Holistic Education - Big Ideas Math · PDF fileHolistic Education BigIdeasLearning.com ......
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Holistic Education BigIdeasLearning.com ® At many times in the history of our planet, being an “educated person” had a broader meaning than it has today. To help bring a more holistic approach to education at the middle school level, we have introduced three major features. Many of the activities, examples, and exercises describe real-life, exciting applications of the mathematics. The Teaching Editions frequently include additional information, fun facts, and data about the examples and exercises. Appendix A includes four major projects that relate mathematics to Literature, Art, History, and Science. Appendix A includes four “Big Idea” projects. A2 Appendix A Alice’s Adventures in Wonderland Lewis Carroll was a mathematician who also wrote literature books for children. Essential Question How does mathematical problem solving influence a story plot? Read Alice’s Adventures in Wonderland by Lewis Carroll. In each chapter, rewrite one of the episodes so that it contains some of the math that you have studied this year. Getting Started 1 Things to Remember 2 ● You can download each chapter of the book at My.BigIdeasMath.com. ● Add your own illustrations to your project. ● Try to include as many different math concepts as possible. Your goal is to include at least one concept from each of the Literature Project A.1 Sample: You could rewrite Alice’s shrinking adventure as follows. Alice’s normal height was 4′7′′ or 55 inches. After drinking the bottle marked “Drink Me,” Alice could feel herself shrinking more and more. After several minutes, Alice was only two-elevenths of her original height. Would Alice have to bend over to walk through a door that is only 1 foot high? The illustrations on these two pages are from the 1907 edition of Alice’s Adventures in Wonderland. They were drawn by Arthur Rackham (1867–1939), a book illustrator from England. Literature di Ai ld f “Bi Id ” j t ppe at least one concept from each of the A8 Appendix A My Big Ideas Projects Why Does Ice Float? Among the planets in our solar system, Earth is clearly the “water planet.” Water occurs on Earth’s surface as a liquid, solid, and gas. Ocean waters cover about 70% of Earth’s surface. Fresh water in lakes and rivers covers less than 1%. Thick sheets of ice permanently cover Earth’s polar regions, and glaciers occur in its higher mountains. Water in the form of clouds covers about half of Earth’s surface at any time. Essential Question How does floating ice affect you and the world in which you live? There are three parts to this question. First, you have to understand why things float in water. Make lists of things that float in water and things that do not float in water. How can you describe, scientifically, the difference between these two types of objects? Second, you have to discover what is special about water. Almost all other elements and compounds have the property that their solid forms sink in their liquid forms. Third, you have to research how water in solid form influences the environment and living organisms. You may want to explore ocean currents, weather, and various cycles including the water cycle. Getting Started 1 Things to Include 2 ● Does vegetable cooking oil float in water? Does ice float in vegetable oil? ● Compare the density of water and the density of ice. How do these densities relate to the fact that ice floats in water? ● What percent of an iceberg is above the water? What percent is below? ● What environmental and biological systems would not work if ice sunk in the oceans instead of floating? ● Explain how the floating of ice helps keep the oceans warm and therefore helps aquatic life exist in Earth’s polar oceans. Science Project A.4 3 ● ● ● ’s Earth’s North Polar Ice Cap Floating Iceberg surface. Fresh water in than 1%. Thick sheets arth’s polar regions, and glacie ater in the form o e at any tim es fl fl s quest Make lists of t water. How can you de se two types of objects? er what is special about water. Almost all unds have the property that their solid orms. is below ● What en systems in the oc ● Explain keep the helps aq polar oc , an glaciers d glaciers d g aciers occur occur occur occur fo of clou m of clou rm of clo rm of clou clou ouds c ds co ds cover ds covers ds covers ds cover ds covers covers covers vers m ny tim ny tim y time. e. e. e. fl oating ti oating oating oating i ing ic oating ic ing ic ng ic g ic g ic icea e af e af e affe e affect affect affect y e affect y ect you ou a ou and the world in world in fl esti stion stion. tion. on. Fi st, you you First, yo First have to u have to u have to u ha nderstand ts of t of things that ngs that that hings t fl fl oat in wa in wa oat in w oa ter and ter and fl n you des ou describe, sci cribe, sci sci crib entifi entifi en cally, cally cally, fi ● Science e ojec h nclu ges e’s we –19 Art Project Circle Art Circles have been used in art for thousands of years. Essential Question How have circles influenced ancient and modern art? Find examples of art in which circles were used. Describe how the artist might have used properties of circles to make each piece of art. Getting Started 1 Things to Include 2 ● Describe how ancient artists drew circles. ● Describe the symbolism of circles in ancient art. ● Find examples of how circles are used to create mosaic tile patterns. ● Measure the angles that are formed by the patterns in the circle art you find. For instance, you might describe the angles formed by the netting in the Native American dreamcatcher. ● Find examples of the use of circles in modern art. ● Use circles to create your own art. Describe how you used mathematics and the properties of circles to make your art. Art Project A.3 Things to Remember 3 ● Add your own illustrations to your project. ● Try to include as many different math concepts as possible. Your goal is to include at least one concept from each of the chapters you studied this year. ● Organize your report in a folder, and think of a title for your report. Sample: Here is a technique for making a pattern that uses circles in a stained glass window. 1. Use a compass to draw a circle. 2. Without changing the radius, draw a second circle whose center lies on the first circle. 3. Without changing the radius, draw a third circle whose center is one of the points of intersection. 4. Without changing the radius, continue to draw new circles at the points of intersection. 5. Color the design to make a pattern. sands of years. influenced ancient were used. Describe how the h i of art Native American Dreamcatcher l at ater the tha g is cen biol ice oati f ice d th art ● ● ● roject A4 Appendix A My Big Ideas Projects Section A.2 History Project A5 Mathematics in Ancient Egypt The ancient Egyptian civilization in North Africa began around 3150 b.c. with the union of Upper and Lower Egypt under the first pharaoh. The rule of the pharaohs ended in 31 b.c. when the Romans conquered Egypt and made it a province. The ancient Egyptians’ achievements included a system of mathematics, glass technology, medicine, literature, irrigation and agricultural techniques, and art. Their mastery of surveying, quarrying, and construction techniques allowed them to build pyramids, temples, and obelisks. Essential Question How is mathematical knowledge that was originally discovered by the ancient Egyptians used today? Getting Started 1 Things to Include 2 ● Explain how the ancient Egyptians multiplied two whole numbers. Give an example. ● Explain how the ancient Egyptians divided two whole numbers. Give an example. ● How did the ancient Egyptians write whole numbers? Give some examples. ● How did the ancient Egyptians write fractions? Give some examples. ● How did the ancient Egyptians use ratios to measure the height of a pyramid? Give an example. Write your name using ancient Egyptian hieroglyphics. Describe how ancient Egyptians used mathematics. How does this compare with the ways in which mathematics is used today? History Project A.2 Sample: To multiply two whole numbers, the ancient Egyptians repeatedly multiplied by 2. The “doubling lists” used to multiply 53 by 85 are shown. The lists stop when the last number in the first list is greater than the first number in the second list. ● 1 53 2 106 ● 4 212 8 424 ● 16 848 32 1696 ● 64 3392 Because 85 =1 +4 +16 +64, 85 ⋅53 =53 +212 +848 +3392 =4505. Things to Remember 3 ● Add your own illustrations to your project. ● Try to include as many different math concepts as possible. Your goal is to include at least one concept from each of the chapters you studied this year. ● Organize your report in a folder, and think of a title for your report. Egypt with the union Ancient Papyrus ● Becaus 85 ⋅ 53 The Blue Sphinx Ancient Egyptian Numbers Ancient Egyptian Alphabet What does this spell? pharaoh. The rule of the pharaohs red Egypt and made it a province. uded a system of mathem ation and agr ying, and and o now oday? write whole numbers? Give some examples. d the ancient Egyptians wr some examples. Egyptians us height of a xample. ame using ancient ptian hieroglyphics. Describe how ancient Egyptians u compare with the ways in which m are the at f mathem hematics, hematics, ematics, matics, tics, , c gric agric d agricult ultu ultura ltural t tural te ural te al te l te te h chn chniq chnique chniques chniques, chniques, chniques, chniques, hniques, ques ques, an and co d con d cons const constr onstru nstruc nstruc struc struc ruc truc uc uctio tio tion tion t tion te tion tec tion techn ion techn on techn n techn chn hniques ques iques iques iques obeli obeli obeli b li d obeli d obeli d obelisk sk sks sks sks. sks. sks. sks. ks. s. ld wledg wledge edge wledge edge w g edge edgeth that was th that w s th ori originally y? ● How did How did How did Ho th the e a actions? fractions? fractions? action fractio a frac G Give Give s Give so som om om so ● How did How did ow did idthe anci h the ancie the ancien ncien ien cien entE t E t E t Eg ratios to ratios meas measur asure ure th ure th re th e th e heh e h e h pyram pyrami pyramid? G amid? G id? G ? Giv ive vean ive an e an exa an exa iv ive m Wr Write Write yo rite your na ur name Egy Egyptian hi History ch piece of art. For instance, you might describe the angles formed by the netting in the ican dreamcatcher. of circles art. ematics cles to make ibe how the h i of a rt angle angles for N i A Native Ame Native Ame Native A Nativ ric rican dr ● Find exa d ex d exa Find exa Find ex Fi Find mples of t es of t s of t mples of t mples of t mples mple he use he use he use o he use of of he use of c in modern dern dernart. t art. art. ● Use circles to cr es to create yo te your your o ur o our o ur o y wn wn a wn ar wn ar Describe h be h e how y ow y ow you u ow you us you use u use used ma d mathem mathem d m d and the pr and the pr and the pr p ope opertie operties o operties o erties of circ f circles your ar your art. your art. Art
Transcript of Holistic Education - Big Ideas Math · PDF fileHolistic Education BigIdeasLearning.com ......
Holistic Education
BigIdeasLearning.com
®
At many times in the history of our planet, being an “educated person” had a broader meaning than it has today. To help bring a more holistic approach to education at the middle school level, we have introduced three major features.
Many of the activities, examples, and exercises describe real-life, exciting applications of the mathematics.
The Teaching Editions frequently include additional information, fun facts, and data about the examples and exercises.
Appendix A includes four major projects that relate mathematics to Literature, Art, History, and Science.
Appendix A includes four “Big Idea” projects.
A2 Appendix A My Big Ideas Projects Section A.1 Literature Project
Alice’s Adventures in Wonderland
Lewis Carroll was a mathematician who also wrote literature books for children.
Essential Question How does mathematical problem solving infl uence a story plot?
Read Alice’s Adventures in Wonderland by Lewis Carroll. In each chapter, rewrite one of the episodes so that it contains some of the math that you have studied this year.
Getting Started1
Things to Remember2 ● You can download each chapter of the
book at My.BigIdeasMath.com.
● Add your own illustrations to your project.
● Try to include as many different math concepts as possible. Your goal is to include at least one concept from each of the chapters you studied this year.
● Organize your math stories in a folder, and think of a title for your report.
Literature ProjectA.1
Sample: You could rewrite Alice’s shrinking adventure as follows.
Alice’s normal height was 4′7′′ or 55 inches. After drinking the bottle marked “Drink Me,” Alice could feel herself shrinking more and more. After several minutes, Alice was only two-elevenths of her original height. Would Alice have to bend over to walk through a door that is only 1 foot high?
The illustrations on these two pages are from the 1907 edition of Alice’s Adventures in Wonderland. They were drawn by Arthur Rackham (1867–1939), a book illustrator from England.
Literature
di A i l d f “Bi Id ” j t
ppe
at least one concept from each of the
A8 Appendix A My Big Ideas Projects Section A.4 Science Project A9
Why Does Ice Float?
Among the planets in our solar system, Earth is clearly the “water planet.” Water occurs on Earth’s surface as a liquid, solid, and gas. Ocean waters cover about 70% of Earth’s surface. Fresh water in lakes and rivers covers less than 1%. Thick sheets of ice permanently cover Earth’s polar regions, and glaciers occur in its higher mountains. Water in the form of clouds covers about half of Earth’s surface at any time.
Essential Question How does fl oating ice affect you and the world in which you live?
There are three parts to this question. First, you have to understand why things fl oat in water. Make lists of things that fl oat in water and things that do not fl oat in water. How can you describe, scientifi cally, the difference between these two types of objects?
Second, you have to discover what is special about water. Almost all other elements and compounds have the property that their solid forms sink in their liquid forms.
Third, you have to research how water in solid form infl uences the environment and living organisms. You may want to explore ocean currents, weather, and various cycles including the water cycle.
Getting Started1
Things to Include2 ● Does vegetable cooking oil
fl oat in water? Does ice fl oat in vegetable oil?
● Compare the density of water and the density of ice. How do these densities relate to the fact that ice fl oats in water?
● What percent of an iceberg is above the water? What percent is below?
● What environmental and biological systems would not work if ice sunk in the oceans instead of fl oating?
● Explain how the fl oating of ice helps keep the oceans warm and therefore helps aquatic life exist in Earth’s polar oceans.
Science ProjectA.4
Things to Remember3 ● Add your own illustrations to your project.
● Try to include as many different math concepts as possible. Your goal is to include at least one concept from each of the chapters you studied this year.
● Organize your report in a folder, and think of a title for your report.
’s
Earth’s North Polar Ice Cap
Floating Iceberg
surface. Fresh water inthan 1%. Thick sheetsarth’s polar regions, and glacieater in the form oe at any tim
es flfl
s questMake lists of twater. How can you dese two types of objects?
er what is special about water. Almost all unds have the property that their solid
orms.
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● What ensystemsin the oc
●●● Explain keep thehelps aqpolar oc
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–19
Appendix A My Big Ideas Projects Section A.3 Art Project
Circle Art
Circles have been used in art for thousands of years.
Essential Question How have circles infl uenced ancient and modern art?
Find examples of art in which circles were used. Describe how the artist might have used properties of circles to make each piece of art.
Getting Started1
Things to Include2 ● Describe how ancient artists
drew circles.
● Describe the symbolism of circles in ancient art.
● Find examples of how circles are used to create mosaic tile patterns.
● Measure the angles that are formed by the patterns in the circle art you fi nd. For instance, you might describe the angles formed by the netting in the Native American dreamcatcher.
● Find examples of the use of circles in modern art.
● Use circles to create your own art. Describe how you used mathematics and the properties of circles to make your art.
Art ProjectA.3
Things to Remember3 ● Add your own illustrations to your project.
● Try to include as many different math concepts as possible. Your goal is to include at least one concept from each of the chapters you studied this year.
● Organize your report in a folder, and think of a title for your report.
Sample: Here is a technique for making a pattern that uses circles in a stained glass window.
1. Use a compass to draw a circle.
2. Without changing the radius, draw a second circle whose center lies on the fi rst circle.
3. Without changing the radius, draw a third circle whose center is one of the points of intersection.
4. Without changing the radius, continue to draw new circles at the points of intersection.
5. Color the design to make a pattern.
sands of years.
infl uenced ancient
were used. Describe how the h i of art
Mexican Tile
Ancient Roman Mosaic
Native AmericanDreamcatcher
l at
aterthetha
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oati
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TT
●
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A4 Appendix A My Big Ideas Projects Section A.2 History Project A5
Mathematics in Ancient Egypt
The ancient Egyptian civilization in North Africa began around 3150 b.c. with the union of Upper and Lower Egypt under the fi rst pharaoh. The rule of the pharaohs ended in 31 b.c. when the Romans conquered Egypt and made it a province.
The ancient Egyptians’ achievements included a system of mathematics, glass technology, medicine, literature, irrigation and agricultural techniques, and art. Their mastery of surveying, quarrying, and construction techniques allowed them to build pyramids, temples, and obelisks.
Essential Question How is mathematical knowledge that was originally discovered by the ancient Egyptians used today?
Getting Started1
Things to Include2 ● Explain how the ancient Egyptians
multiplied two whole numbers. Give an example.
● Explain how the ancient Egyptians divided two whole numbers. Give an example.
● How did the ancient Egyptians write whole numbers? Give some examples.
● How did the ancient Egyptians write fractions? Give some examples.
● How did the ancient Egyptians use ratios to measure the height of a pyramid? Give an example.
Write your name using ancient Egyptian hieroglyphics.
Describe how ancient Egyptians used mathematics. How does this compare with the ways in which mathematics is used today?
History ProjectA.2
Sample: To multiply two whole numbers, the ancient Egyptians repeatedly multiplied by 2. The “doubling lists” used to multiply 53 by 85 are shown. The lists stop when the last number in the fi rst list is greater than the fi rst number in the second list.
● 1 53 2 106 ● 4 212 8 424 ● 16 848 32 1696 ● 64 3392
Because 85 = 1 + 4 + 16 + 64,85 ⋅ 53 = 53 + 212 + 848 + 3392 = 4505.
Things to Remember3 ● Add your own illustrations to your project.
● Try to include as many different math concepts as possible. Your goal is to include at least one concept from each of the chapters you studied this year.
● Organize your report in a folder, and think of a title for your report.
Egypt
with the union
Ancient Papyrus
●
Becaus85 ⋅ 53
The Blue Sphinx
Ancient Egyptian Numbers
Ancient Egyptian Alphabet
What does this spell?
pharaoh. The rule of the pharaohs red Egypt and made it a province.
uded a system of mathemation and agr
ying, andand o
nowoday?
write whole numbers? Give someexamples.
d the ancient Egyptians wrsome examples.
Egyptians usheight of a
xample.
ame using ancient ptian hieroglyphics.
Describe how ancient Egyptians ucompare with the ways in which mare
the
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