Finding Value in     the Renaissance
	Class: Math Theme(s):

Lorenzo Lotto Saint Jerome Penitent 1515 Oil on panel Enlarge Lorenzo Lotto, who painted this picture in 1515, signed a contract in 1513 to create an altarpiece for the largest amount paid to an artist in Venice, 500 ducats (Venetian dollars)

The amount of money a Renaissance artist received for making a work of art varied widely. An artist of great reputation could expect to receive more money for a commission than a young artist just starting out. The materials that a patron ordered also determined the price of a work of art. For example, a payment for a stone statue might see the artist through a year of living expenses, while the same statue in bronze would cost ten times that amount. Casting a bronze statue took considerably more technology than carving stone, and the ability to create bronze sculpture was considered a modern triumph during the Renaissance. While a statue of a saint carved from stone would look very similar to a statue of the same saint by the same artist cast in bronze, bronze was the more impressive medium, and many patrons were willing to pay for it.

Artists didn't always receive payment in coins. Records left behind by both artists and patrons show that some Renaissance artists received payments of wheat, wine and cloth. If travel was required, a patron might provide an artist with a place to live while he or she worked on a commission.

An artist was often required to pay other crafts people from the payments collected for a work of art. For example, an altarpiece had to be constructed by a carpenter and a wood carver might decorate the framing. If gold leaf was to be applied, it was common for a gilder to do that work. An artist also might be expected to purchase certain kinds of colors for a painting. Ultramarine blue was very rare and expensive but many patrons insisted on it since it was the only blue considered appropriate for the robes of Mary, the mother of Jesus.

Of course the value of an item cannot always be summed up by how much the item costs. If your family has a pet — a dog or cat or goldfish — it probably didn't cost as much as other items your family owns, like a car or television. But in an emergency, like a fire, your family would almost certainly try to save the family pet before they thought of the car or television. A car or television may cost more but they are easier to replace than a family pet.

Works of art created during the Renaissance are expensive because of their rarity and their great contribution to the history of art. We also highly value the art of the Renaissance today because it represents a period in European history that contributed so much to the modern world we live in.

Resources
Kemp, Martin. Behind the Picture: Art and Evidence in the Italian Renaissance, New Haven: Yale University Press. 1997.

Classroom Time
One 40 minute period

Objectives
Students will:

• Solve word problems representing life and art in the Renaissance, using multiple strategies.
• Solve problems with whole numbers, decimals, fractions, percents and ratios.
• Create and extrapolate information from a multiple-bar graph.

Pennsylvania Academic Standards

Materials

• The "Background" section of this lesson, reproduced as a student handout.
• Calculators
• Pencils

Math Lesson

1. Setting the Stage
(Note: The background section of this lesson might serve as a handout to help students in this activity.)

Discuss the history of modern mathematics to students:
Fibonacci was a medieval mathematician (born around 1170 and died around 1250), who studied Indian and Arabian mathematical systems. He introduced Europe to the Arabic symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 with, most importantly, a symbol for zero 0. Before Fibonacci, Europeans used Roman numerals to calculate figures. With Roman numbers, 2003 could be written as MMIII or, just as clearly, it could be written as IIIMM — the order does not matter since the values of the letters are added to make the number. In the system Fibonacci brought to Europe, the order does matter since 23 is quite a different number than 32. Also, since the position of each digit is important, there may be a zero needed to get the digits into their correct places (2003 for example).

2. The Renaissance Connection
All of the story problems that follow are taken from historic documents of Renaissance Italy, and represent real-life amounts, currencies and formulas. As students work the problems, they will learn more about everyday life for artists in the Renaissance.

1. Alberto the Painter received 250 ducats (gold coins used as currency in Venice) to create a painting for a wealthy family in Venice. Because the family expects the painting to be delivered ready to hang, Alberto will spend 20% of his payment to have a frame made for the painting. After purchasing the frame, how many ducats would Alberto have left?
   
   
2. Cosimo has completed a large oil painting but before he delivers it to the patron who ordered it, he must apply a varnish to the painting. The formula he uses to make the varnish is 25% oil copal varnish, 25% poppy oil, and 50% spike oil. If he has 12 ounces of poppy oil, how much spike oil will he need to complete the formula? How much oil copal will he need?
   
   
3. Between the years 1434 and 1471, the Medici family spent 663,755 florins (coins used as currency in Florence) on buildings, charities and taxes. If the Medici family spent 340,576 on buildings and 189,450 on charities, how much did they spend on taxes?
   
   
4. Antonia painted a portrait of a duke standing next to a bookcase. In life, the duke stood six feet tall. When the painting was completed the image of the duke measured 36 inches and the bookcase measured 48 inches. What was the actual height of the bookcase?
   
   
5. Lorenzo was commissioned to create an altarpiece for a church in his town. The altarpiece is a triptych; it has a large panel in the center and two smaller panels on either side. The central panel measures 3 feet tall by 2.5 feet wide. The two smaller panels each measure 3 feet tall by 1.5 feet wide. What is the total area of the altarpiece?
   
   
6. Raphael bought a palazzo for 1365 florins. The palazzo has five shops on the lower level. Raphael rented out each of the five shops for 3 florins a month. How many years would it take for Raphael to earn the purchase price of the palazzo?
   
   
7. In 1470, the standard rate of payment for a painter of frescos in Venice was 10 bolognini (currency used in Renaissance Italy) per foot. Ten bolognini is equal to 1/10 of a ducat. How many ducats would a painter earn for painting a fresco 10 feet long?
   
   
8. Inventories of the wealthy patron family of de Medicis recorded art, weapons, clothes, and antiques. Values of each item were recorded in florins (currency of Renaissance Florence). According to the chart, which item was the most valuable? Which was the least valuable? What is the average value of the items on the chart, rounded to the nearest whole number?

3. Summary
Fibonacci's 1202 book on how to do arithmetic in the decimal system, called Liber abbaci (meaning Book of Calculating,) laid out the rules for the Arabic system. The new math had dramatic effects on the Renaissance, especially merchants who found great advantages in accounting using the "new" system. The system is still in use today, as Fibonacci's rules for adding, subtracting, multiplying and dividing numbers are still taught in elementary school.

4. Assessment:

Renaissance Story Problem Answers:

1. 200 ducats; 2. 24 ounces of spike oil, 12 ounces of oil copal; 3. 133,729 florins; 4. 8 feet; 5. 16.5 square feet; 6. 7 years and 7 months; 7. 10 ducats; 8. the Flemish tapestry was least valuable at 25 florins. The flask was the most valuable at 2,000 florins. The average value of all items is 415 florins.

5. Related Activity
Have students look for additional information in books, encyclopedias, or the Internet.

Vocabulary
bolognini: currency used in Renaissance Venice, Italy. 10 bolognini is equal to 1/10 of a ducat.

commission: to hire an artist or workshop to make a work of art. The individual or company paying the artist will often give some guidelines concerning the subject, medium or size of the artwork. The artwork itself may be called a commission.

ducats: currency used in Renaissance Venice, Italy. Ducats were gold coins, equal to value of 10 Bolognini.

florins: currency used in Renaissance Florence, Italy. Florins could be either gold or silver coins.

fresco: a painting on a wall or ceiling made by brushing pigments into fresh plaster.

oil copal varnish: an oil containing resins which dry to a hard, protective finish.

palazzo: a large and usually official residence in Italy.

patron: someone who orders a commission or otherwise financially supports an artist.

poppy oil: an oil used to thin oil paint, can be substituted for linseed oil.

spike oil: a substance similar to turpentine used to thin oils and speed drying time.

triptych: a painting or carving made of three panels. Often triptychs served as altarpieces where the panels were hinged together so that when the outer panels were folded the middle part was entirely covered.

Lesson Plans