Overview: Teaching perimeter and area with geometric line art through works from Piet Mondrian.

This 3rd grade math lesson uses the art of Piet Mondrian to teach and practice geometric concepts of perimeter and area.  Visual art is a natural place for students to apply their knowledge and understanding of geometric concepts. There are so many great lesson plans and resources out there for arts integration in geometry. And, this lesson is focused on using the work of Piet Mondrian as a real-life access point to these concepts.

## Standards

CCSS.MATH.CONTENT.3.MD.D.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

NCCAS.VA:Cr1-3.b: Apply knowledge of available resources, tools, and technologies to investigate own ideas through the art-making process.

### Engagement/Pre-Assessment

1. Lead students in a review a variety of polygons, including rectangles of differing areas and perimeters.
2. Next, introduce students to the artist Piet Mondrian (biographical information here). Show students examples of his artwork (slideshow here: show slides 9-19 in particular, as this is the color scheme students will be working with).
3. Then, facilitate a discussion that asks students to make connections between the artwork they just saw and math. (For example, how does Mondrian make his shapes interesting? Lead students to recognize that the shapes have different lengths and widths, areas, perimeters.)
4. Ask students to make any other observations about artistic elements of Mondrian’s work (color, line).

### Lesson Steps

1. Divide the class into small groups of 3-4 students, and give each group a print of a piece of Mondrian’s art. Ask students to identify the shapes in their piece of artwork and for as many shapes as possible, find: area, width, perimeter, area.
2. Next, ask students to figure out if any of the shapes in their piece of art have the same perimeter but different area. Or, the same area, yet different perimeter. Moreover, they may also compare their math to other groups looking at various pieces of art.
3. Then, using graph paper, ask students to experiment with creating polygons that have same area and different perimeter, as well as same perimeter but different area.

### Assessment

Students will create a piece of Piet Mondrian-inspired artwork that includes various polygons (same/different area, same/different perimeter).

1. Distribute graph paper to students. Explain that they will use this graph paper to create their various polygons.
2. Next, draw students’ attention to the following guidelines. Students will be assessed on the Mondrian Geometric Art Rubric.

### Guidelines

–  Your piece of art should have two polygons with same area/different perimeter, and two with same perimeter/different area.
–  You may use graph paper as a reference.
–  Your polygons may be red, yellow, or blue, with black lines, as this was often the color scheme Mondrian used. You are encouraged to leave some white space as well.
–  Your black lines may be thick or thin.
Artist Statement
–  Describe your art in comparison to Mondrian’s style.
–  Show and explain your mathematical work regarding the area/perimeter of your polygons.