Benne So - Volume 2 · 5 CHALLENGING THE GENIUS MATHEMATICAL CURRICULUM AFRICAN MATHEMATICAL GENIUS...

1

The Genius Academy

Benne So - Volume 2

2

African Mathematical Genius

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

Benne So - Volume 2

3

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

4

Table Of Contents

Challenging the Genius Mathematics Curriculum 4

Message from Dr. Shabazz 5

Introduction 8

Book Two

Theme 4: Time 9

Theme 5: Change 58

Theme 6: Seasons 98

5

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.

6

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.

7

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.

8

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 Cur-

riculum prepares children for their future leadership.

9

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 Math-

ematical 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.

11

K emet is where we find the earliest documentation of measur-

ing 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.

Mathematics - Time

12

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

13

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.

14

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

15

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 calen-

dar 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 astrono-

mers 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.

16

Reading The Clock

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 rep-

resents either one second or one minute).

long hand

(minute hand)

short hand

(hour hand)

second hand

17

The time is 1:00

because the short

hand is pointing

to the 1 and the

long hand is

pointing to the 12.

The time is 2:00

because the short

hand is pointing

to the 2 and the

long hand is

pointing to the 12.

The time is 3:00

because the short

hand is pointing

to the 3 and the

long hand is

pointing to the 12.

The time is 4:00

because the short

hand is pointing

to the 4 and the

long hand is

pointing to the 12.

The time is 5:00

because the short

hand is pointing

to the 5 and the

long hand is

pointing to the 12.

The time is 6:00

because the short

hand is pointing

to the 6 and the

long hand is

pointing to the 12.

The time is 7:00

because the short

hand is pointing

to the 7 and the

long hand is

pointing to the 12.

The time is 8:00

because the short

hand is pointing

to the 8 and the

long hand is

pointing to the 12.

The time is 9:00

because the short

hand is pointing

to the 9 and the

long hand is

pointing to the 12.

The time is 10:00

because the short

hand is pointing

to the 10 and the

long hand is

pointing to the 12.

The time is 11:00

because the short

hand is pointing

to the 11 and the

long hand is

pointing to the 12.

The time is 12:00

because the short

hand is pointing

to the 12 and the

long hand is

pointing to the 12.

Telling Time

18

Reading The Clock

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.

long hand

(minute hand)

short hand

(hour hand)

19

XII

Working With Time Write the correct time under the clock

20

Units of Time

Your eyes blink about every second.

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

II

21

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?

22

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.”

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?

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

23

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

Daily Organizer - List what you do on a daily basis at specific times

24

Geometry

Point A Point B

Points have no size or

dimension. They are used to

tell position of lines and

objects. Points are named

with capital letters.

A line is a straight path that

extends in both directions

without ending.

A line segment is part of a

line. It has two endpoints.

A ray is a part of a line that

extends in one direction to

infinity(never ending).

When two lines or line

segments intersect, they meet

and cross at a point.


segments never cross

(intersect), they are parallel

lines.

90°


segments cross (intersect) or

join to form a 90° angle, they

are perpendicular. The sign

used to show that lines are

perpendicular is .

)


segments intersect, they

form angles.

ABC (Angle ABC) The point where lines

intersect to form angles is

called a vertex (point B).

vertex

Figures that have the same

size and shape are

congruent.

Figures that have the same

shape but are not the same

size are similar.

A

B

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.

A

B

C

25

Working with Geometry

1. Draw a line segment.

2. Circle the ray.

a. b. c.

3. A plane is a flat surface with a limited amount of points. Circle: True or False

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.

26

Geometry - Polygons

Polygons are flat, two-

dimensional shapes.

Polygons are closed figures

that have at least three

straight sides and angles or

vertexes.

5

5 5

5 3 3

3

Regular polygons are

polygons that have sides of

equal length and angles of

equal measure.

4

7 7

6

4 10

8

Irregular polygons are

polygons with sides of

unequal length and angles

of unequal measure.

A triangle is a polygon that

has three sides and

vertexes.

9 9

6

An isosceles triangle is a

triangle with exactly two

equal sides.

5 7

9

A scalene triangle is a

triangle with no equal sides.

11 11

11

An equilateral triangle is a

triangle with all equal sides.

A right triangle is a triangle

with a 90° angle(right angle).

27

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. d. e. f.

3. Locate the angles and vertexes on this triangle. A

B C

4. Draw a line of symmetry on the isosceles triangle.

a. b. c. d.

28

Quadrilaterals are polygons

that have four sides, four

vertexes, and four angles.

Parallelograms are

quadrilaterals that have

parallel line segments in both

pairs of opposite sides.

Trapezoids are quadrilaterals

that have one pair of parallel

sides.

Squares are quadrilaterals

with all equal sides. A

square has 4 right angles.

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.

A Pentagon is a polygon with

5 sides, 5 vertexes and 5

angles.

A Hexagon is a polygon with

6 sides, 6 vertexes and 6

angles.

Geometry - Polygons

29

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. c. d.

4. A triangle has ___________ sides.

a. 4 b. 3 c. 2 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 or False

30

Geometry and Addition

60

90 30

The sum of all the angles of a

triangle is 180°.

90 90

90 90

The sum of all angles of a

polygon with 4 sides

(quadrilateral) is equal to

360°.

The sum of all angles of a

circle is equal to 360°.

3cm 3cm

3cm 3cm

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


square you add all the sides.

Remember all 4 sides are

equal: 2cm + 2cm + 2cm + 2cm =

8cm

4cm

1cm


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

4cm 5cm

3cm


triangle you add all three

sides:

4cm + 3cm + 5cm = 12cm

3cm 6cm

To find the total length of

these two lines you add them

together:

3cm + 6cm = 9cm

The total length of this line is

9cm.

31

Is this figure a polygon?

If yes, tell why:

Is this figure a polygon?

If yes, tell why:

If each side of this polygon

measures six inches, what is

the perimeter? Explain your

answer.

Do these two line segments

bisect each other?

What does bisect mean?

How many angles do these

two lines make?

Are these two lines parallel or

perpendicular? Explain your

answer.

8

15

11

What is the perimeter of this

triangle?

What kind of triangle is

this?

12 12

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

32

Geometry - Angles

Acute angles are angles that

measure more than 0° but less

than 90°.

Obtuse angles measure more

than 90° but less than 180°.

A straight line is equal to

180°.

A right angle is equal to 90°.

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°.

Quadrant 2 Quadrant 1

Quadrant 3 Quadrant 4

Quadrant 1 angles - between

0° and 90°.


90° and 180°.


180° and 270°.


270° and 360°.

33

Working with Angles

1. Draw an acute angle.

2. Complementary angles form _____________.

a. supplementary angles b. right angles c. obtuse angles d. 50°

3. A reflex angle is more than 180°. Circle: True or False

4. These are ______________ angles.

a. supplementary b. complementary c. acute d. reflex

5. Label the quadrants.

6. This straight line measures _____________ .

a. 45° b. 90° c. 180° d. 360°

7. Draw an obtuse angle.

34

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: True or False

4. What is the perimeter of this equilateral triangle? 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 3cm 6cm

35

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.

36

10

9

8

7

6

5

4

3

2

1

11:00-11:30 11:30-12:00 12:00-12:30 12:30-1:00

Number & Time Points Were awarded for class participation

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?

37

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°)



A. Straight (180°)

B. Acute (<90°)

C. Obtuse (>90° but <180°)

D. Right (90°)



A. Straight (180°)

B. Acute (<90°)

C. Obtuse (>90° but <180°)

D. Right (90°)



A. Straight (180°)

B. Acute (<90°)

C. Obtuse (>90° but <180°)

D. Right (90°)



A. Straight (180°)

B. Acute (<90°)

C. Obtuse (>90° but <180°)

D. Right (90°)



A. Straight (180°)

B. Acute (<90°)

C. Obtuse (>90° but <180°)

D. Right (90°)



A. Straight (180°)

B. Acute (<90°)

C. Obtuse (>90° but <180°)

D. Right (90°)



38

Geometry - Tell whether the two figures are congruent

Congruent?

Congruent?

Congruent?

Congruent?

Congruent?

16

6 6

16

16

6 6

16

Congruent?

Congruent?

Congruent?

39

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.


for this figure.


for this figure.


for this figure.


for this figure.


for this figure.


for this figure.

40

Symmetry & Kemetic Mdu Ntr (Hieroglyphic) Alphabet

List the ones that are symmetrical:

vulture

A

Reed leaf

I

Two leaves

Y

Arm & hand

A

Quail chick

W

Foot

B

Mat

P

Horned viper

F

Owl

M

Water

N

Mouth

R

Courtyard

H

Twisted flax

H

Placenta

h

Animal’s belly

CH

Folded cloth

S

Pool

SH

Hill slope

K

Basket

K

Jar stand

G

Loaf

T

Tethering rope

TH

Hand

D

Snake

DJ

41

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

42

Geometry - Space Figures

CUBE

RECTANGULAR

PRISM

PYRAMID

CONE

CYLINDER

SPHERE

43

vertex

edge

Cubes have six faces. Each face is a

square.

lateral face

base

Prisms have two parallel, congruent

polygon-shaped bases. The sides of

prisms are all parallelograms. Each

face that is not a base is called a lateral

face.

triangular

face

base

A Pyramid’s base can have the shape of

any polygon like the prism. All other

faces of a pyramid are triangular.

vertex

base

Cones have one flat, circular base that

rises to a point(the vertex).

base

Cylinders are solids with two circular

bases.

Spheres have no flat faces and no

vertices. A sphere has the outline of a

circle when viewed at an angle.

Geometry - Space Figures

Face

44

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 _________________.


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 d. square

6. Planet Earth is shaped like a _________________.


45

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

the tessellation?


the tessellation?


the tessellation?

Can you think of a polygon to make

a tessellation? Draw your

tessellation above.

Can you think of another polygon

to make a tessellation? Draw your

tessellation above.

Can you think of another polygon to

make a tessellation? Draw your

tessellation above.

46

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.

47

Create

A

Cube!

48

Create

A

Kemetic Pyramid!

49

Mental Math/Cumulative Review

1. Write 5:00 p.m. in military time.

2. Your head is shaped like a _________________.


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.

50


7. a. How many rectangles are there?

b. Which shape has the least amount?

c. How many rhombuses are there?

d. Which shape has the most?

8. How much longer is line segment a than line segment b?

line segment a = 10cm line segment b = 7cm

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. d. 10:06 p.m.

10. Draw an acute angle. Locate the vertex.

11. Are these figures congruent?

12. Create a tessellation using triangles.

6

5

4

3

2

1

51


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

?

52

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

ADDITION & SUBTRACTION - no regrouping

53

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


Add from right to left

54

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.

55

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 anoth-

er player. If the other player doesn’t have the requested card, the tell the player go “Geo Fish!”.

56

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?

57


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

58

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

60

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.

Mathematics - Change

61

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

62

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 Sys-

tem, and the International or Metric System. We use the US Customary System.

63

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.

64

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 fol-

lowing:

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 0 0 0

2 2 2 2

2 6 2 6

2 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.

65

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

66

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

67

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 (also equivalent to 5²)

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

Multiplication & Division Facts

68

2X1=2

2÷1=2

1x2=2


4÷2=2

2X3=6

6÷3=2

3x2=6

6÷2=3

2X4=8

8÷4=2

4x2=8

8÷2=4

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


69

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


100÷10=10

10X11=110

110÷11=10

11x10=110

110÷10=11

10X12=120

120÷12=10

12x10=120

120÷10=12


70

3X1=3

3÷1=3

1x3=3

3X2=6

6÷2=3

2x3=6

6÷3=2


9÷3=3

3X4=12

12÷4=3

4x3=12

12÷3=4

3X5=15

15÷5=3

5x3=15

15÷3=5

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

3X9=27

27÷9=3

9x3=27

27÷3=9

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


71

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 12x10=120

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 12x12=144 or 122=144

72

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

73

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

74

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

Multiplication Table

75

X 0 1 2 3 4 5 6 7 8 9 10 11 12

0 0

1 1

2 4

3 9

4 16

5

6

7

8

9

10

11

12

Complete the Multiplication Table

76

X

Create a Multiplication Table

77

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?

3 x 3 =

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?

78

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


10 x 10 = 10² =100


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?

79

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=

80

Working with Exponents

1. 1² =

2. 33 =

3. 4² =

4. 6² =

5. 10² =

6. 15 =

7. 3³ =

8. 24 =

81

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 Root Logarithm

23 = 8 The cubed root of 8 is 2 Log base 2 of 8 is 3

52 = 25 The square root of 25 is 5 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 ___

33 = ___

____ __ = ___ The square root of 36 is 6 Log base ____ of ____ is ___

82

Count by

2’s, fill in

the blanks 2 8 18

Count by

3’s, fill in

the blanks 9 24

Count by

5’s, fill in

the blanks 10 30

Count by

10’s, fill in

the blanks 50

Multiplication - Fill in the missing blanks

83

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)*:

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.

3

3

3

84

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

inch in. 12 inches

equals 1 foot

foot ft. 1 foot equals 12

inches

yard yd. 3 feet equals 1

yard or 36

inches equals 1

yard

Measure Abbreviation Equivalent

meter m 1 meter equals

100 centimeters

centimeter cm 100 centimeters

equals 1 meter

kilometer km 1000 meters

equals 1

kilometer

85

Computing Area

5in

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

10cm

4cm

The area of a rectangle is

length x width.

Length = how long

Width = how wide

The area of this rectangle is 40cm2

because 10x4=40.

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:

2x10=20

2x4=8

20+8=28

4m

3m

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.

86

Multiplication - Using a ruler to measure the sides, find the perimeter & area of each figure.

87


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 d. reflex

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?

88

7 x 6 =

459 =

4 x6 =

8÷8 =

2 x 5 =

42÷6 =

0÷2 =

0 x 8 =

5÷5 =

5 x 7 =

8÷2 =

1 x 5 =

8 x 9 =

24÷8 =

2 x 8 =

12÷2 =

7 x 1 =

18÷6 =

32÷8 =

4 x 2 =

27÷9 =

6 x 7 =

45÷5 =

0 x 4 =

6 x 1 =

15÷5 =

4 x 9 =

42÷6 =

9 x 2 =

7÷7 =

56÷8 =

5 x 6 =

18÷2 =

6 x 3 =

72÷9 =

2 x 0 =

3 x 8 =

20 ÷4 =

9 x 6 =

36÷4 =

9 x 9 =

36÷6 =

25÷5 =

3 x 3 =

54÷9 =

7 x 5 =

28÷7 =

3 x 7 =

MULTIPLICATION & DIVISION

89

6 x 6 =

455 =

3 x6 =

16÷8 =

2 x 7 =

42÷7 =

0÷9 =

4 x 8 =

35÷5 =

5 x 9 =

18÷2 =

8 x 5 =

9 x 9 =

56÷8 =

2 x 4 =

14÷2 =

7 x 6 =

54÷6 =

32÷4 =

4 x 4 =

27÷3 =

6 x 6 =

45÷9 =

7 x 4 =

6 x 4 =

30÷5 =

3 x 9 =

42÷7 =

9 x 9 =

28÷7 =

64÷8 =

5 x 7 =

18÷9 =

8 x 3 =

72÷8 =

6 x 0 =

3 x 7 =

28 ÷4 =

6 x 6 =

20÷4 =

10 x 9 =

18÷6 =

15÷5 =

3 x 8 =

54÷6 =

7 x 7 =

28÷4 =

4 x 7 =


90

9

X1

1 9

3

X0

3 0

2

X1

1 2

0

X0

7 0

6 0

8

X0

1 6

6

X1

5 0

5

X0

4 0

4

X0

1

X1

1 1

0

X1

1 0

9

X0

9 0

3

X1

1 3

7 0

8

X0

2 0

2

X0

4 0

4

X0

1 6

6

X1

1

X1

1 1

2

X2

2 2

3

X3

3 3

4

X4

4 4

5 5

5

X5

6 6

6

X6

7 7

7

X7

8 8

8

X8

9

x9

9 9

10

X10

10 10

0

X0

10 0

4

X1

1 4

1 7

7

X1

1 3

3

X1

1 5

5

X1

1 9

9

X1


91

9

X2

2 18

3

X3

3 3

2

X2

2 4

0

X5

1 0 0

8 32

8

X4

3 18

6

X3

5 25

5

X5

4 16

4

X4

1

X9

1 9

0

X8

1 8

9

X3

9 27

3

X5

3 15

8 0

8

X0

2 0

2

X9

4 20

4

X5

6 6

6

X6

1

X1

1 10

2

X9

2 18

3

X7

3 21

4

X7

4 28

5 40

5

X8

6 12

6

X2

7 63

7

X9

8 48

8

X6

9

X9

9 81

10

X10

10 10

7

X0

10 70

4

X6

4 24

7 14

7

X2

3 9

3

X3

5 25

5

X9

9 45

9

X9


92

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


93

4

2

+2

25

- 3

1

7

+1

54-13=

2

3

+3

33

-11

3

5

+1

65

- 4

1

2

3

+4

32

-01

5

1

2

+3

50

-30

6

4

1

+2

59

-24

6

2

2

+1

25

- 2

7

4

1

+3

36

- 3

2

4

3

+5

56

- 2

9+3+2+4=

33

-23

1

2

3

+6

69

-33

5

4

6

+2

44

-21

3

5

6

+1

68

-22

5+3+0=

36

-12

7

9

1

+1

98-12=

1

2

3

2

+5

34

-22

10+20+30=

60-20=

22

30

27

+40

46

-24

31

10

54

+23

54

-24


94


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.

Have students recognize the patterns in

multiplication and come up with

cartoons, stories, rhymes, etc. to remember

them. For example:

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.

9’s

09

18

27

36

45

54

63

72

81

90

95

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:

5 X 0 = 0 0 X 5 = 0 0 ÷5 = 0 Can not divide by zero

5 X 1 = 5 1 X 5 = 5 5÷ 1 = 5 5 ÷5 = 1

5 x 2 =10 2 x 5 = 10 10÷ 2 = 5 10 ÷5 = 2

5 x 3 = 15 3 x 5 = 15 15÷ 3= 5 15 ÷5 = 3

.

.

.

.

5 x 12 = 60 12 X 5 = 60 60÷ 12 = 5 60 ÷5 = 12

Have students label the parts of the equation, circle and label a fact family, point out the inverse opera-

tion, commutative property, property of zero, and the identity property of multiplication.

96


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?

97


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

98

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

100

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.

101

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

102

Vocabulary Calendar—Any of various systems of recording time in which the beginning, length, and divisions of a year are arbi-

trarily 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 tem-

perature 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.

103

Historical Look

Alaska, North America

Although the first Iditarod , “The Last Great Race”, was held in 1973, it’s histo-

ry dates back to 1925, when Nome was hit by an epidemic of diphtheria. A se-

rum 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 tempera-

tures 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.

104

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.

105

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)

106

Days of the week/months of the year in other languages:

English Kiswahili Spanish French Japanese

Sunday Jumapili domingo dimanche Nichi•yoobi

Monday Jumatatu lunes lundi Getsu•yoobi

Tuesday Jumanne martes mardi Ka•yoobi

Wednesday Jumatano miércoles mercredi Sui•yoobi

Thursday Alhamisi jueves jeudi Moku•yoobi

Friday Ijumaa viernes vendredi Kin•yoobi

Saturday Jumamosi sábado samedi Do•yoobi

January Januari enero janvier Ichi•gatsu

February Februari febrero février Ni•gatsu

March Machi marzo mars San•gatsu

April Aprili abril avril Shi•gatsu

May Mei mayo mai Go•gatsu

June Juni junio juin Roku•gatsu

July Julai Julio juillet Shichi•gatsu

August Agosti agosto août Hachi•gatsu

September Septemba septiembre septembre Ku•gatsu

October Oktoba octubre octobre Jyuu•gatsu

November Novemba noviembre novembre Jyuuichi•gatsu

December Desemba diciembre décembre Jyuuni•gatsu

107

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

Reading a Calendar

May

200_

Shows the

Month of the

year.

Shows the day

of of the week.

1st day of the

month; Shows

the date of the

month.

The Year

108

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 ___________________

Year ____________________

Days

109


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

Finding Days and Dates On the Calendar 1. What Is the date of the fourth Wednesday in this month?

2. How many Fridays do we have in this month?

3. What is the date of the second Monday in this month?

4. On what day is the 25th ?

5. What month is it?

6. What is the last day in this month?

7. How many days are in this month?

8. What year is it?

110

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.

111

It’s Sunny. The temperature is

hottest.

It’s Windy.

The temperature is

lowered because of

the windchill.

It’s Cloudy.

The temperature is

not very high because

rain is expected.

It’s partly cloudy.

The temperature is

not very high.

It’s warm.

It’s rainy.

The temperature is

low because of the

rain.

It’s Snowy.

The temperature is

coldest.

Weather in Fahrenheit

90° 75°

67°

70°

60° 10°

112

Reading Temperature From A Thermometer

C° F°

212°

Boiling

Point

of Water

95° A hot

day

68° Room

Temperature

98° Normal

body

temperature

32°

Freezing

point of

water

100°

Boiling Point

of Water

37° Normal body

temperature

33° A hot day

20° Room Temperature

0° Freezing point of water

113

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.

114

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°

115

Complete a weather & temperature calendar for the current month.

Draw a picture of what the weather is like.


116

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 x²

then Multiplication X

then Division ÷

then Add +

and finally Subtract -

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

117

Working with Order of Operation

Ex. 15 - 6 + 4=

9 + 4= (add and subtract from left to right which ever comes first)

13

1. 17 - 3 x 2 =

2. 9 ÷ 3 + 11 =

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 =

Add Subtract

Multiply and Divide first!

118

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 =

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) =

Follow

The

Order!

119

Input/Output Machines

send up a 5, multiply it by 2, 10 comes down.

Send up a 4, multiply by 2, 8 comes down.

x 2

5 10

3

2

10

6

9

12

7

4 8

8

÷3

12

33 11

9

3

15

6

30

24

18 6

27

33 drives in, divided by 3, 11 comes out.

18 drives in, divided by 3, 6 comes out.

x2

- 1

2

1

5

6 36 35

4

3

7

8

9

10 100 99

6 drives through, it’s squared and then loses 1, 35 is left.

10 drives through, it’s squared and then loses 1, 99 is left.

120


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.

121


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?

122


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.

123

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, temper-

ature, 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

124


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?

125


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

126

3863 Waverly Hills

Lansing, MI 48917

517-484-0428

[email protected]

www.thegeniusacademy.org

We Are Available For Consulting!

127

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

Benne So - Volume 2 · 5 CHALLENGING THE GENIUS MATHEMATICAL CURRICULUM AFRICAN MATHEMATICAL GENIUS...

Documents

Transcript of Benne So - Volume 2 · 5 CHALLENGING THE GENIUS MATHEMATICAL CURRICULUM AFRICAN MATHEMATICAL GENIUS...