Math Art with Fibonacci

We read the book Blockhead: The Life of Fibonacci and then did some math art.

In Blockhead: The Life of Fibonacci Fibonacci is ridiculed for daydreaming as a child, but then grows up and becomes a merchant. In his travels he learns about Arabic numerals, counts everything and poses several mathematical questions. Both Fibonacci's Rabbit Question and number pattern are clearly explained during the context of the story.

Lucinda at Navigating by Joy recommended this book and I'm so glad she did. This is the type of book that inspires a variety of activities. We used it to inspire us to create Fibonacci Spirals. It would have gone well with our Roman Numeral Unit when we played Roman Numeral Bingo. Pisa, the Leaning Tower, nature study, ancient travel and boats, and trading could all be covered with this book.

Fibonacci's pattern 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on is created by adding the previous two numbers in the sequence together to get the next number. The Fibonacci numbers are abundant in nature and can be used to create beautiful spirals.

After reading the story we got out some graph paper and began coloring.

This picture represents the first three numbers in the sequence.
Red Square - 1x1
Orange Square - 1x1
Yellow Square - 2x2

The next four numbers in the sequence were added.
Green Square - 3x3
Light Blue Square - 5x5
Dark Blue Square - 8x8

The spiral is created by connecting the corners of the squares in order of their creation. This spiral was created with strait lines, but it could also have been drawn with curves.

Next we worked on the Rabbit Problem.
If one pair of baby rabbits takes one month to become a pair of adults, and adult rabbits have one pair of baby rabbits per month, how many pairs of rabbits will there be at the end of one year?

Month	Babies	Adults	Total
0	1	0	1
1	0	1	1
2	1	1	2
3	1	2	3
4	2	3	5
5	3	5	8
6	5	8	13
7	8	13	21
8	13	21	34
9	21	34	55
10	34	55	89
11	55	89	144
12	89	144	233

233 Pairs of Rabbits! No wonder there were so many bunnies running around in Colorado where we used to live. To see more of our Math Activities please visit our Math Page.

Sign-up to follow Highhill Education by email below.

Enter your email address:


Delivered by FeedBurner

* I did not receive any compensation for this recommendation. I'm just a homeschooling mom who has found many products that I like. If you're interested in the products I recommend on this blog I want to make it easy for you to find them. 
** I am an Amazon associate and receive a small portion of the sales on orders made after clicking in from this site, which I promptly spend on homeschooling books and supplies for my children.

Byzantine Empire - Lego Hagia Sophia Dome

Week 2 - We learned about what happened after the western half of the Roman Empire fell and built a model of the Hagia Sophia's dome.

After the western Roman Empire fell, Europe was in turmoil, but the eastern empire thrived for another 1000 years. Here is a very simple and brief overview of the time period between 500 AD and 1000 AD known as the Dark Ages in western Europe and the Byzantine Empire in eastern Europe and western Asia.

Because the Roman Empire grew to a great size and became difficult to defend, the empire was split in two. Rome was the capital of the west and Constantinople was the capital of the east.

The western Roman Empire ran out of money and couldn't pay the army, so the army invaded Rome. Soon after, the capital and lands were invaded by many other tribes such as the Goths, Visigoths and Vandals.

The turmoil lead to a complete breakdown in leadership and infrastructure. To survive, the people of the west formed small kingdoms. (Each circle represents a kingdom.) The kingdoms fought with each other.

In the east, Christianity was flourishing by force. The city of Constantinople was strengthened with walls and an extensive water system which included grand underground cisterns. The people had public baths, running water, public entertainment and lived in relative comfort.

While the Byzantine Empire continued to thrive, an Emperor named Charlemagne began to unite the lands of Northern Europe. He forced Christianity, repaired roads, and built schools. Although the country wasn't ready, the period when Charlemagne ruled was a mini-Renaissance.

Meanwhile, the Muslims were growing across Northern Africa. Eventually they crossed into Spain across the Straits of Gibraltar and restored the economy by introducing water management technology and new crops. They brought their religion and came to be known as the Moors.

When Charlemagne died, the empire he built crumbled. Not long after the Vikings attacked at many locations.

In Brittan they were confronted and expelled by Alfred the Great, but in Northern France they managed to win land known today as Normandy.

William the Conqueror, a descendent of the Normandy Vikings, fought with Harold Goodwin in the Battle of Hastings in 1066 for the English crown.

While the people of Northern Europe were gathering together for the Crusades, the Moors in Spain were busy translating ancient texts from Arabic into Latin and sowing the seeds for the Renaissance.

To learn more about the Byzantine Empire, we watched the video Engineering an Empire - Byzantine.

The Byzantine Empire lasted 1000 years before it was eventually conquered by the Ottoman Turks. One of the first powerful emperors of the Byzantine Empire was Justinian. He was disliked by the people for his greed and brutality, but tried to make peace by building an incredible Christian Church.

The Hagia Sophia, located in Istanbul, was built in the year 537. With ground breaking technology, the Byzantines were able to create a huge interior space by building a dome, buttressed by semi-domes. After the Ottoman Turks conquered the city, the Hagia Sophia was converted into a mosque and was the main influence for constructing other mosques in the region. For that reason, the book Mosque by David Macaulay is an excellent book for obtaining a better idea of how the church was built.

Our Hagia Sophia dome was constructed from Legos.

We began with four arches,

and a dome.

After several collapses, the main supports were reconstructed from different blocks. Incidentally, the original dome of the Hagia Sophia also collapsed and had to be rebuilt.

The dome is supported on four arches.

The area in the corners between the arches is known as the pendentives. This technique of resting a dome on four arches and pendentives was developed by the Romans, but the Hagia Sophia is the first large scale building which uses the technique.

The dome was carefully put into place.

Sign-up to follow Highhill Education by email below.

Enter your email address:


Delivered by FeedBurner

This post is linked to:
Sola Gratia

Schwarzenacker - Ancient Roman City - Homburg, Germany

The Roman Museum in Homburg, Germany was once a Celtic settlement and later a Roman settlement. During the early 1900's the settlement was rediscovered when construction uncovered many buried silver Roman coins. The coins were most likely buried when the Germans kicked the Romans out of the area, only to be left in the ground for over 1000 years.

Schwarzenacker was on two major cross routes between Trier, Strassbourg, Metz and the Rhine River. At one time the city was home to craftsmen, weavers, and doctors.

 

Today the museum is an active archaeological site.

Many of the underground structures contain oval shaped cutouts which were once used to display statues of the Roman Gods.

Much of the site lies buried beneath the ground.

Several structures have been reconstructed like this home.

Wall murals have been reconstructed in full color.

The basement area of homes usually contained a heat source and the floor was supported with pillars.

The windows contained bars to keep out unwanted guests.

This is the reconstruction of a temple.

This furniture is representative of furniture in a Roman home.

Many frescoes of Gods were brightly painted.

Notches in a stone structure were once used to support wooden beams on which upper floors were built.

The floor would be built on the wooden beams.

This stone hole in the ground is the remnant of a Roman refrigerator.

Waste water was directed out of the city through stone ditches narrow enough to step or leap over.

Rome Unit Study - Writing Assignments

In conjunction with our Roman Unit Study the kids did several short Roman writing assignments.

• Concrete, surveying tools to build straight roads, etc. What do you think was Rome's best tool or invention?
• How did aqua ducts and running water change life for the Romans?
• Write about how a Roman Fort is similar to an American Air Force Base.
• Write a postcard to a friend or family member far away like the Roman soldiers did.
• Pretend you are a Roman soldier and you just saw an elephant for the first time. Write down your thoughts.
• Many of the things the Ancient Romans did are considered immoral by our standards. Choose one immoral act of the Romans to write about. (Gladiators, slavery, enforcing views and way of life on others).
• Pretend you are the historian Pliny and you just saw Vesuvius erupt. Write about what you saw.
• Pretend you are a charioteer at the Circus Maximus. Write your story.
• You are a Roman water engineer working on a new water system. Describe your design. What are your concerns?
• Interview Hadrian and ask the function of the Pantheon. How was it designed? What was it's original name?
• How was Hadrian's Wall similar to the Great Wall of China?

This post is linked to: 
Sola Gratia

Rome Unit Study Books

In conjunction with our Roman Unit Study we read several books. City, The Story of Rome and Roman Myths are my top three recommendations for a Rome Unit Study. The other books will enhance a Rome Unit Study even more.

The Story of Rome (Yesterday's Classics) by Mary MacGregor is a living history book which begins with early Roman Mythology and ends just after the death of Julius Caesar.

Our Young Folks' Plutarch (Yesterday's Classics) is a series of biographies of Ancient Greeks and Ancient Romans which covers basically the same time period. Both books contain similar stories.

Reading both books simultaneously with my eleven year old helped us to comprehend many of the significant events in Roman history as well as the people involved.

In The Eagle (The Roman Britain Trilogy) the reader is taken on a journey to the days of the Roman Frontier. Recommended for 6th grade and up.

A Roman Fort is a non-fiction book with nice pictures and explanations which paints a picture of what it would have been like to live in a Roman Fort. Recommended for elementary and up.


City: A Story of Roman Planning and Construction by David Macaulay gives an accurate fictional account of building a Roman City. In the story the city planers layout the city, build aquaducts, thermal baths, housing and other aspects of the Roman City. Both my nine and eleven year old children enjoyed this book.

I read the non-fiction book Ancient Rome as a reference. It helped me to gain a better understanding of the various territories of the Roman Empire.


The Roman's adopted myths from many cultures and made them their own. Therefore, many Roman Myth books are nearly identical to Greek Myth books with the exception of the names of the Gods.

Roman Myths by Geraldine McCaughrean was not a Greek Myth book. It contained several myths unique to the Romans. Beginning with the fall of Troy from Greek legend, the book included the story of Romulus and Remus as well as the story of the Sabine Women. Recommended for grade 3 and up. 


Pompeii is a subject that fascinates and terrifies. My six and nine year olds enjoyed reading book Pompeii...Buried Alive! (Step into Reading) They had many questions and so we found the more detailed book The Buried City of Pompeii: Picturebook . My nine year old son is currently reading the Magic Tree House series to my six year old. Vacation Under the Volcano (Magic Tree House, No. 13) , book 13, is all about Pompeii.


Galen was a doctor to Roman Emperors and Gladiators. He served four different emperors and learned about anatomy by dissecting animals since dissecting animals was illegal. Reading Galen and the Gateway to Medicine , a simple chapter book is a fun way to learn about life and medicine during the Roman times.


Last, but not least, the book Life of a Roman Slave (Way People Live) gave an eye opening view of what it would have been like to be a slave. Slavery is bad in any culture, but  Roman slavery was much different than American Slavery. If I had to be a slave I would much rather be Roman, than American. I read this book and passed on much of the information to the kids, but my eleven year old could have easily read it on her own.

* I did not receive any compensation for this recommendation. I'm just a homeschooling mom who has found many products that I like. If you're interested in the products I recommend on this blog I want to make it easy for you to find them. 
** I am an Amazon associate and receive a small portion of the sales on orders made after clicking in from this site, which I promptly spend on homeschooling books and supplies for my children.