Winter Break Packetandover.dadeschools.net/andover/documents/files/Math Holiday Packet...Winter Break Packet for ... Korean 626,000 ... In this activity, you will be using Algebraic

Winter Break Packet for

Mathematics

The student activities in this packet are designed to reinforce major mathematics concepts and skills that have been previously taught, while also being fun and stimulating. The activities are differentiated by grade level: K-2, 3-5, 6-8, and 9-12. It is also hoped that these activities will encourage family interaction over the winter break. Please note that elementary-level activities will require greater parent/family supervision or assistance.

Mathematics Winter Break Packet Grades 6 - 8

If you are in need of additional information about the Winter Break Activity Packet for mathematics, please contact the Mathematics Office at 305 995-7079.

Al-jabr Adapted from http://education.ti.com/go/NUMB3RS © 2006 Texas Instruments Incorporated

The word "algebra" is derived from the Arabic word al-jabr. This term is found in Mohammed ibn Musa al-Khwarizmi’s book The Comprehensive Book of Calculation by Balance and Opposition, written around the year 825. Balance is a translation of the word al-jabr, which eventually became algebra. In al-Khwarizmi’s book, he did not use the modern algebraic notation, neither did he use equations. Instead, everything was in words. For example, he used the Arabic word shay, or thing, in place of X. The text was a manual for solving equations. He mainly dealt with square (of the unknown), roots of the square, and absolute numbers (constants). He noted six different types of quadratic equations, such as squares equal to roots (ax2 = bx) and squares equal to numbers (ax2 = c). Today, from scuba diving to crime fighting, Algebraic equations are used to solve problems. Fighting crime may not be the first thing that springs to mind when you think of Algebra. But CSI Miami, Numb3rs and NCIS on CBS television, are just a few of the shows that feature the use of math in solving crimes. Pictured, right: Students in Lois Coles' math class use graphing calculators hooked into a navigation system to the teacher's laptop, which projects on a screen their progress on a math problem. In the background is eighth-grader Jarod LeFan. So the neat tricks TV cops use, such as deblurring number plates and reconstructing accidents from skid marks, are not as far fetched as they seem. In the fight against crime for both TV cops and the real police force, the secret weapon is mathematics. In this activity, you will be using math to solve a problem from the prime time CBS television show Numb3rs.



NUMB3RS Activity: Meltdown

In “Harvest,” Don and David discover a secret operating room in the basement of an old motel, which is being used to perform illegal kidney transplants. They find blood-soaked sheets and a pile of ice melting on a sheet of plastic in a corner. When Charlie sees the FBI’s pictures, he notices that the size of the puddle formed by the melting ice depends on the time the picture was taken. He and Amita discuss how this information can be used to determine when the ice first started to melt. This will tell them when their suspects last used the operating room. In this activity, we will assume that the ice is on a level surface, that it melts into a circular puddle of constant thickness, and that the room’s temperature remains constant. 1. If the ice melts at a constant rate, what does that tell us about the rate at which

the area of the puddle increases?

________________________________________________________________

2. Use the formula A = π r2 to complete the following table for the area of a growing puddle. Leave your answers in terms of π .

Puddle Number 1 2 3 4

Radius 5 cm 10 cm 15 cm 20 cm

Area

3. How does the area of the puddle increase when the radius increases from its

original size by 5 cm, 10 cm, and 15 cm? Can you generalize the change in area for an increase of n cm?

________________________________________________________________



NUMB3RS Activity: Meltdown

4. Algebraically, how much larger is (n + r)2 than r2? Compare this to your answers

to #3.

________________________________________________________________

Suppose Charlie has two pictures of the melting ice; the first one was taken at 8:45 A.M. and the second one was taken at 9:45 A.M. In the first picture, he determines the radius of the puddle to be 30 cm. In the second picture, it has grown to 32 cm.

5. What is the area in square centimeters (cm2) that the puddle covered in each

picture? What is the corresponding rate of increase in the area (cm2/min)? (Use 3.14 for π .)

________________________________________________________________ 6. When did the ice start to melt? (Hint: use the rate of increase in the area to find

how long it took the puddle to grow to a radius of 30 cm.)

________________________________________________________________


The Language of Algebra People use language to communicate with each other. English is the language most commonly spoken in the United States. There are at least fifteen other languages, each of which is spoken by more than 100,000 Americans. All languages have at least two things I common. First, they let words stand for objects and ideas. Second, they have rules that tell speakers how to put words together.

Top 10 Non-English Languages Spoken at Home by Americans

(1990 Census) Language Number

of Speakers Spanish 17,339,000French 1,703,000German 1,547,000Italian 1,309,000Chinese 1,249,000Tagalog 843,000Polish 723,000Korean 626,000Vietnamese 507,000Portugese 430,000

Mathematics has been called the universal language and Algebra is the gatekeeper of mathematics. To compare Algebra to a language, we must look at the two common things a language must have. Does Algebra have those two attributes?

• First, Algebra uses letters to stand for objects and ideas • Second, It has universal rules that tell how to put mathematical ideas together

Based on these criteria, Algebra can be considered a language. In fact, no matter where a student is born in the world, when they take Algebra, they learn the same rules about using variables and formulas and they also learn other rules that are universal such as the order of operations. In fact, whatever mathematical rules apply in America, they also apply in Europe, Canada, Central American and every other place on the face of the Earth. Since the 16th century, variables and formulas have been the key concepts and instruments of algebra. Formulas offer an easy example of connected variables and therefore provide a helpful preparation for the further study of functions in calculus. Formulas, together with the related concepts of introducing variables and solving equations, are a cornerstone for the further study of mathematics. In this activity, you will be using Algebraic relationships to answer questions write formulas and to complete patterns.


The Language of Algebra

ACTIVITY SHEET

1. In a certain rectangle, the length is 10 inches more than the width. Complete the table below:

W

W + 10

Width (in.) 5 11 15 w x + 21 Length (in.) 34 n

2. Astronauts who travel to the moon weigh six times as much on Earth as they weigh on the moon. Complete the table below:

Weight on moon (pounds) 10 50 n 2n Weight on Earth (pounds) 180 X

3. An apartment rents for $800 a month. The monthly rent is expected to increase $15 each year. What will be the rent at the end of 9 years?


The Language of Algebra

ACTIVITY SHEET

4. In 2002, the first class rate was changed to 37¢ for the first ounce of mail and 23¢ for each additional ounce. A chart showing the postage for weight up to 5 ounces is shown below. What is the cost for an 8 ounce letter?

Weight 1 oz. 2 oz. 3 oz. 4 oz. 5 oz. 6 oz. 7 oz. 8 oz. Postage $.37 $.60 $.83 $1.06 $1.29

5. The input and output values are listed in the table below. What is the rule for this set of values?

Input 3 4 5 6 7 8 Output 12 14 16 18 20

6. Determine the pattern.

a. 1, 2, 3, 4, ___, ___, ___

b. 1, 3, 5, 7, ___, ___, ___

c. 2, 4, 6, 8, ___, ___, ___

d. 7, 6.3, 5.6, 4.9, ___,___, ___

e. 5, 13, 21, 29, ___, ___, ___

f. 24, 12, 6, 3, ___, ___, ___


CUT, FOLD, AND CONSTRUCT Adapted from M-DCPS’s Geometry Measures Up Packet

Many students study surface area and wonder; “When are we every going to need to know this?” Yet, every year around the holiday winter season, millions of students eagerly await their wrapped presents under the tree never considering that their gift has a specific surface area. Without careful attention to the surface area, gift wrappers would waste a million miles of gift wrapping paper if they did not think carefully about the shape of each gift they wrapped.

Holiday gift giving began long before Christmas. The Romans would give gifts to one another on pagan festivals like Saturnalia, the winter solstice, and the Roman New Year. The tradition of gift giving became associated with Christmas because of the offerings of the Three Wise Men, though early on the Church discouraged the practice of gift giving because of its pagan associations. But by the Middle Ages the tradition had become so popular that it became a mainstay of the holiday season. Early on gifts were wrapped in simple tissue paper or more sturdy brown paper. In the nineteenth century, gifts were sometimes presented in decorated cornucopias or paper baskets. Early gift wrappers had to be especially dexterous; scotch tape wasn't invented until 1930! And it wasn't until 1932 that the rolls of adhesive tape were sold in dispensers with cutter blades. Before then packages were tied up with string and sealing wax. Innovations with gift wrap have continued. The 1980's introduced decorative plastic and paper gift bags, though these "new" bags weren't as new as some people thought. The Victorians had often given their gifts in decorated bags. The introduction of stick-on bows and cascade ribbons in the 80's and 90's further helped less than perfect gift wrappers. Nowadays one can wrap a gift without even using paper, by going on-line and sending an e-card wrapped in "virtual paper." In this activity, you will be working with the surface areas of Regular Polyhedrons. You will cut out, fold, and construct the five Regular Polyhedrons.



ACTIVITY SHEET

A Regular Polyhedron is a solid, three-dimensional figure each face of which is a regular polygon with equal sides and equal angles. Every face has the same number of vertices, and the same number of faces meet at every vertex. An inscribed (inside) sphere touches the center of every face, and a circumscribed sphere (outside) touches every vertex. There are five and only five of these figures, also called the Platonic Solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Before cutting out the figures, find the measurements of the sides and the heights of the triangles where appropriate. Write the measurements in the table below. If there are four sides that have the same dimensions, indicate the dimensions x 4.

Figure Dimensions Area of Base Surface Area Volume

CUBE

ICOSAHEDRON

OCTAHEDRON

TETRAHEDRON

Cut out each shape along the exterior sides. Decorate each shape. Fold along the interior segments. Assemble the solids by tucking in the tabs and gluing or taping. Display your solids by hanging them on a hanger or mounting them on a board (i.e., shoe box lid).



CUBE



OCTAHEDRON



TETRAHEDRON



ICOSAHEDRON



DODECAHEDRON




FRACTIONS – DECIMALS - PERCENTS Adapted from NCTM Journal ‘mathematics teaching in the MIDDLE SCHOOL,’ Aug. 2007

Television is certainly one of the most influential forces of our time. Through the device called a television set or TV, you are able to receive news, sports, entertainment, information and commercials. The average American spends between two and five hours a day glued to "the tube"! Have you ever wondered about the technology that makes television possible? How it is that dozens or hundreds of channels of full-motion video arrive at your house, in many cases for free? How does your television decode the signals to produce the picture? There are two amazing things about your brain that make television possible. By understanding these two facts, you gain a good bit of insight into why televisions are designed the way they are. The first principle is this: If you divide a still image into a collection of small colored dots, your brain will reassemble the dots into a meaningful image. The human brain's second amazing feature relating to television is this: If you divide a moving scene into a sequence of still pictures and show the still images in rapid succession, the brain will reassemble the still images into a single, moving scene. Televisions and computer screens (as well as newspaper and magazine photos) rely on this fusion-of-small-colored-dots capability in the human brain to chop pictures up into thousands of individual elements. On a TV or computer screen, the dots are called pixels. The picture below is magnified to show the pixels that make up an image on a television.

In this activity, you will use a grid of 100 squares to create images by coloring squares using four or more colors (Squares left blank are considered white). You will then count the number of squares that contain a particular color and write the totals. You will use this to determine the percent of each color used to create the image. You will then write the equivalent decimal and fractional form for each of the colors used in the example.



EXAMPLE

purple purple purple purple purple purple purple purple purple purple

purple green green green green green green green green purple

purple green orange orange orange orange orange orange green purple

purple green orange blue blue blue blue orange green purple

purple green orange blue purple purple blue orange green purple

purple green orange blue purple purple orange green purple

purple green orange blue blue blue blue orange green purple

purple green orange orange orange orange orange orange green purple

purple green green green green green green green green purple

purple purple purple purple purple purple purple purple purple purple

Color Table Example

Color Number Fraction Decimals Percent

Green 28 10028 or

257 0.28 28%

Blue 12 10012 or

253 0.12 12%

Purple 40 10040 or

52 0.40 40%

Orange 20 10020 or

51 0.20 20%



ACTIVITY SHEET

Use four or more colors to create a boat, car, ship or any other inanimate object in the grid of 100 squares below. Then use the Color Table to record the number of times you used a color in making your picture. Then change the value to its equivalent fractional, decimal and percent forms. Reminder: Blank spaces are considered white.

Color Table

Color Number Fraction Decimals Percent



ACTIVITY SHEET Fill in the missing percent, decimal, and/or fraction for each of the following:

Number of

Squares out of 100

Fraction Decimal Percent Equivalent

Dollar Amount

1 75 43

0.75 75% $0.75

2 51

0.2

3 30 0.3

4 2512

48%

5 60

6 37%

7 0.56

8 44

9 2523

10 107

11 91%

Explain how you would change a fraction to a percent, decimal, and equivalent dollar amount:


THE GOLDEN RATIO Adapted from NCTM Journal ‘mathematics teaching in the MIDDLE SCHOOL,’ Oct. 2007

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is approximately 1.6180339887. At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio can be expressed as a mathematical constant, usually denoted by Greek letter (phi). The golden ratio is a special number that is derived mathematically from:

251+

The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b.

It is important not to confuse the golden ratio with the Golden mean (philosophy), the felicitous middle between two extremes, Golden numbers, an indicator of years in astronomy and calendar studies, or the Golden Rule. In this activity, you will use proportional thinking to investigate the golden ration and see how approximations of the golden ratio are exhibited in parts of the human body.



/N 1.

ble 1.

tep 3:

e

/H nd record them in table 1.

tep 4:

/E and record them in table 1.

tep 5:

d

e ratio X/Y in the table 1.

ACTIVITY SHEET

Investigating the Golden Ratio

Are we golden? Is the golden ratio somewhere in each of us? Gather two to five friends and/or family members to help you fill out table 1. Step 1: Measure the height (B) and the navel height (N) of each person. Calculate the ratio Band record them in table Step 2: Measure the length (F) of an index finger and the distance (K) from the fingertip to the big knuckle of each member of your group. . Calculate the ratio F/K and Record them inta S Measure the length (L) of a legand the distance (H) from thhip to the kneecap of each person. Calculate the ratio La S Measure the length (A) of an arm and the distance (E) fromthe fingertips to the elbow of each person. Calculate the ratio A S Measure the length (X) of a profile (the top of the head to the level of the bottom of the chin) and the length (Y) (the bottom of the ear to the level of the bottom of the chin) of eachperson. Calculate and recorth



ACTIVITY SHEET

xample measuremen

press Ea tio in Both its Fraction an cimal Form

Name B/N L/N A/E

1. Paulette

E ts:

Ex ch Ra d De F/K X/Y

3965

or 1.666 5.15.2

or 1.66 3.17

34 or 1.97

1027

or 2.7 5.43.8

or 1.84

2. Kim 4472

or 1.633 5.18.2

or 1.86 1936

or 1.89 1227

or 2.25 48

or 2.0

3. Roy

4. Ray

5. Linda

USE TABLE 1 TO RECORD YOUR MEASUREMENTS

able

press Ea tio in Both its Fraction an cimal FormName B/N F/K L/N A/E X

1.

2.

3.

4.

5.

hich ratios in your table were close to the golden ratio and which were not?

T 1

Ex ch Ra d De /Y

W Are you Golden? Explain why or why not.


MY FOOD PYRIMAD Your food and physical activity choices each day affect your health—how you feel today, tomorrow, and in the future. The Dietary Guidelines for Americans, 2005, gives science-based advice on food and physical activity choices for health. What is a "Healthy Diet"? The Dietary Guidelines describe a healthy diet as one that

• Emphasizes fruits, vegetables, whole grains, and fat-free or low-fat milk and milk products;

• Includes lean meats, poultry, fish, beans, eggs, and nuts; and • Is low in saturated fats, trans fats, cholesterol, salt (sodium), and added sugars. • The recommendations in the Dietary Guidelines and in MyPyramid are for the

general public over 2 years of age. The recommendations in the Dietary Guidelines and in MyPyramid are for the general public over 2 years of age.

A healthful lifestyle is easier than you might think. The path to good health isn't the same for everyone and yours may change over time. To travel down your personal path, take small steps that are right for you, one at a time. Every step adds up, so you’ll reach your health goals before you know it. One easy step is to know what is in the nutritional facts about your favorite cereals. Nutrition facts such as total fat, cholesterol, dietary fiber and sugars are printed on the side of every cereal box. In this activity, you will record the nutrition facts of several cereals and create stem-and-leaf plots. You will then find the measures of central tendencies for the nutrition facts that you record.

MY FOOD PYRIMAD

ACTIVITY SHEET

Use at least five cereal boxes to complete the tables about the nutritional facts found on the side of the boxes. Then use the information to find the measures of central tendencies, mean median, mode and range.

Stem Leaf

Find the mean, median, mode and range for the total fat. Mean: Median:

Name of Cereal Total Fat

Mode: Range:

Stem Leaf

Find the mean, median, mode and range for the Cholesterol.

Name of Cereal Cholesterol

Mean: Median: Mode: Range:

MY FOOD PYRIMAD

ACTIVITY SHEET

Record the nutritional facts found on the side of the boxes and then find the measures of central tendencies, mean median, mode and range.

Name of Cereal Dietary Fiber Stem Leaf

Find the mean, median, mode and range for the dietary fiber. Mean: Median: Mode: Range:

Name of Cereal Sugar

Stem Leaf

Find the mean, median, mode and range for the sugar. Mean: Median: Mode: Range:

PRIME NUMBERS Adapted from NCTM Journal ‘mathematics teaching in the MIDDLE SCHOOL,’ Sept. 2007

Euclid proved in the 3rd century BC that there are an infinite number of prime numbers. A prime number can be divided only by itself and the number 1. Primes serve as the building blocks for our number system because every positive integer an be expressed as a product of prime numbers and these numbers cannot be evenly reduced any further than by multiplying themselves by 1. Prime numbers have applications in cryptography and other fields. Some facts:

• The only even prime number is 2. All other even numbers can be divided by 2.

• If the sum of a number's digits is a multiple of 3, that number can be divided by 3.

• No prime number greater than 5 ends in a 5. Any number greater than 5 that ends in a 5 can be divided by 5.

• Zero and 1 are not considered prime numbers.

• Except for 0 and 1, a number is either a prime number or a composite number. A composite number is defined as any number, greater than 1, that is not prime.

Twin Prime Numbers A twin prime is a prime number that differs from another prime number by two. Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are (5, 7), (11, 13), (41, 43), and (821, 823). Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin. Palindromic Prime Numbers A palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns. The first few decimal palindromic primes are: 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, … It may be noticed that in the above list there are no 2- or 4-digit palindromic primes, except for 11. The largest currently known prime, 232,582,657– 1, was found by Dr. Curtis Cooper and Dr. Steven Boone of Central Missouri State University on Sept. 4, 2006. It has 9,808,358 digits. The Electronic Frontier Foundation is offering a $100,000 award to whoever is the first to find a prime number with at least ten million digits; it seems likely that this will be claimed within the next few years.


Eratosthenes' Sieve Eratosthenes was the third librarian of the famous Alexandrian library, which was placed in a temple of the Muses called the Mouseion. Apart from many other mathematical and scientific discoveries, Eratosthenes worked on prime numbers. He is best remembered for two things - very good approximation of the Earth's circumference and for inventing a prime number sieve. This 'sieve' is still very important tool in number theory research. The Sieve gives you a method for finding prime numbers using a table of numbers (see Table 1).

1. Cross 1 out.

2. Then starting from 2, circle 2 but cross out every multiple of 2 from your sieve. You are taking out all the multiples of 2 - being multiples of 2 they will not be prime numbers. Use the same principle with every prime number that you know...

3. Starting with 3, circle 3, but cross out every multiple of 3 from your sieve.

4. Starting with 5, circle 5, but cross out every multiple of 5 from your sieve.

5. Starting with 7, circle 7 but cross out every multiple of it.

6. Continue until you exhaust your number 'sieve'. The numbers that are circled are

primes. They should have no divisors apart from themselves and 1.

Table 1


ACTIVITY SHEET

1. Use the Eratosthenes sieve and table 2 below to find all prime numbers less than

200.

Table 2

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100101 102 103 104 105 106 107 108 109 110111 112 113 114 115 116 117 118 119 120121 122 123 124 125 126 127 128 129 130131 132 133 134 135 136 137 138 139 140141 142 143 144 145 146 147 148 149 150151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170171 172 173 174 175 176 177 178 179 180181 182 183 184 185 186 187 188 189 190191 192 193 194 195 196 197 198 199 200

2. What is a twin prime number?

3. How many twin prime pairs are there between 100 and 200? List the pairs

below, for example (101, 103). Use the table 2 above to help find the twin primes.


ACTIVITY SHEET

4. What is a palindromic prime number? Provide at least three examples.

5. List the palindromic prime number between 2 and 200. Use the table 2 to help

find the palindromic primes

6. Express the positive even integers in the table as the sum of two prime numbers.

Use table 2 for a list of prime numbers.

Positive Even

IntegersPrime

Number 1Prime

Number 2 Addition Sentence1 12 5 7 5 + 72 243 304 365 426 587 648 829 10010 11011 11412 12213 13014 14415 15016 16617 17818 18619 19020 200


ACTIVITY SHEET

7. Show the prime factorization for the numbers 28 in two different ways.

8. Write the prime factorization for the number 200:

_____________________________________________________________

9. Write the prime factorization for the number 415:

_____________________________________________________________

10. Why are the prime numbers referred to as the “basic building blocks” of our number system?

TANGRAMS

Tangram (Chinese: literally "seven boards of skill") is a dissection puzzle. It consists of seven pieces, called tans, which fit together to form a shape of some sort. The objective is to form a specific shape with seven pieces. The shape has to contain all the pieces, which may not overlap.

Tans Sorted as a Rectangle Tangrams A Tangram Man

The Tangram very possibly originated from the yanjitu furniture set during the Chinese Song Dynasty. According to historical Chinese records, the furniture set was originally a set of 6 rectangular tables. Later, an additional triangular table was added to the set, and people can arrange the 7 tables into a big square table. There is some variation to such furniture set during the Ming Dynasty, and later became a set of wooden blocks for playing. The word "tangram" is built from TANG + GRAM. The word "Tangram" was first used by Thomas Hill, later President of Harvard, in his book Geometrical Puzzle for the Youth in 1848. The author and mathematician Lewis Carroll reputedly was a great enthusiast of tangrams and possessed a Chinese book with tissue-thin leaves containing 323 tangram designs. Napoleon owned a Tangram set and Chinese problem and solution books while he was imprisoned on the island of St. Helena Tangrams were brought to America by Chinese and American ships during the first part of the nineteenth century. The earliest example known is made of ivory in a silk box and was given to the son of an American ship owner in 1802. In this activity, you will construct your own tangrams and identify properties of the seven tangram pieces and explore area relationships with tangrams.

http://en.wikipedia.org/wiki/Chinese_language

TANGRAMS

Directions for Making Tangrams

1 5

2

37

4

6

1) Fold the lower right corner to the upper left corner along the diagonal. Crease

sharply. Cut along the diagonal.

2) Fold the upper triangle formed in half, bisecting the right angle, to form Piece 1 and

Piece 2. Crease and cut along this fold. Label these two triangles "1" and "2."

3) Connect the midpoint of the bottom side of the original square to the midpoint of the

right side of the original square. Crease sharply along this line and cut. Label the

triangle "3."

4) Fold the remaining trapezoid in half, matching the short sides. Cut along this fold.

5) Take the lower trapezoid you just made and connect the midpoint of the longest

side to the vertex of the right angle opposite it. Fold and cut along this line. Label

the small triangle "4" and the remaining parallelogram "7."

6) Take the upper trapezoid you made in Step 4. Connect the midpoint of the longest

side to the vertex of the obtuse angle opposite it. Fold and cut along this line.

Label the small triangle "5" and the square "6."

TANGRAMS

Area and Perimeter with Tangrams

1) If the area of the composite square (all seven pieces -- see below) is one unit, find

the area of each of the separate pieces in terms of the area of the composite square.

Piece # area

1 2 3

4 5 6

7

2) If the smallest triangle (piece #4 or #5) is the unit for area, find the area of each of the separate pieces in terms of that triangle.

1 5

2

3 7

4

6

Piece # area

1 2 3 4 5 6

7

TANGRAMS

Area and Perimeter with Tangrams (Continued)

3) If the smallest square (piece #6) is the unit for area, find the area of each of the

separate pieces in terms of that square. Enter your findings in the table below. 4.) If the side of the small square (piece #6) is the unit of length, find the perimeter of

each piece and enter your findings in the table.

piece # area perimeter

1 2 3 4 5 6 7

TANGRAMS

Spatial Problem Solving with Tangrams Use the number of pieces in the first column to form each of the geometric figures that appear in the top of the table. Make a sketch of your solution(s). Some have more than one solution while some have no solution.

Make These Polygons

Use this many pieces

Square

Rectangle

Triangle

Trapezoid

Trapezoid

Parallel-ogram

2

3

4

5

6

7

THE ARCHITECT An architect is a person who is involved in the planning, designing, modeling and oversight of a building's construction. The word "architect" (Latin: architectus) derives from the Greek arkhitekton (arkhi, chief + tekton, builder"). In the broadest sense an architect is a person who translates the user's needs and wants into a physical, well built structure. An architect must thoroughly understand the building and operational codes under which his or her design must conform. That degree of knowledge is necessary so that he or she is not apt to omit any necessary requirements, or produce improper, conflicting, ambiguous, or confusing requirements. Architects must understand the various methods available to the builder for building the client's structure, so that he or she can negotiate with the client to produce a best possible compromise of the results desired within explicit cost and time boundaries. The idea of what constitutes a result desired varies among architects, as the values and attitudes which underlie modern architecture differ both between the schools of thought which influence architecture and between individual practicing architects.

Jorge Mas Canosa Middle School

Architects must frequently make building design and planning decisions that affect the safety and well being of the general public. Architects are required to obtain specialized education and documented work experience to obtain a license to practice architecture, similar to the requirements for other professionals. The requirements for practice vary from state to state. In this activity, you will calculate the area of the rooms of an architect’s floor plan and record the values in a table. Then you will find the totals square footage of the floor plan.


THE ARCHITECT

ACTIVITY SHEET

Shown below is an architect’s floor plan of a home. Use the grid to calculate the area of each room and write it in the table below. Then find the total square footage of the floor plan.

Room Area Calculations Bedroom 1 Bedroom 2 Bedroom 3 Bathroom Master Bedroom Master Bathroom Living Room Kitchen Dining Room Foyer Hallway Total Area


THE ARCHITECT

ACTIVITY SHEET

Explain how you calculated the areas for the Master Bedroom and Living Room. Explain how you calculated the total square footage of the home.


THE ARCHITECT What is this job like? Architects design houses and buildings. They plan offices and apartments. They design schools, churches, and airport terminals. Their plans involve far more than a building's looks. Buildings must be safe and strong. They must also suit the needs of the people who use them. The architect and client first discuss what the client wants. The architect sometimes helps decide if a project would work at all or if it would harm the environment. The architect then creates drawings for the client to review. They may be involved in all stages of the construction of a building. If the ideas are OK, the architect draws up the final plans. These plans show how the building will look and how to build it. The drawings show the beams that hold up the building. They show the air-conditioner, furnace, and ventilating systems. The drawings show how the electricity and plumbing work. Architects used to use pencil and paper to draw their plans. Today, more and more architects are using computers. Architects generally work in comfortable conditions. They spend most of their time in offices. However, they spend some time at building sites to see how projects are going.

How much does this job pay? The middle half of all architects earned between $46,690 and $79,320 a year in 2004. The highest-paid 10 percent earned more than $99,800 a year. How many jobs are there? Architects held about 129,000 jobs in 2004. Most jobs were in small architecture firms. About 1 in 4 was self-employed. This means they practiced as partners in a firm or on their own. Some worked for builders or government agencies. What about the future? U.S. Department of Labor, Bureau of Labor Statistics expects the number of jobs for architects to grow about as fast as the average for all occupations through 2014. Despite this growth, however, new architects face competition. This job attracts many people, so there are lots of applicants for openings. Applicants who gained experience working for an architectural firm while in school have a competitive advantage. Those who know about computer-aided design and drafting technology also have a better chance to get a job. In this activity, you will design your own floor plan for a home that you would like t o build. You will use a scale drawing to calculate the area and write a description of your home.


THE ARCHITECT

ACTIVITY SHEET

On the graph paper, design your own floor plan for a home that you would like to build. Write the scale of your drawing on the graph. Record the dimensions of each room and the area in table. Use the average room size given in the table to ensure that your dimensions are realistic. The lot size is 12,000 square feet; therefore, the total square footage of your house can be no greater than the square footage of your lot. Remember to leave some space for your yard.

Room Average size Your Dimensions Area

Living Room 19 feet by 8.5 feet

Dining Room 18 feet by 12 feet

Kitchen 20 feet by 9 feet

Bedrooms and Bathrooms

500 square feet (total area)

Other Rooms

Yard

Total Square Footage of Home:

ACTIVITY SHEET

Write a description of the home that you designed.


THE ARCHITECT

GRAPH PAPER


Documents

Winter Break Packetandover.dadeschools.net/andover/documents/files/Math Holiday Packet...Winter Break Packet for ... Korean 626,000 ... In this activity, you will be using Algebraic