do these two line segments
bisect each other?
What does bisect mean?
12
12
15
How many angles do these
two lines make?
Are these two lines parallel or
11
perpendicular? Explain your
answer.
What is the perimeter of this
triangle?
What kind of triangle is
this?
31
11
How many lines do you see?
How many line segments?
How many angles?
How many polygons?
Do the lines bisect?
What’s the perimeter?
Geometry - Angles
Acute angles are angles that Obtuse angles measure more A straight line is equal to
measure more than 0° but less than 90° but less than 180°.
180°.
than 90°.
A right angle is equal to 90°.
Quadrant 2
Quadrant 3
Complementary angles are
angles that join to form a
right angle. The sum of their
angles equals 90°.
Supplementary angles are
angles that join to form a
straight line. The sum of
their angles equals 180°.
A Reflex angle is an angle
that measures more than
180°, but less than 360°.
32
Quadrant 1
Quadrant 4
Quadrant 1 angles - between
0° and 90°.
Quadrant 2 angles - between
90° and 180°.
Quadrant 3 angles - between
180° and 270°.
Quadrant 4 angles - between
270° and 360°.
Working with Angles
1. Draw an acute angle.
2. Complementary angles form _____________.
a. supplementary angles
b. right angles
3. A reflex angle is more than 180°.
Circle:
True
4. These are ______________ angles.
a. supplementary
b. complementary
or
False
c. acute
5. Label the quadrants.
6. This straight line measures _____________ .
a. 45°
b. 90°
c. 180°
c. obtuse angles
d. 360°
7. Draw an obtuse angle.
33
d. reflex
d. 50°
Working with Geometry & Addition
1. What is the total length of these two line segments?
6cm
7cm
6cm
2. What is the perimeter of this trapezoid?
3cm
3cm
4cm
3. The sum of the angles of a triangle is equal to 360°.
Circle:
4. What is the perimeter of this equilateral triangle?
True
or
False
2cm
5. The sum of the angles of a quadrilateral is equal to __________.
a. 360°
b. 180°
c. 90°
d. 45°
6. What is the total distance of these line segments?
5cm
34
3cm
6cm
Angles On The Clock
The two hands of a clock form different angles at different times.
At 9:00 a Right angle (90°) is formed.
Clock Dance - This is a multi-sensory activity and game that teaches students how to tell time. It is recommended that
the teacher demonstrate this activity, practice with the students and then call on students to demonstrate their
proficiency.
Stand with one arm and hand pointing straight up and the other arm in front of the body, bent at the elbow with hand
and fingers pointing up tell the students that this is 12:00. Rotate either or both arms to your left (which appears to be
clockwise to students) and tell them the time you are signifying. Students should move their arms to the right to see
that they are matching a clock. This activity will teach students to tell time by hours and by minutes. As they slowly
rotate their straight arm (the minute hand of their clock) with jerking stops, they can count by fives to 60 and complete
a circle. This activity takes a little practice, but once the children catch on they can be asked to show the time and tell the
time. Other suggestions for this activity include: open eyes, closed eyes being a.m. and p.m. respectively; identifying
acute, obtuse and right angles.
35
Number & Time Points Were awarded for class participation
10
9
8
7
6
5
4
3
2
1
11:00-11:30
11:30-12:00
12:00-12:30
During what time was the most number of points awarded? How many were awarded?
Were the most points awarded around 11:15 or 12:15? How did you come to this conclusion?
During what time was the least amount of points awarded? How many were awarded?
Were the most points given around 11:45 or 12:45? How did you come to this conclusion?
36
12:30-1:00
Geometry- Describe the following angles
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
A. Straight (180°)
B. Acute (<90°)
C. Obtuse (>90° but <180°)
D. Right (90°)
If these were clock hands,
what time would it be?
37
Geometry - Tell whether the two figures are congruent
Congruent?
Congruent?
Congruent?
Congruent?
Congruent?
Congruent?
16
6
6
16
16
6
6
16
Congruent?
Congruent?
38
Geometry - Line of Symmetry
What is the line of
symmetry?
A. The line where two points
meet.
B. A line that divides a
figure into mirror images.
C. A line that extends into
space forever.
Draw the line of symmetry
for this figure.
Draw the line of symmetry
for this figure.
Draw the line of symmetry
for this figure.
Draw the line of symmetry
for this figure.
Draw the line of symmetry
for this figure.
Draw the line of symmetry
for this figure.
Draw the line of symmetry
for this figure.
39
Symmetry & Kemetic Mdu Ntr (Hieroglyphic) Alphabet
List the ones that are symmetrical:
Twisted flax
H
vulture
A
Placenta
h
Reed leaf
I
Animal’s belly
CH
Two leaves
Y
Folded cloth
S
Arm & hand
A
Pool
SH
Quail chick
W
Hill slope
K
Foot
B
Basket
K
Mat
P
Jar stand
G
Horned viper
F
Loaf
T
Owl
M
Tethering rope
TH
Water
N
Hand
D
Mouth
R
Snake
DJ
Courtyard
H
40
Three Dimensional Objects - Space Figures
Polygons and circles are flat, or two-dimensional objects. They have length and width but no height or
depth. Figures that have height or depth in addition to length and width are three-dimensional or space
figures. Among these are cubes, prisms, pyramids and spheres.
Cubes, prisms, pyramids and other similar solids have sides that we call faces. Faces are flat surfaces
that are in the shapes of polygons. Faces meet at edges. The edges are line segments. The line segments
meet in vertexes.
Space Objects
41
Geometry - Space Figures
PYRAMID
CUBE
RECTANGULAR
PRISM
CYLINDER
CONE
42
SPHERE
Geometry - Space Figures
lateral face
vertex
edge
Face
base
Cubes have six faces. Each face is a
square.
triangular
face
Prisms have two parallel, congruent
polygon-shaped bases. The sides of
base
prisms are all parallelograms. Each
A Pyramid’s base can have the shape of
face that is not a base is called a lateral any polygon like the prism. All other
face.
faces of a pyramid are triangular.
vertex
base
base
Cones have one flat, circular base that
rises to a point(the vertex).
Cylinders are solids with two circular
bases.
43
Spheres have no flat faces and no
vertices. A sphere has the outline of a
circle when viewed at an angle.
Working with Three Dimensional Objects
1. A can of corn is similar to a ________________.
a. sphere
b. cylinder
c. cube
d. prism
2. This apple is similar to a _________________.
a. sphere
b. cylinder
c. cube
d. prism
3. All three-dimensional objects including spheres have edges.
Circle:
True or False
4. A cube has ___________ faces.
5. A cone has a ___________ base.
a. rectangular
b. triangular
c. circular
6. Planet Earth is shaped like a _________________.
a. sphere
b. cylinder
c. cube
d. prism
44
d. square
Tessellations
A Tessellation is a pattern that repeats itself to cover a flat surface such as a wall, ceiling or floor. Look around the room.
Do you see any tessellations?
What polygon is being used to make What polygon is being used to make What polygon is being used to make
the tessellation?
the tessellation?
the tessellation?
Can you think of a polygon to make Can you think of another polygon Can you think of another polygon to
a tessellation? Draw your
to make a tessellation? Draw your
make a tessellation? Draw your
tessellation above.
tessellation above.
tessellation above.
45
Fractals
A Fractal is a geometric shape which (a) is self similar and (b) has fractional (fractal) dimensions. Fractal geometry is
the language used to describe, model and analyze complex forms found in nature.
The Sierpinski Triangle, a famous fractal.
Creating a fractal
1. Draw an equilateral triangle with midpoints.
2. Connect the midpoints.
3. Color in all the triangles except for the central one.
4. Repeat steps 2 –3 for each new triangle.
The Sierpinski Triangle can be created from Pascal’s Triangle by shading out all the little triangles except for the odd
numbered ones.
46
Create
A
Cube!
47
Create
A
Kemetic Pyramid!
48
Mental Math/Cumulative Review
1. Write 5:00 p.m. in military time.
2. Your head is shaped like a _________________.
a. sphere
b. cylinder
c. cube
d. prism
3. Find the perimeter of this pentagon if all sides are equal to 4cm.
4. The trapezoid is ____________ in line.
a. third
b. first
c. fifth
d. sixth
5. Circle the scalene triangle.
a.
b.
c.
d.
6. Draw a parallelogram.
49
Mental Math/Cumulative Review
7.
a.
b.
c.
d.
How many rectangles are there?
Which shape has the least amount?
How many rhombuses are there?
Which shape has the most?
6
5
4
3
2
1
8. How much longer is line segment a than line segment b?
line segment a = 10cm
9. If it is 10:15p.m. now, what time was it 6 minutes ago?
a. 10:21 p.m.
b. 10:09 p.m.
c. 10:09 a.m.
10. Draw an acute angle. Locate the vertex.
11. Are these figures congruent?
12. Create a tessellation using triangles.
50
line segment b = 7cm
d. 10:06 p.m.
Mental Math/Cumulative Review
13. Locate the base and vertex of this cone.
14. What type of angle is formed when it is 3:06a.m.?
a. reflex
b. obtuse
c. right
d. acute
15. Draw a line segment.
16. A ray extends in one direction infinitely.
Circle:
True or False
17. If the total perimeter of this triangle is equal to 9cm, what is the length of the missing side?
2cm
4cm
?
51
ADDITION & SUBTRACTION - no regrouping
25
+ 20
25
-20
73
+14
74
-14
31
+35
35
-31
65
+24
65
-24
34
+42
42
-31
53
+30
53
-30
74
+24
74
-24
22
+15
25
-12
13
+36
36
-13
30
+56
56
-30
23
+32
33
-23
39
+60
69
-30
61
+23
63
-21
68
+11
68
-11
47
+12
47
-12
16
+12
16
-12
24
+51
54
-22
20
+60
60
-20
27
+40
47
-24
54
+23
54
-23
52
ADDITION & SUBTRACTION - no regrouping
Add from right to left
253
+ 202
254
-201
733
+142
747
-142
315
+353
359
-316
655
+243
655
-243
3417
+4282
4258
-3124
5342
+3056
5342
-3021
7459
+2430
7459
-2430
2236
+1563
2563
-1252
13341
+36658
36425
-13312
30556
+56433
56098
-35074
23945
+32034
33754
-23532
39247
+60742
69574
-30462
613358
+236641
635458
-212335
685568
+114321
680986
-110624
472395
+127503
477324
-124212
163924
+126065
169978
-127856
2498531
+5101267
5483649
-2261428
2057468
+6031521
6009655
-2007324
2789012
+4010986
4736985
-2435961
54432721
+23257167
54882541
-23671310
53
Additional Activities
Have students design and build a house using toothpicks or balsa wood. After the house is complete have
them describe the house geometrically. For Example:
a. The roof of this house is shaped like a trapezoid.
b. The windows are quadrilaterals/rectangles.
c. The chimney is shaped like a prism.
Students can draw a car and repeat the above activity.
Have students go around the school and describe the shapes of different objects in the school.
Students can create angles with their arms.
Ask students to show a specific time with their arms and then tell what kind of angle.
Students can measure objects around school or home to find perimeter.
54
Daily Drill
Telling Time
Have students record the time each day they come to class. Let one student come to the front and
give the correct time.
Use a manipulative to tell the time by each hour, each half hour, each quarter hour, by ten minute
and five minute intervals.
Geometry Match
Draw all the shapes, angles, etc. on a set of index cards. Draw the words that correspond to these geometric shapes on a
different set of cards. Scramble the two sets of cards together. Have students match the geometric shapes to the correct
word.
“Geo Fish!”
Create geometric flash cards with at least four duplicates of each type of card. Make different sets of cards, I.e., angles,
types of lines, etc. Shuffle the cards and deal to student groups, (between 2-4 students in a group). This is similar to
playing go fish. Students then have to make matches with the cards in their hand by requesting that card from another player. If the other player doesn’t have the requested card, the tell the player go “Geo Fish!”.
55
Across The Curriculum
SCIENCE: GALAXY EXPLORATION
Goal: To demonstrate exploration of space through knowledge of galaxy.
Objectives:
1. Identify 3 major constellations
2. Describe and explain the space shuttle inclusive of multicultural contributions. (Ex: African—American
astronauts like Ron McNair, Mae Jemison, Guion Bluford )
3. Identify 5 major constellations
4. Explain directions
5. Explain and demonstrate gravity
6. Identify 10 constellations
7. Describe and explain meteors, asteroids, comets
HISTORY/GEOGRAPHY: MULTICULTURAL CONTRIBUTIONS
Goal: To identify great civilizations throughout time
Objectives:
1. Describe and explain 5 major ancient civilizations of people of color
2. Describe and explain the environment and resources that led to their development
3. Describe and explain the peoples, beliefs and economics
4. Explain their great contributions to the world
4. Describe and explain the reason for their downfall
5. Locate and explain their celebrations and rituals
*How would ithe world be today if these countries had never existed?
56
Across The Curriculum
LANGUAGE ARTS: GREAT AFRICAN EMPIRES AND MAAFA
Goal: To understand the significance of ancient empires to world civilization.
Objectives:
1. Listen to and read stories of the great empires
2. Name 3 major empires and 3 kings or queens associated with the empires
3. Show location of empires on a map
4. Name other countries that developed from the ancient kingdoms
5. Name the leaders of the contemporary civilizations that currently exist in those countries
6. Explain current contributions of those countries
HEALTH: LIFE OF KINGS AND QUEENS
Goals: To understand the major health issues that affect the world
Objectives:
1. Describe a healthy meal for Breakfast, Lunch and Dinner (A healthy diet)
2. Explain benefits of a healthy diet
3. Name a disease that affeet peoples of different continents/countries/ethnicities
4. Discuss ways of preventing disease
5. Discuss lifestyle for a healthy life
57
Across The Arts
Physical Education
Students will do push-ups counting by threes from 3- 30 in English and another language. One class will make a 360
degree circle by holding hands while another class makes the diameter and another the radius. Other activities include
making parallel lines, perpendicular lines, congruent lines, horizontal lines, vertical lines and intersecting lines.
Music - Timeline of Songs
Students will sing songs from different countries that they have studied
Art
Students will make a clock using a paper plate and brass fasteners and construction paper
Cooking
Star sandwich for science
Ingredients Loaf of bread
Sliced cheese
Soft spread margarine
Turkey ham slices
Star cookie cutter
Directions -
Spread margarine on a slice of bread
Put a slice of cheese on top
Cut out stars from the turkey ham
Put the stars on top of the cheese
Put in the oven on 350 degrees and bake until cheese melts
58
59
Mathematics - Change
T
he people of Kemet were not static - they were didactic. This means
they were constantly changing and growing in response to their
environment. They even developed a system of multiplication by
doubling.
Change is critical for growth and development. Everything created by
humans is engineered and to engineer, knowledge of advanced mathematics
is necessary. Multiplication and division, like addition and subtraction,
are reciprocal processes that create number patterns. To achieve the greatness
of our ancestors, Nia (purpose) must be maintained to acquire the skills
necessary to succeed. Using these math skills enables creativity in the new
age of technology.
60
Change: Nia and Reciprocity
MATHEMATICS: CHANGE
Goal: To understand and compute using multiplication and division while finding area and perimeter.
Objectives:
1. Recite multiplication tables 10, 5, 3, 2, and 1
2. Recite inverse operation, (division tables)
3. Fill in missing blanks for tables
4. Define and compute exponents
5. Define area of square, rectangle and triangle
6. Find area of geometric figures
7. Recite and write multiplication tables 1-10
8. Recite and write inverse operation, (division tables)
9. Compute area of square, rectangle and triangle
10. Find total perimeter of truss
11. Practice addition, subtraction, multiplication and division problems
61
Vocabulary
Multiplication—The act of adding a number to itself a certain number of times.
Multiplicand—A number that is to be multiplied by another number.
Multiplier—A number by which another number is to be multiplied.
Product—the answer to a multiplication problem.
Division—The act of separating a number into two or more parts or groups.
Dividend—A number to be divided.
Divisor—The number by which the dividend is divided.
Quotient—The answer to a division problem.
Exponent—A number or symbol placed to the right of and above another number, symbol, or expression, denoting the
power to which the latter is to be raised.
Root—A quantity taken an indicated number of times as an equal factor, the base in an exponential expression.
Logarithm—The exponent that indicates the power to which a number is raised to produce a given number.
There are three major systems of measurement units in wide use; the US Customary System, the British Imperial System, and the International or Metric System. We use the US Customary System.
62
Vocabulary
Measure—To find the size, amount, capacity, or degree.
Area—The measure of a region, expressed in square units.
Perimeter—The distance around a figure.
63
Historical Look
India
The Harappan people of India, 2500 BCE, was followed by the Vedic civilization. The Vedic civilization, parent of modern
India, used the gunja seed, similar to the grain in English measure, as the unit of weight for precious metals.
Scotland
John Napier of Scotland, circa 1600, solved multiplication problems using sets of rods. To multiply 13 by 2 do the following:
Draw a square and divide it in half vertically. Write 1 and 3 across the top of each new rectangle and the 2 to the right
of the second rectangle:
1
3
1
3
1
3
1
3
0
2
0
0
2
0
2
2
6
2
2
2
6
6
Divide each rectangle in half diagonally. Multiply the 3 by the 3. Write the ones in the bottom triangle and the tens in
the top triangle. Repeat for 1 and 2.
To find the product add the numbers along the diagonals. The product of 13 and 2 is 26.
64
Multiplication and Division
Multiplication and division, like addition and subtraction, are inverse operations of each other.
Multiplication is a faster form of addition. To multiply is to add a series of one number to itself a specific number of
times. This is determined by the multiplier. A few of the signs for multiplication are: x and •.
4 x 3 = 12 (4 + 4 + 4 = 12)
and
3 • 4 = 12 (3 + 3 + 3 + 3 = 12)
In the equation 4 x 3 = 12,
4 is the multiplier
3 is the multiplicand
12 is the product
Division is the process of finding out how many times one number will fit into another. The signs for division are:
÷, and — (the fraction bar).
12 ÷ 4 = 3 (4 goes into 12 three times because 3 x 4 = 12)
12 ÷ 3 = 4 (3 goes into 12 four times because 4 x 3 = 12)
In the equation 12 ÷ 4 = 3,
12 is the dividend
4 is the divisor
3 is the quotient
65
Multiplication and Division
Multiplication and division are used to solve many problems in life. Among these are your weight, the amount of
money you earn, how many days you attend school in one year, how many treats your teacher has to buy for class, etc.
Ex. Ms. Brooks has 5 students in her class and she wants to give each one of them 2 treats. How many treats does she
need to buy?
There are several ways to solve this problem:
1. Hold up two fingers and count by 5’s
2. Hold up five fingers and count by 2’s
3. Add 5 + 5
4. Add 2 + 2 + 2 + 2 + 2
By using either of these techniques you will find that Ms. Anderson has to buy 10 treats for her class.
To check by the inverse operation: 10 treats ÷ 5 students = 2 treats each
Ex. Mr. Anderson is making a photo album of his class. He has collected 12 pictures and has 6 pages in his album.
How many pictures can he put on each page?
There are several ways to solve this problem as well:
1. Draw 12 lines, count 6 and put a ring around them, count 6 again and put a ring around them. Count
how many rings you have when you have all the lines ringed.
2. Ask yourself, “6 times what number equals 12?”
3. Count on your fingers by 6’s until you get to 12, the number of fingers you’re holding up when you get
to 12 is the answer.
By using either one of these techniques you will find that Mrs. Thompson can fit 2 pictures on each page.
To check by the inverse operation: 2 pictures x 6 pages = 12 pictures total
66
Multiplication & Division Facts
5X1=5
5÷1=5
1x5=5
5÷5=1
5X2=10
10÷2=5
2x5=10
10÷5=2
5X3=15
15÷3=5
3x5=15
15÷5=3
5X4=20
20÷4=5
4x5=20
20÷5=4
5X5=25
25÷5=5
5X6=30
30÷6=5
6x5=30
30÷5=6
5X7=35
35÷7=5
7x5=35
35÷5=7
5X8=40
40÷8=5
8x5=40
40÷5=8
5X9=45
45÷9=5
9x5=45
45÷5=9
5X10=50
50÷10=5
10x5=50
50÷5=10
5X11=55
55÷11=5
11x5=55
55÷5=11
5X12=60
60÷12=5
12x5=60
60÷5=12
(also equivalent to 5²)
67
Multiplication & Division Facts
2X1=2
2÷1=2
1x2=2
2X2=4
4÷2=2
2X3=6
6÷3=2
3x2=6
6÷2=3
2X4=8
8÷4=2
4x2=8
8÷2=4
(also equivalent to 2²)
2X5=10
10÷5=2
5x2=10
10÷2=5
2X6=12
12÷6=2
6x2=12
12÷2=6
2X7=14
14÷7=2
7x2=14
14÷2=7
2X8=16
16÷8=2
8x2=16
16÷2=8
2X9=18
18÷9=2
9x2=18
18÷2=9
2X10=20
20÷10=2
10x2=20
20÷2=10
2X11=22
22÷11=2
11x2=22
22÷2=11
2X12=24
24÷12=2
12x2=24
24÷2=12
68
Multiplication & Division Facts
10X1=10
10÷1=10
1x10=10
10X2=20
20÷2=10
2X10=20
20÷10=2
10X3=30
30÷3=10
3x10=30
30÷10=3
10X4=40
40÷4=10
4x10=40
40÷10=4
10X5=50
50÷5=10
5x10=50
50÷10=5
10X6=60
60÷6=10
6x10=60
60÷10=6
10X7=70
70÷7=10
7x10=70
70÷10=7
10X8=80
80÷8=10
8x10=80
80÷10=8
10X9=90
90÷9=10
9x10=90
90÷10=9
10X10=100
10X11=110
110÷11=10
11x10=110
110÷10=11
10X12=120
120÷12=10
12x10=120
120÷10=12
(also equivalent to 10²)
100÷10=10
69
Multiplication & Division Facts
3X1=3
3÷1=3
1x3=3
3X2=6
6÷2=3
2x3=6
6÷3=2
3X5=15
15÷5=3
5x3=15
15÷3=5
3X9=27
27÷9=3
9x3=27
27÷3=9
3X3=9
9÷3=3
3X4=12
12÷4=3
4x3=12
12÷3=4
3X6=18
18÷6=3
6x3=18
18÷3=6
3X7=21
21÷7=3
7x3=21
21÷3=7
3X8=24
24÷8=3
8x3=24
24÷3=8
3X10=30
30÷10=3
10x3=30
30÷3=10
3X11=33
33÷11=3
11x3=33
33÷3=11
3X12=36
36÷12=3
12x3=36
36÷3=12
(also equivalent to 3²)
70
Multiplication Tables
1x1=1 or 12=1
2x1=2
3x1=3
4x1=4
5x1=5
6x1=6
1x2=2
2x2=4 or 22=4
3x2=6
4x2=8
5x2=10
6x2=12
1x3=3
2x3=6
3x3=9 or 32=9
4x3=12
5x3=15
6x3=18
1x4=4
2x4=8
3x4=12
4x4=16 or 42=16
5x4=20
6x4=24
1x5=5
2x5=10
3x5=15
4x5=20
5x5=25 or 52=25
6x5=30
1x6=6
2x6=12
3x6=18
4x6=24
5x6=30
6x6=36 or 62=36
1x7=7
2x7=14
3x7=21
4x7=28
5x7=35
6x7=42
1x8=8
2x8=16
3x8=24
4x8=32
5x8=40
6x8=48
1x9=9
2x9=18
3x9=27
4x9=36
5x9=45
6x9=54
1x10=10
2x10=20
3x10=30
4x10=40
5x10=50
6x10=60
1x11=11
2x11=22
3x11=33
4x11=44
5x11=55
6x11=66
1x12=12
2x12=24
3x12=36
4x12=48
5x12=60
6x12=72
7x1=7
8x1=8
9x1=9
10x1=10
11x1=11
12x1=12
7x2=14
8x2=16
9x2=18
10x2=20
11x2=22
12x2=24
7x3=21
8x3=24
9x3=27
10x3=30
11x3=33
12x3=36
7x4=28
8x4=32
9x4=36
10x4=40
11x4=44
12x4=48
7x5=35
8x5=40
9x5=45
10x5=50
11x5=55
12x5=60
7x6=42
8x6=48
9x6=54
10x6=60
11x6=66
12x6=72
7x7=49 or 72=49
8x7=56
9x7=63
10x7=70
11x7=77
12x7=84
7x8=56
8x8=64 or 82=64
9x8=72
10x8=80
11x8=88
12x8=96
7x9=63
8x9=72
9x9=81 or 92=81
10x9=90
11x9=99
12x9=108
7x10=70
8x10=80
9x10=90
10x10=100 or 102=100 11x10=110
7x11=77
8x11=88
9x11=99
10x11=110
11x11=121 or 112=121 12x11=132
7x12=84
8x12=96
9x12=108
10x12=120
11x12=132
71
12x10=120
12x12=144 or 122=144
Creating Fact Families using The Inverse Operation - Complete the table.
1x1=1
1÷1=1
2x1=2
3x1=3
1x2=2 2x1=2 2÷2=1 2÷1=2
2x2=4 4÷2=2
3x2=6
1x3=3 3x1=3 3÷3=1 3÷1=3
2x3=6 3x2=6 6÷2=3 6÷3=2
3x3=9
1x4=4
2x4=8
3x4=12
1x5=5
2x5=10
3x5=15
1x6=6
2x6=12
3x6=18 6x3=18 18÷6=3 18÷3=6
1x7=7
2x7=14
3x7=21
1x8=8
2x8=16
3x8=24
1x9=9
2x9=18
3x9=27
1x10=10
2x10=20
3x10=30
1x11=11
2x11=22
3x11=33
1x12=12
2x12=24
3x12=36
4x1=4
5x1=5
6x1=6
4x2=8
5x2=10
6x2=12
4x3=12
5x3=15
6x3=18
4x4=16
5x4=20
6x4=24
4x5=20
5x5=25
6x5=30
4x6=24
5x6=30
6x6=36
4x7=28
5x7=35
6x7=42
4x8=32
5x8=40
6x8=48
4x9=36
5x9=45
6x9=54
4x10=40
5x10=50
6x10=60
4x11=44
5x11=55
6x11=66
4x12=48
5x12=60
6x12=72
72
Creating Fact Families using The Inverse Operation - Complete the table.
7x1=7
8x1=8
9x1=9
7x2=14
8x2=16
9x2=18
7x3=21
8x3=24
9x3=27
7x4=28
8x4=32
9x4=36
7x5=35
8x5=40
9x5=45
7x6=42
8x6=48
9x6=54
7x7=49
8x7=56
9x7=63
7x8=56
8x8=64
9x8=72
7x9=63
8x9=72
9x9=81
7x10=70
8x10=80
9x10=90
7x11=77
8x11=88
9x11=99
7x12=84
8x12=96
9x12=108
10x1=10
11x1=11
12x1=12
10x2=20
11x2=22
12x2=24
10x3=30
11x3=33
12x3=36
10x4=40
11x4=44
12x4=48
10x5=50
11x5=55
12x5=60
10x6=60
11x6=66
12x6=72
10x7=70
11x7=77
12x7=84
10x8=80
11x8=88
12x8=96
10x9=90
11x9=99
12x9=108
10x10=100
11x10=110
12x10=120
10x11=110
11x11=121
12x11=132
10x12=120
11x12=132
12x12=144
73
Multiplication Table
X
0
1
2
3
4
5
6
7
8
9
10
11
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
10
11
12
2
0
2
4
6
8
10
12
14
16
18
20
22
24
3
0
3
6
9
12
15
18
21
24
27
30
33
36
4
0
4
8
12
16
20
24
28
32
36
40
44
48
5
0
5
10
15
20
25
30
35
40
45
50
55
60
6
0
6
12
18
24
30
36
42
48
54
60
66
72
7
0
7
14
21
28
35
42
49
56
63
70
77
84
8
0
8
16
24
32
40
48
56
64
72
80
88
96
9
0
9
18
27
36
45
54
63
72
81
90
99
108
10
0
10
20
30
40
50
60
70
80
90
100
110
120
11
0
11
22
33
44
55
66
77
88
99
110
121
132
12
0
12
24
36
48
60
72
84
96
108
120
132
144
74
Complete the Multiplication Table
X
0
0
0
1
2
3
4
1
2
3
4
5
6
1
4
9
16
5
6
7
8
9
10
11
12
75
7
8
9
10
11
12
Create a Multiplication Table
X
76
Working with Multiplication and Division
1. Ms. Smith has 15 pieces of candy and 3 students to give treats. How many pieces will each student receive.
15 ÷ 3 =
2. If you had 3 uncles and they each gave you 2 dollars, how much money would you have?
(hold up 3 fingers and count by 2’s)
Using the graph to the right:
3. If each guitar represents 3, how many guitars are there?
3x3=
4. If each radio represents 2, how many radios are there?
5. If each piano represents 10, how many pianos are there?
6. If there are 10 rows in the auditorium and 6 people can sit in each row, how many people can be seated in the
auditorium? 10 x 6 =
7. If there are 5 rows in your classroom and 5 people can sit in each row, how many people can sit in your classroom?
8. If 20 people were able to sit in a classroom that had 4 rows, how many people sat in each row?
20 ÷ 4 = ( 4 times what number equals 20)
9. If 30 people were able to sit in an auditorium that had 10 rows, how many people sat in each row?
77
Exponents
On the previous multiplication and division fact sheets, there were problems such as 2 x 2 = 4 (also read as 2²).
When a number has a smaller number at the top to its right it is being powered to an exponent (ex. 2³). Exponents show
how many times a number, the base, is used as a factor. The answer is a power of the factor raised to the exponent.
5 x 5 = 5² =25
It is read as “5 to the second power” or “5 squared.”
2 x 2 = 2² =4
It is read as “2 to the second power” or “2 squared.”
10 x 10 = 10² =100
It is read as “10 to the second power” or “10 squared.”
3 x 3 x 3= 33 =27
It is read as “3 to the third power” or “3 cubed.”
Can you show what five to the fourth power would look like?
2 to the third power?
4 squared?
78
More on Exponents
Exponents show how many times a number is used as a factor. The answer that you get is said to be a
power of the factor raised to the exponent.
5 x 5 x 5 = 5³
(3 factors of 5)
base
exponent
The above problem is read as “five to the third power.”
To find the answer:
5³=
5 x 5 x 5=
5 x 5 = 25
(compute the first two)
25 x 5 = 125
(compute the last one)
So, five to the third power is equal to 125.
Can you compute two to the third power?
23=
79
Working with Exponents
1. 1² =
2. 33 =
3. 4² =
4. 6² =
5. 10² =
6. 15 =
7. 3³ =
8. 24 =
80
Exponents, Roots, and Logarithms
The inverse operation of exponents is roots or radicals and logarithms. The root is the base in an exponential expression.
The logarithm (or simply log) is the exponent. For instance,
Exponent
23 = 8
52 = 25
Root
The cubed root of 8 is 2
The square root of 25 is 5
Logarithm
Log base 2 of 8 is 3
Log base 5 of 25 is 2
Use the color codes above to complete the following:
42 = 16
The _____________ root of 16 is ___
Log base ___ of 16 is 2
24 = ___
The______________ root of ___ is ___
Log base ____ of ____ is ___
The square root of 36 is 6
Log base ____ of ____ is ___
33 = ___
____ __ = ___
81
Multiplication - Fill in the missing blanks
Count by
2’s, fill in
the blanks
2
8
Count by
3’s, fill in
the blanks
Count by
5’s, fill in
the blanks
18
9
24
10
30
Count by
10’s, fill in
the blanks
50
82
Engineers & Multiplication
Engineers use multiplication to help them perform several tasks. One in particular is calculating the area of different
surfaces and figures. For example, to calculate the amount of steel needed to build this Warren Truss (a truss is a major
type of engineering structure)*:
3
3
3
First find the perimeter of one triangle:
Remember the perimeter is the distance around a figure. The perimeter of one triangle is 9 because each side is equal to 3.
Then find out how many triangles there are in all:
If you count correctly, you will see that there are 21 triangles.
Then use multiplication to find the total perimeter of the truss:
21 x 9 = 189
*each member is doubled.
83
A Briefing on Measuring Length and Distance
The U.S. Customary System or the English System is our standard for measuring length. The Metric system is used
in Europe and other parts of the world.
The U.S. Customary System:
The Metric System:
Measure
Abbreviation
Equivalent
Measure
Abbreviation
Equivalent
inch
in.
12 inches
equals 1 foot
meter
m
1 meter equals
100 centimeters
foot
ft.
1 foot equals 12
inches
centimeter
cm
100 centimeters
equals 1 meter
yard
yd.
3 feet equals 1
yard or 36
inches equals 1
yard
kilometer
km
1000 meters
equals 1
kilometer
84
Computing Area
10cm
4cm
5in
4m
The area of a square is
S² or (side X side).
The area of this square is
25in2 because 5x5=25
Another way to find the
perimeter of a square is to
multiply the length of 1 side
times 4.
The perimeter of this square is
4x5=20in
The area of a rectangle is
length x width.
3m
Length = how long
Width = how wide
The area of this rectangle is
because 10x4=40.
40cm2
Another way to find the perimeter of a
rectangle is to multiply the length by 2
and then the width by 2 and add.
The perimeter of this rectangle is 28cm
because:
The area of a triangle is (base
x height)÷2.
Base = the bottom of a
triangle
Height = how tall
The area of this triangle is
6m2 because 4x3=12, and
12÷2=6.
2x10=20
2x4=8
20+8=28
85
Multiplication - Using a ruler to measure the sides, find the perimeter & area of each figure.
86
Mental Math/Cumulative Review
1. Write = or ‡
a. 5 x 3 ____ 3 x 5
b. 4 x 5 _____ 2 x 7
c. 2 x 6 _______ 3 x 4
d. 4 x 1 _____ 16 ÷4
2. What is a tessellation? Draw a tessellation with cubes.
Using the graph to the right:
3. If each guitar represents 5, how many are there?
4. If there are 8 pianos total, how many does each piano
represent?
5. Write 5:00p.m. in military time.
6. There are 14 students in Dr. Corley’s class. If we split them into two teams, how many students will be on each team?
7. These are ______________ angles.
a. supplementary
b. complementary
c. acute
8. If it is 9:30a.m. now, what time will it be in 15 minutes?
9. What is the area of this triangle if the base is 2 cm and the height is 8 cm?
87
d. reflex
MULTIPLICATION & DIVISION
7x6=
459 =
4 x6 =
8÷8 =
2x5=
42÷6 =
0÷2 =
0x8=
5÷5 =
5x7=
8÷2 =
1x5=
8x9=
24÷8 =
2x8=
12÷2 =
7x1=
18÷6 =
32÷8 =
4x2=
27÷9 =
6x7=
45÷5 =
0x4=
6x1=
15÷5 =
4x9=
42÷6 =
9x2=
7÷7 =
56÷8 =
5x6=
18÷2 =
6x3=
72÷9 =
2x0=
3x8=
20 ÷4 =
9x6=
36÷4 =
9x9=
36÷6 =
25÷5 =
3x3=
54÷9 =
7x5=
28÷7 =
3x7=
88
MULTIPLICATION & DIVISION
6x6=
455 =
3 x6 =
16÷8 =
2x7=
42÷7 =
0÷9 =
4x8=
35÷5 =
5x9=
18÷2 =
8x5=
9x9=
56÷8 =
2x4=
14÷2 =
7x6=
54÷6 =
32÷4 =
4x4=
27÷3 =
6x6=
45÷9 =
7x4=
6x4=
30÷5 =
3x9=
42÷7 =
9x9=
28÷7 =
64÷8 =
5x7=
18÷9 =
8x3=
72÷8 =
6x0=
3x7=
28 ÷4 =
6x6=
20÷4 =
10 x 9 =
18÷6 =
15÷5 =
3x8=
54÷6 =
7x7=
28÷4 =
4x7=
89
MULTIPLICATION & DIVISION
9
X1
8
X0
6 0
1
X1
1
X1
1
1
5
7
9
6
9
1
3
X3
2
6
3
10
4
X0
3
10
3
X1
1
90
5
1
10
1 3
6
X1
6
4
X4
3
4 4
8
X8
8 8
4
X1
0
5
X1
0
0
3
X1
7
X7
7 7
0
X0
4
7
4
X0
9 0
4 0
6
X6
10
X10
7
X1
1 0
2
0
X0
2
5 0
2
X0
2
X2
1
5
X0
9
X0
2 0
1
5
X5
9
x9
1 6
0
X1
8
X0
2
X1
3 0
6
X1
1 1
7 0
5
3
X0
1 9
1
9
1 4
9
X1
MULTIPLICATION & DIVISION
9
X2
8
2
18
8
X4
32
1
X9
1
1
X1
40
9
X9
7
14
0
X8
2
9
81
7
X2
6
2
X2
3
6
X3
5
1 8
0
3 9
4 20
3
X7
2 18
6
X2
12
10
X10
25
9
X3
2
X9
2
X9
1 10
5
X8
3
3 18
9
8
X0
8 0
5
3
X3
10
7
63
7
X0
10
3
X3
5
91
25
2
0
X5
4
5
X5
3
X5
10 70
5
X9
3 15
6
X6
6 6
4
X7
3 21
7
X9
4
X4
4 16
9 27
4
X5
10 0
8
48
4
X6
9 45
4 28
8
X6
4 24
9
X9
ADDITION & SUBTRACTION - no regrouping
424
253
+ 202
234
-202
123
733
+142
755
-142
311
315
+353
348
-316
101
655
+243
543
-243
2100
3415
+4282
4225
-3124
1501
5342
+3056
5342
-3231
110
5459
+2430
7569
-2438
5200
2236
+1563
2353
-1252
20000
13841
+36058
36525
-13302
13010
30556
+56433
56398
-35054
43020
23835
+32034
34754
-21612
60742
19247
+20010
58875
-30462
130001
613357
+236641
632448
-212335
200110
685567
+112321
465986
-110926
400101
272395
+127503
375324
-124312
610012
163921
+126065
137968
-127846
1300201
2498531
+5101267
2463649
-2261444
1911134
2057432
+4031321
6249655
-2217342
3104235
2784012
+4010421
4536985
-2432470
21110112
54432721
+23257165
34792531
-23662320
92
ADDITION & SUBTRACTION - no regrouping
4
2
+2
25
- 3
1
7
+1
1
2
3
+4
32
-01
5
1
2
+3
50
-30
7
4
1
+3
36
- 3
2
4
3
+5
56
- 2
5
4
6
+2
44
-21
3
5
6
+1
68
-22
1
2
3
2
+5
34
-22
10+20+30=
2
3
+3
54-13=
33
-11
3
5
+1
65
- 4
59
-24
6
2
2
+1
25
- 2
9+3+2+4=
33
-23
1
2
3
+6
69
-33
5+3+0=
36
-12
7
9
1
+1
6
4
1
+2
22
30
27
+40
60-20=
93
46
-24
31
10
54
+23
98-12=
54
-24
Additional Activities
Have students design a floor plan using geometric shapes. They can use a ruler to measure the
dimensions or use graphing paper. They can then calculate the area and perimeter of each room.
A thatch home in Kenya shaped like a cone.
Using any program that creates slide shows, such as Kid Pix or Powerpoint, have kids design a
slide show explaining the basic operations of mathematics. Additionally, they can type their
multiplication tables in a word processing program or Excel.
9’s
Have students recognize the patterns in
multiplication and come up with
cartoons, stories, rhymes, etc. to remember
them. For example:
09
18
27
36
45
54
Double Trouble 11’s, Tekhnu (obelisk) 3’s, Blast off 9’s; in order for
This rocket to take off, you must do a count down twice. After
counting from 0 to 9 twice you have your multiples of 9.
94
63
72
81
90
Daily Drill

Have students complete a multiplication/division fact family each morning.

Choose a table for students to complete each day by following the example below:
5X0=0
5X1=5
5 x 2 =10
5 x 3 = 15
.
.
.
.
5 x 12 = 60
0X5=0
1X5=5
2 x 5 = 10
3 x 5 = 15
0 ÷5 = 0
5÷ 1 = 5
10÷ 2 = 5
15÷ 3= 5
12 X 5 = 60
60÷ 12 = 5
Can not divide by zero
5 ÷5 = 1
10 ÷5 = 2
15 ÷5 = 3
60 ÷5 = 12
Have students label the parts of the equation, circle and label a fact family, point out the inverse operation, commutative property, property of zero, and the identity property of multiplication.
95
Across The Curriculum
SCIENCE: ENERGY
Goal: To understand and demonstrate types of energy
Objectives:
1. Demonstrate and explain sources of energy including wind, sun, water, and fire
2. Demonstrate and explain kinetic and potential energy
3. Demonstrate and explain pulleys
4. Demonstrate and explain magnets
5. Demonstrate and explain circuits
6. Demonstrate and explain an engine
*Create a project using a form of energy discussed.
HISTORY/GEOGRAPHY: REVOLUTION
Goal: To become aware of revolutionary changes that transform societies
Objectives:
1. Recognize and explain form of oppression that have been used to dominate peoples of the world
2. Describe industrial revolution
3. Name and describe contributions of African Americans’ and other people of color in the revolutionary
processes
4. Name and locate 50 states and all of the Caribbean islands
5. Present ABC’s of Black History and/or another culture
*What would life be like without machines?
*What events could possibly create another revolution?
96
Across The Curriculum
LANGUAGE ARTS: ENSLAVEMENT
Goal: To develop an understanding how bias and oppression have changed and impacted the lives of people of the
world
Objectives:
1. Discuss stories related to bias
2. Discuss life before and after the European Slave Trade
3. Identify and discuss prominent leaders that have fought against bias and oppression
4. Read and write a book report on a non-fictional narrative of an oppressed person
5. Follow the life of a particular person & list major changes in his/her life
6. Construct an adjective word wall of words that are biased
7. Write a paper comparing people or power to oppress another and people who are oppressed
8. Construct a fictional story depicting yourself as an oppressed person and describe how you would feel
HEALTH: EXERCISE
Goal: To understand the importance of exercise for all living beings
Objectives:
1. Name stages of development
2. Explain reasons for exercise
3. Develop an exercise plan
4. Develop an exercise plan for each life stage
5. Explain types of exercises needed for each life stage
6. Discuss respiratory, circulatory, skeletal and nervous systems’ need for exercise
97
Across The Arts
Physical Education
Students will do sit-ups counting by fours from 4-40 in English and alternate days with another language
Students will begin previous exercises reciting the multiplication tables of the number pattern
Students will do the bump for doubling numbers in addition
Music - How music helped change lives
Students will learn at least one popular ethnic song and will explain its meaning or purpose.
Art
Students will create a multiplication board using arts and crafts materials
Ex: String 5 plastic beads on pipe cleaners
Make a multiplication board of fives
Cooking
Students will make banana splits using double scoops to watch change in matter over time
Ingredients Vanilla ice cream
chocolate ice cream
strawberry ice cream or flavor of choice
bananas
chocolate syrup
chopped nuts
cherries
Directions -
Scoop two scoops of each flavor
Add two slices of banana
Pour on chocolate, nuts and two cherries
Count all doubles by twos
98
99
s
tudying the heavens and the universe must have been a favorite pasttime of the
ancient people of Kemet. Around 5,000 B.C.E., the people of Kemet were using an
astronomical calendar. They developed solar, stellar and lunar calendars. They
recognized that the solar year was defined by a period of 365 days, 5 hours, 48
minutes and 46 seconds—the time it takes the Earth to make one complete revolution around
the sun. Their calendar had 12 months of 30 days each adding 5 days at the end of the year
to celebrate birthdays of the Gods. Each 30 day month was divided into 3 weeks of 10 days
with 24 hours in each. The year was divided into 3 seasons to correspond with the Nile and its
effect on the people. Instead of a leap year every 4 years to account for the quarter day each
year, the Kemites added a new year every 1,460 years.
The people of Kemet associated the stars with Gods to create a circle of 360 degrees, and
the 12 signs of the zodiac. The tradition of the fascination with the heavens continues with
the Dogon people of Mali, West Africa who explained Sirius and Sirius B to contemporary
scientists.
Life for Kemites was mathematics. Kemites were self-determined to create an
understanding of order in the universe. Practicing self-determination opens the mind for
creativity.
100
Seasons: Self-Determination and Order
MATHEMATICS: EGYPTIAN ZODIAC
Goal: To develop an understanding of time concepts as they relate to the year, months, days and seasons of the
year
Objectives:
1. Name the months, days and seasons of the year in English, Kiswahili, French, Spanish and Japanese
2. Identify months, days and dates on a calendar
3. Name key facts of a calendar
4. Name the African-Centered Holidays
5. Create a calendar
6. Discuss weather and its relationship to the calendar
7. Measure temperature with a thermometer
8. Estimate temperature by season
9. Discuss hot and cold temperatures using Fahrenheit and Celsius
10. Find temperature on a thermometer
11. Compute changes in temperature
12. Graph the weather and temperature
13. Use order of operations and exponents to practice computations
101
Vocabulary
Calendar—Any of various systems of recording time in which the beginning, length, and divisions of a year are arbitrarily defined or otherwise established..
Day—The period of light between dawn and nightfall in a period of 24 hours.
Date—Time stated in terms of the day, month, and year.
Temperature— The degree of hotness or coldness of a body or environment.
Fahrenheit— Of or pertaining to a temperature scale that registers freezing point of water at 32 degrees and boiling point
at 212 degrees under standard atmospheric pressure. [Gabriel D. Fahrenheit (1686—1736) ]
Celsius— Of or pertaining to a temperature scale that registers freezing point of water at 0 degrees and the boiling point
at 100 degrees under normal atmospheric pressure. [Anders Celsius (1701—1744) ]
Thermometer—An instrument for measuring temperature, usually containing mercury, that rises and falls with temperature changes.
Weather—The state of the atmosphere at a given time and place, described by variables such as temperature, moisture,
wind velocity, and barometric pressure.
Season—One of the four divisions of the year, (Spring, Summer, Autumn, and Winter), indicated by the passage of the
sun through an equinox or solstice and derived from the apparent north-south movement of the sun caused by the fixed
direction of the earth’s axis in solar orbit.
102
Historical Look
Alaska, North America
Although the first Iditarod , “The Last Great Race”, was held in 1973, it’s history dates back to 1925, when Nome was hit by an epidemic of diphtheria. A serum was transported from Anchorage to Nenana, Alaska by train. Mushers
(dogsled drivers) then relayed the serum to the residents of the town. Near some
of the checkpoints of the race such as near the Bering Sea, wind chill temperatures can fall as low as –73 degrees Celsius( - 100 degrees Fahrenheit).
Al Grillo/Associated Press
Germany/Poland
Daniel Gabriel Fahrenheit, a German physicist, invented the alcohol thermometer in 1709. In
1714, he invented the mercury thermometer that is still in use today. He also invented the
Fahrenheit scale that is commonly used in the United States.
Sweden
Anders Celsius was an astronomer that invented the Celsius thermometer, also known as the
centigrade scale.
He was a professor of astronomy at the University of Uppsala and also studied the Aurora
Borealis, or Northern Lights.
103
The Calendar
There are 24 hours in 1 day
7 days in 1 week
12 months in 1 year
52 weeks in 1 year
365 days in 1 year
366 days in 1 leap year
(A leap year occurs every 4 years. This is why you sometimes see the year written as 365 1/4 days in a year)
Facts About the Calendar
There are 28 days in February; it is the shortest month of the year. When there is a leap year, the extra day is added to
the month of February, so during leap year there are 29 days in the month of February.
The following months have 30 days: April, June, September and November.
The following months have 31 days: January, March, May, July, August, October and December.
From Sunday to Saturday is 1 week.
Saturdays and Sundays are the weekend. There is usually no school on weekends.
104
Days of the week
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Months of the Year
January (first month)
February
March
April
May
June
July
August
September
October
November
December (last Month)
105
English
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Days of the week/months of the year in other languages:
Kiswahili
Spanish
French
Jumapili
domingo
dimanche
Jumatatu
lunes
lundi
Jumanne
martes
mardi
Jumatano
miércoles
mercredi
Alhamisi
jueves
jeudi
Ijumaa
viernes
vendredi
Jumamosi
sábado
samedi
January
February
March
April
May
June
July
August
September
October
November
December
Januari
Februari
Machi
Aprili
Mei
Juni
Julai
Agosti
Septemba
Oktoba
Novemba
Desemba
enero
febrero
marzo
abril
mayo
junio
Julio
agosto
septiembre
octubre
noviembre
diciembre
106
janvier
février
mars
avril
mai
juin
juillet
août
septembre
octobre
novembre
décembre
Japanese
Nichi•yoobi
Getsu•yoobi
Ka•yoobi
Sui•yoobi
Moku•yoobi
Kin•yoobi
Do•yoobi
Ichi•gatsu
Ni•gatsu
San•gatsu
Shi•gatsu
Go•gatsu
Roku•gatsu
Shichi•gatsu
Hachi•gatsu
Ku•gatsu
Jyuu•gatsu
Jyuuichi•gatsu
Jyuuni•gatsu
Reading a Calendar
Shows the
Month of the
year.
May
Sunday
1st day of the
month; Shows
the date of the
month.
Monday
Tuesday
Wednesday Thursday
Friday
Saturday
1
2
3
4
5
7
8
9
10
11
12
13 of of the week.
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
The Year
200_
107
6
Shows the day
Create-A-Calendar
Can you create a calendar for the year, month and date you were born?
Make sure you fill in the correct year. Put the month you were born in at the top. Fill in the days of the week
where they belong and for the day you were born, draw a picture of yourself.
Month ___________________
Days
Year ____________________
108
Finding Days and Dates On the Calendar
1.
2.
3.
4.
5.
6.
What Is the date of the fourth Wednesday in this month?
How many Fridays do we have in this month?
What is the date of the second Monday in this month?
On what day is the 25th ?
What month is it?
What is the last day in this month?
7. How many days are in this month?
8. What year is it?
Sunday
Monday
Tuesday
Wednesday Thursday
Friday
Saturday
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
109
What is weather and how does it relate to the calendar?
Weather is the way the air around you changes from throughout the year. It is the way water changes in the air. If there
were no water we wouldn’t have clouds, rain, snow, thunder or fog.
To describe weather some of the things you can say are: it’s sunny, cloudy, rainy, snowy, icy, windy or foggy.
Weather is different in different parts of the world. To describe weather over a long period of time in different places we
say “climate.” The Arctic has a cold climate while the tropical areas have hot climates.
At certain times of the year, there are certain kinds of weather that usually remain the same from year to year. We call
these seasons.
Winter - usually cold and/or stormy
Summer - warm and sunny
Spring - after winter; usually cold at night but warm during the day. The sun goes higher in the sky and the day is
longer. You set your clocks an hour ahead of time.
Autumn - also called fall. Nights are longer and cooler, usually frosty or misty in the morning.
You set your clocks back an hour.
Some places have just two seasons—wet and dry, while others have Spring, Summer, Autumn and Winter for a total of
four seasons.
110
Weather in Fahrenheit
It’s Sunny.
90°
The temperature is
hottest.
75°
It’s Windy.
The temperature is
lowered because of
the windchill.
It’s Cloudy. 67°
The temperature is
not very high because
rain is expected.
70°
It’s partly cloudy.
The temperature is
not very high.
It’s warm.
It’s rainy.
The temperature is
low because of the
rain.
111
60°
It’s Snowy.
The temperature is
coldest.
10°
Reading Temperature From A Thermometer
100°
Boiling Point
of Water
212°
Boiling
Point
of Water
98° Normal
body
temperature
37° Normal body
temperature
33° A hot day
95° A hot
day
68° Room
Temperature
F°
20° Room Temperature
32°
Freezing
point of
water
C°
112
0° Freezing point of water
Finding Temperatures
Write the letter of the problem next to the correct temperature on the
Fahrenheit thermometer. Use thermometers on the previous page.
A. 80° will be located between what two numbers?
B. If the boiling point of water is 100° in Celsius, what will this be in
Fahrenheit?
C. Locate the normal body temperature in Fahrenheit.
D. Locate a very hot day in Fahrenheit.
E. Where would -10° be located?
F. Locate the freezing point of water in Fahrenheit.
G. Locate a cold day in Fahrenheit.
113
The Rise & Fall of Temperature
During the course of a day the temperature rises and falls at different times. If you know
the initial temperature and are told how much the temperature has risen or fallen, you can
determine the final temperature.
Look at the first two examples, determine how we came up with the conclusion, and complete
the table.
Starting
temperature
Change
Final
Temperature
Conclusion
35°F
rises 12°
47°F
rise means to increase, so add
12 to 35
52°F
falls 10°
42°F
fall means to decrease, so
subtract 10 from 52
76°F
falls 4°
34°C
rises 7°
12°C
falls 6°
17°F
rises 13°
25°C
falls 11°
114
Complete a weather & temperature calendar for the current month.
Draw a picture of what the weather is like.
Sunday
Monday
Tuesday
Wednesday
115
Thursday
Friday
Saturday
Order of Operation
When working number sentences with more than one operation, the order in which you do them is very
important to get the correct answer.
To make it easier to remember, just remember this;
Please Excuse My Dear Aunt Shante.
first Parentheses
then Exponents
then Multiplication
then Division
then Add
and finally Subtract
()
x²
X
÷
+
-
This order should be followed from left to right (if operation is not in sentence, skip to next operation).
Example:
(5x2) + 3² - 5 =
(10) + 3² - 5 = Parentheses First
10 + 9 - 5 = Exponents Next
19-5 = Addition Next
14 = Then Subtract
116
Working with Order of Operation
Su
1. 17 - 3 x 2 =
d
Ad
Ex. 15 - 6 + 4=
9 + 4= (add and subtract from left to right which ever comes first)
13
ra
bt
ct
2. 9 ÷ 3 + 11 =
Multiply and Divide first!
3. 12 - 3 + 2 =
4. 6 x 7 - 8 =
5. 8 + 10 ÷ 2 =
6. 5 x 3 ÷ 5
7. 8 - 8 + 8
8. 1 + 2 x 3 - 2 ÷ 2 =
117
Working with Exponents and Order of Operations
Remember: Please Excuse My Dear Aunt Shante
1. (5 x 4) + 6=
2. (2² + 3) ÷ 7 - 1 =
3. (30 ÷10) x 3 + 6 - 3² =
Follow
The
Order!
4. 7 x (2 + 1) - 4 =
5. 8 ÷ 2³ + 19 =
6. 6² + 2²
7. 4² + (5+7) x 2 - 11 =
8. (1² +2² +3² +4²)÷ (7 x 5 -32) =
118
Input/Output Machines
÷3
x2
12
5
10
send up a 5, multiply it by 2, 10 comes down.
33 11
3
9
2
3
10
15
6
6
9
30
12
24
7
18
4
8
Send up a 4, multiply by 2, 8 comes down.
6
33 drives in, divided by 3, 11 comes out.
18 drives in, divided by 3, 6 comes out.
27
8
2
1
5
6
-1
x2
36
35
100
99
6 drives through, it’s squared and then loses 1, 35 is left.
4
3
7
8
9
10
119
10 drives through, it’s squared and then loses 1, 99 is left.
Mental Math/Cumulative Review
1. Which exponent shows this model?
a. 32
b. 21
c. 22
d. 42
2. There are 20 people in class sitting in 4 rows. How many people are sitting in each row? Which equation will show
this statement?
a. 20 - 4= ?
b. 4 x 20 = ?
c. 20 ÷4 = ?
d. 20 + 4 = ?
3. What’s the area of the shaded
region in square units?
4. Which multiplication fact will help you solve 15 ÷ 3?
a. 4 x 2
b. 3 x 15
c. 0 x 3
d. 5 x 3
5. Perimeter tells you the distance around a figure. True or false.
6. If there are 7 days in a week, how many days are in 6 weeks?
7. Are these figures congruent?
8. If it is 9:10 p.m. now, what time will it be in 16 minutes? Describe the angle made by the hands on a clock.
120
Mental Math/Cumulative Review
9. Find the perimeter of this floor plan.
11 in
5in
12in
6in
5 in.
10. How many hours are in 2 days?
11. Interpret the following bar graph:
If each shaded block represents 8, how many airplanes are there?
If each shaded block represents 6, how many cars are there?
If there are 16 trucks in all, how much does each shaded block
represent?
If there are 7 boats, how much does each shaded block represent?
12. Kweku’s mom is 32 and his dad is 38. How much older is his dad than his mom?
13. Water freezes at 32°F and 0°C. During which season do you think water will
freeze outside?
14. Hom much time will elapse between your birthday this year and your birthday next year?
121
Additional Activities
Have students create a musical skit with exponents and order of operations. If you allow the students to
do the creating, they will come up with something they really like and will remember it. They may want
to use melodies from some of their favorite songs, which may change from year to year. This does not
mean that you cannot make suggestions or corrections.
Get a piece of paper, fold it in half (vertically or horizontally). Unfold the paper. The paper is now
divided into 2 equal parts. Have students write this as 21; 2 parts and 1 crease. Next, fold it back along
the first crease and then fold it in half again. Unfold the paper you now have four boxes. Have students
write this as 22; 4 parts and 2 creases. Continue this pattern to figure out powers of 2.
122
Daily Drill

Have students write the date (month, day, and year) at the start of each class period.

Write the full date on the board or have posted in the classroom each day.
Have students create a weather journal that tells the date, time recorded, temperature, season, and weather condition, such as sunny, cloudy, etc.

Saturday, June 7, 2003
Season: Summer
High Temperature: 76° F
Low Temperature: 49° F
Mostly sunny, a few clouds
123
Across The Curriculum
SCIENCE: WEATHER
Goal: To explain weather patterns.
Objectives:
1. Identify clouds (thunder/lightening)
2. Demonstrate rain
3. Explain evaporation, condensation
4. Explain 3 states of water--solid, liquid, gas
5. Demonstrate and explain weather fronts
6. Demonstrate and explain weather instruments
7. Create weather station
8. Track daily weather conditions and graph the results
9. Describe natural disasters, weather conditions
10. Describe earthquakes and volcanic eruptions, tornadoes, hurricanes, flooding, tidal waves
*Design the perfect home to withstand any natural disaster.
HISTORY/GEOGRAPHY: CONFLICT and CONFUSION
Goal: To recognize different ways to resolve conflict.
Objective:
1. Describe segregation
2. Name prominent civil rights leaders
3. Name and explain 3 major court decisions (Dred Scott, Plessy vs. Ferguson, Brown vs. Board of Education of Topeka)
4. Name and explain civil rights legislation and court amendments
5. Describe ways used to fight civil injustice
6. Talk to elder family members about their participation in the civil rights movement
*Choose a leader of that time and tell why you would follow that person. What would you do today to stop racial
discrimination?
124
Across The Curriculum
LANGUAGE ARTS: HARLEM RENAISSANCE
Goal: To develop an appreciation of African culture and literature as literary contributions
Objective:
1. Listen to poetry and music from the Harlem Renaissance period
2. Discuss the importance of the arts
3. Create a project using music from the period
4. Recite excerpts from poetry
5. Construct an adjective word wall using adjectives to describe the music and poetry
6. List several poets, writers and musicians from the period and their works
7. Explain the significance of the Harlem Renaissance
HEALTH: ATTIRE
Goal: To understand change in weather, seasons and the use of appropriate dress
Objectives:
1. Name seasons of the year and the weather that corresponds to them
2. Discuss dressing for different types of weather
3. Explain and read a weather thermometer
4. Discuss food, growth and productivity in relation to seasons
5. Explain 3 stages of weather
125
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Lansing, MI 48917
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126
Across The Arts
Physical Education
Students will create a song using prepositions and follow the directions using a paper plate
Music - The Great Season
Students will listen to the great African American musicians of the Harlem Renaissance
Ex:
Duke Ellington, Ella Fitzgerald, Count Basie, Billie Holiday, Louis Armstrong
Students will learn at least one of the dances of that time period
Art
Students will mix colors and fingerpaint the seasons by using color representations
Cooking
Students will make Chicken Soup and sing the song “Chicken Soup”
Ingredients One Chicken
3 Carrots
3 stalks of celery
½ cup rice
One teaspoon salt
One gallon of water
Directions -
Skin chicken and cut up into pieces
Slice carrots and celery
Put chicken and salt into one gallon of water and bring to boil
Simmer for 30 minutes
Add celery, carrots and rice
Bring to boil again for five minutes
Simmer for 20 more minutes
127