## Geometry in the World of Art: Mirroring Kandinsky

• Lesson
1

This lesson allows students to apply what they have learned in previous lessons by designing their own art. Students use Kandinsky’s style of art and their own creativity to make paintings that reflect their understanding of geometry.

Introduce the lesson by telling students that they are going to become artists. Explain that their art needs to contain geometric elements (triangles, points, lines, line segments, squares, circles) similar to Kandinsky’s artwork.

Cut different geometric shapes from colored paper and model how to create a picture using the shapes. Have students identify all of the geometric elements found in one of Kandinsky’s paintings using samples from previous lessons. This should take about several minutes and should be done independently.

Discuss as a class the students’ findings and compare what different students observed. By this time, students should see that Kandinsky’s art contains many of the same geometric shapes.

Have students design a rough draft of their picture on the You Are the Artist activity sheet.

 You Are the Artist
Use the list of terms as a guide. Allow time for students to revise their draft. Then distribute paper to the students and have them create a final drawing using markers or crayons.

As you move around the room, ask students to explain why they selected the geometric figures for their particular drawing. Ask them to describe the properties that make the best choice for the picture they created.

Gather the class together and invite students to share their drawings. Encourage them to describe how the properties work in their drawings to create a picture. The drawings may be used on a bulletin board in the classroom or in the hall. Posting some of the students’ responses allows others to understand the mathematical connections with the art.

Assessments

1. At this stage of the unit, students should know how to:

• Apply their knowledge of geometry in another curriculum area
• Explain their designs using geometric vocabulary

2. Use the students’ artwork as the performance assessment for this lesson. Evaluate the students’ effective use of a variety of geometric shapes and lines to create unity and coherence in the drawings.
3. Make notes about each student’s success in meeting the objectives of this lesson on the Class Notes Teacher Resource Sheet. These notes will be useful when you plan remedial or enrichment learning experiences.
4. The following activity serves as a summary assessment of all the learning objectives for the unit. Ask students to study their drawing from the lesson. Then ask them to create a model such as the Graphic Organizer. Use this as a planning tool for organizing writing. Ask the students to write an essay that addresses most of the questions on the Questions for Writing About Kandinksy Overhead.
Before they begin writing, ask students to explain the decisions they had to make before drawing, during drawing, and after drawing. Ask them to organize the questions above into three categories. You might wish to use the Thinking About My Drawing Student activity sheet. Remind students to explain how their study of Kandinsky’s paintings helped them understand how to use geometric shapes in art.
When the students are ready, ask them to read their paper and show their artwork to the class. Encourage them to pose and answer questions that can be answered looking at the artwork. Ask them to make connections between their process for drawing and their finished product with those of their classmates.

Questions for Students

1. How did Kandinsky use parallel lines in his paintings? What purpose did the parallel lines have in your drawings?

2. What shapes can you identify in Kandinsky’s paintings that you used in your drawings?

3. How did Kandinsky use circles in his paintings? How did you use circles in your drawings?

4. How did Kandinsky use both perpendicular and intersecting lines in his paintings? How did you use perpendicular and intersecting lines in your drawings?

Teacher Reflection

• Which students met all the objectives of this lesson? What learning experiences do the others need?
• Which students did not meet the objectives of this lesson? What changes could I make to help those students meet the objectives?
• Which students could communicate about the mathematical components of their drawings? Which could not? What learning experiences do these students need?
• Are there other artists whose work would be good sources for study in math class?
• How should I change this lesson the next time that I teach it?

### Working with Shapes

3-5
Students review basic geometric terms related to triangles. They explore these terms and other geometric concepts by modeling them on the geoboard.

### More Work with Shapes

3-5
Students continue to explore geometric concepts by modeling on the geoboard.  Communication is the Process Standard emphasized in this lesson.

### Finding Lines of Symmetry

3-5
Students identify lines of symmetry and congruent figures. They explore these concepts with paper cutting and modeling on the geoboard.

### Who Was Wassily Kandinsky?

3-5
This lesson provides students with an exploration of the geometric figures Wassily Kandinsky used in his art. Students participate in a scavenger hunt to become familiar with Kandinsky’s works and the geometric figures used in his paintings.

### Seeing Geometry in Art

3-5
Students use paintings studied in the previous lesson to connect their knowledge of geometric shapes and terms with Kandinsky’s use of geometric figures.

### Learning Objectives

Students will:

• Apply their knowledge of geometry by creating their own artwork
• Explain their designs using geometric vocabulary

### NCTM Standards and Expectations

• Describe location and movement using common language and geometric vocabulary.
• Build and draw geometric objects.
• Create and describe mental images of objects, patterns, and paths.
• Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.

### Common Core State Standards – Mathematics

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.A.1
Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.A.2
Correctly name shapes regardless of their orientations or overall size.

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.B.4
Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/''corners'') and other attributes (e.g., having sides of equal length).

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.B.6
Compose simple shapes to form larger shapes. For example, ''Can you join these two triangles with full sides touching to make a rectangle?''

• CCSS.Math.Content.1.G.A.2
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.