Algebra & Functions Linear Equations

About the Artist and Artwork

Bernhard Reinhold began his artistic career in Copenhagen, where he studied with the famous nineteenth-century Neoclassical sculptor Albert Bertel Thorwaldsen. In 1846, Reinhold traveled to Munich and then to Rome, devoting himself to painting. Following this year of intense study, he established a studio in Dresden, where he became a successful painter of genre scenes and portraits.

The concept of childhood as a time of innocence and nurture greatly expanded with the second wave of industrialization in Europe. There and in America, concern for the welfare and education of the young took on new sentimental meanings. In Germany, the written accounts of native folklore by the Brothers Grimm provided the cornerstone of modern German language studies while also providing youngsters with colorful, moralizing literature, which gave rise to a vibrant illustration industry. This appealing young mason set against the Roman campagna plays upon sentimental tastes by combing notions of innocence with the allure of a simpler, distant lifestyle. The youth’s profession as an apprentice honors the traditional status and respect enjoyed by tradesmen prior to industrialization. His patched, but sturdy work clothes, leather apron, and jaunty scarf adding local color to an otherwise ordinary scene of child labor, were common during the nineteenth century. He is preparing to eat his frugal meal of rye bread and bologna sausage, to which a few cherries are added by way of dessert. As he sits upon the stonewall, he is perhaps dreaming of the glorious future, which is to convert the little mason into a great and famous architect.

Lesson Procedure

Day 1

1. Have students look carefully at the image, Young Mason Eating His Dinner. This image is accessible on Digital Crocker at crockerartmuseum.org, on the Striking Gold CD ROM, and slides and overheads available for purchase through School Services.

2. Summarize Young Mason Eating His Dinner to the students and provide a definition of genre painting (a scene of everyday life).

3. Lead an open class discussion with questions, and record all comments on the board. Ask:

   a. How old do you think this boy might be (around 12 years old)? The title tells us that he is a young mason.   Do you know what that is (a mason builds things using bricks)? What tools do you see that he might use in his trade?

     b. Does he look like he makes a lot of money? What do you see that makes you say that? (The clothes he’s wearing may be his work clothes, but probably he owns no clothes that are any better.) What kind of expression is on the boy’s face? Does he appear tired? Do you think he had to walk to work? Do you think he lived nearby?

     c. What do you think about children having a job like this at his age? He probably had very little education and would probably do this kind of hard labor for the rest of his life. How long ago was this painting made? Child labor was common during the time that this painting was made. Do you think we have labor laws in America protecting children now? What about in other countries? How much money do you think this boy made per hour (probably about 22 pounds/year, which was equivalent to about 35 dollars/year)? What is the legal minimum wage in America today?

     d. The way that the artist has organized the elements in this painting is called the composition. It is a triangular shape. The boy’s head is at the top of the triangle. Can you take your finger and trace a triangle shape through the composition?

4. Compare the young mason’s life with what students today hope to achieve. Ask the class what kinds of jobs they hope to get when they can work. Ask them if they want to own a car, an apartment or house, go on vacations, buy new cloths, go to music concerts or other kinds of entertainment events, and eat out at restaurants. How much money do they estimate those things cost? What other things would they like to do or purchase that costs money? Break students into groups and have them discuss the following math problems:

     a. The young mason was making about $35 per year. If he worked every month, how many dollars did he make per month? If he worked 24 days per month, how many cents did he make each day?

     b. You make a wage of $8 per hour and you work 15 hours per week. You get a paycheck every two weeks. How much do you expect your gross (nothing taken out of your paycheck for benefits, taxes, etc.) paycheck to total?

     c. You are going to drive to San Francisco to see a music concert. Your car gets 30 miles per gallon of gasoline. Your driving distance is 90 miles one way from Sacramento to San Francisco. How many gallons of gasoline will you need for the round trip (remember to calculate enough gas to get back home)?

     d. The Fong family went on a vacation. They started with $3,000. Write an expression that represents how much money they had after x days, if they spent $250 each day.

     e. Rufino had some change in his pocket. After his friend gave him $0.75, Rufino had $3.35 altogether. Write an equation that he can use to find the original amount of money, m, he had in his pocket.

     f. Enrique works at a restaurant. It takes him 3 minutes to fill 5 large cups of soda using the soda machine. At this rate, how many minutes will it take him to fill 25 large cups?

     g. Maija wants to rent an apartment with her best friend and split the $487.50 monthly rent. She earns $9.75 per hour at her after-school job. How many hours does she have to work to earn her share of the rent?

     h. If x – 5 = 13, what is the value of x?

     i. What is x if 7x = 98?

     j. In the equation x + y = 9, what is the value of x if y = 3?

     k. What value of x satisfies the equation 6x + 3 = 57?

     l. What is the value of x if -4x + 5 = -27

Day 2 - 3

1. Art production: Discuss the items in the painting that communicate the boy’s everyday life, such as his cloths, his activity, what he’s eating, the time of day, and the setting/environment. Lead the class in a discussion of items that convey everyday life for the students today (household chores, school books, hobbies, tennis shoes, jeans/clothes, cell phone, pizza, basketball/sports, bicycle, etc). What kinds of images will they find in magazines for clothing, food, jobs, activities, housing, etc.? What kind of setting do they imagine themselves (in a park, at school, at home, on a sports field, on a lake, at a theater, in a restaurant, in a museum, etc.)?

2. Break students into pairs to discuss how they might create a triangular composition that communicates everyday life for them. Have students write their ideas down on a piece of notebook or scratch paper. Students will list at least two settings and three ideas, such as chores, clothing, and music. Have students look through magazines and select a few images that could represent those concepts and the settings (needs to be a full page from a magazine to cover the full sheet of copy paper - some text will be okay if it can be covered by the collage work).

3. Once you have approved the three concepts and the setting, distribute one sheet of 8 ½ x 11” white copy paper to each student.  

4. Students will need to look through several magazines and cut out images that represent their daily lives. Remind students to vary the sizes, colors, shapes, and implied textures of the images.

5. After students have selected and cut out several images, students will lay out the images in a triangular composition. Students should try several different placements of the images before deciding on the final composition. Remind students to slightly overlap the images and to review the composition in the focus artwork.

6. When an aesthetically pleasing composition is finalized, students will use glue to complete the collages.

7. On the back of the collage, each student should write about one of the images. Have students write a sentence about the image that involves a rate, such as “I am on the track team and practice every day for 2 hours. It takes me 15 minutes to run one mile.” Then write an equation that applies the rate.

8. Have students share their collages and explain their equations.