You can use the area model to represent multiplying two fractions. The model can be made into a grid throughout the assignment by having the student draw the appropriate number of lines. The number of squares needs to be the least common multiple of both denominators.

 

When multiplying fractions, students will shade the numerators of the fractions. One numerator will be shaded from the left; the other from the bottom. See the example below. (PDF coming soon.) The shaded region that overlaps is the numerator of the product. The denominator remains the number of squares in the grid.

Preparation:

• Laminate a model for each of your students.
• Offer each student enough transparency sheets to cover the entire model and an erasable marker.

 

Student Instructions: Use the model to help you multiply the following fractions. The number of squares in the model is the least common multiple of your denominators. You want both denominators to be a factor of your grid. In using the model, shade from the left side the number of boxes in your first numerator and shade from the bottom the number of boxes in your second numerator. (PDF coming soon.)

 

½ × ¾ =

 

½ was shaded from the left.

¾ was shaded from the bottom.

 

6 of the 16 squares are overlapping shaded regions. This reduces to 3 out of 8, so the answer is ⅜.

 

½ × ¾ = ⅜

 

 

Use the example to help you complete the following:

 

1. ½×⅔=

 

2. ⅗×⅙=

 

3. ⅚×¼=

 

4. ⅔×⅘=

 

 

Use the PDF for the following activity:  (PDF coming soon)

1. Make a list of colors in the work of art and record 5 of the most prominent colors in the first column.

2. Count the number of squares on the work of art that contain the corresponding color in the first column.

3. Create a fraction; reduce to lowest terms

4. Convert fraction to a decimal

5. Calculate percentage

 

Evaluate Data

1. Analyze parts of the painting according to the different percentages of color present

2.  Discuss which colors were used more frequently and less frequently.  Why?

Notes:

1. Count the number of squares on the work of art that contain the corresponding color in the first column.

2. Create a fraction; reduce to lowest terms

3. Convert fraction to a decimal

4. Calculate percentage

When students start making connections between things that they know and things that they are learning¾they attain the information better. There is some connection between pretty much everything in the world; these are the relationships we want our students to begin to realize and understand.

• Look closely at the composition. How does the artist divide the space?
• Describe the brushstrokes and how the paint is applied. Do the brushstrokes imply that the subject was carefully considered or quickly captured? Explain your reasoning.
• This is an almost-abstracted image of a bridge over a pond. What elements does the artist include that prevents the viewers from immediately knowing the subject of the painting?
• The artist was fascinated with light and atmosphere. How is light captured in this work of art? How would you describe the light? Is it warm or stark?
• What type of mood does the artist create? How does the use of warm, earthy hues add to this tone?
• How would the mood of this work change if it were painted in cool, blue tones?
• How does the artist use color and brushstrokes to depict an immediate impression of light and atmosphere and the sensation of pleasure that it brings?

• Discuss the use of the bridge as a means to spatially separate the foreground and background. Do you think this work would be as powerful if the bridge was not included in the composition?
• Do you think the artist intentionally meant to confuse the viewer?
• The artist attempted to capture the transitory effects of light. Do you think he successfully achieved this goal? Why or why not?
• The artist’s contemplation of natural beauty and his desire to capture the essence of nature on canvas led him to a completely new style of painting that would eventually be known as Impressionism. How does this work embody the style of Impressionism?
• This artist was one of the first artists to paint en plein air (outdoors). How do you think the direct study of nature affect his depiction of nature?
• The artist often painted the same view in nature under different conditions of light and season. In your opinion, why do you think the artist would chose to paint the same scene over and over?
• The artist said, “For me, a landscape does not exist in its own right, since its appearance changes at every moment, but the surrounding atmosphere brings it to life—the light and the air which vary continually. For me, it is only the surrounding atmosphere which gives subjects their true value.” How does this quote apply to the painting?

No subject is more readily identified with artist Claude Monet than his private garden and lily pond, both located at his home within the small French village of Giverny. The tangled brushstrokes and thickly applied paint of The Japanese Footbridge at Giverny yield an almost abstracted canvas that is unusual to Monet’s style. However, this work does not stray far from the artist’s typical repertoire as it reveals his fascination with light and atmosphere. Monet’s great pleasure in the contemplation of natural beauty and his desire to capture the essence of nature on canvas led him to the completely new style of painting later termed Impressionism.

 

Monet’s harmonious combination of unmixed colors and varied brushstrokes produced masterful studies in light. These paintings reveal the artist’s immediate impression of a scene while also refusing to be completely legible. The loud color scheme and vigorously applied paint immediately attracts the eye. The flora, sky, and water are depicted through quickly applied, thick layers of paint that blend together at a distance to reveal the scene. They unite the composition and provide a framework for a uniform background while darker, smaller brushstrokes form the arc of the footbridge. The bridge horizontally divides the canvas and provides the scene with a sense of symmetry.

 

Conjuring fiery, dark evocations of twilight, the warm, earthy hues of red, teal, and gold overwhelm the canvas. The viewer’s attention is focused onto the paint itself rather than being drawn into the scene. Just as the background appears to dissolve into the water in the foreground, the left side of the bridge is enveloped by the glow of nature and seems to be melting into the atmosphere. Floating lily pads and mirrored reflections assume equal stature within the painting as distinctions between solid objects and transitory light are blurred. Monet had always been interested in reflections, seeing their fragmented forms as a natural equivalent for his own broken brushwork.

 

Works like this painting show Monet’s interest in types of compositions that became the forerunners of abstraction. After many years of struggle, during which Monet experienced extreme poverty, the painter finally achieved much financial, critical, and popular success. It was during this chapter in his life that he was able to purchase his home in Giverny and employ staff to help cultivate the beautiful gardens now associated with his paintings. By painting en plein air (outdoors), Monet was able to showcase his analysis of his environment under varying conditions of light and season.

 

“For me, a landscape does not exist in its own right, since its appearance changes at every moment, but the surrounding atmosphere brings it to life—the light and the air which vary continually. For me, it is only the surrounding atmosphere which gives subjects their true value.” –Claude Monet