Lesson 8

The purpose of this task is to introduce students to the artwork of Piet Mondrian. Students may notice that his paintings are composed of rectangles of various sizes. Students will create their own versions of Mondrian art in the first activity.

To show students additional artwork by Mondrian, consider visiting a virtual installation of Piet Mondrian's work on the website of Museum of Modern Art (MoMA) or visiting the website of the Tate Gallery.

• Groups of 2
• Display the images.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “These are digital copies of famous paintings by a Dutch artist named Piet Mondrian. He lived from 1872 to 1944. A little more than 100 years ago, he became known for painting in a style that relates to the math we have been studying. Many of his paintings hang in museums all around the world.”
• “How do you think his art connects with what we’ve been studying? Why are we looking at it during math class?” (He used a lot of rectangles. His art looks very precise. He seemed to have planned for the rectangles to have certain side lengths.)
• If not mentioned by students, highlight that some of the lines go from edge to edge of the painting while others are shorter, and that some rectangles seem to have the same area.
• Considering showing students additional artwork by Mondrian.

The purpose of this activity is for students to create an outline for their artwork. In this activity, students draw lines on graph paper, marking out rectangular areas that will be the basis for their Mondrian-inspired artwork. 

• Each student will need a black marker or crayon.

• “We are going to create our own art pieces that are inspired by Mondrian’s work.”
• Read the activity statement as a class.
• Select a student to explain the task in their own words. Invite the class to ask clarifying questions.
• Give students a copy of the blackline master, a straightedge, and black markers or crayons.

• “Use your straightedge and pencil to partition your grid. Try at least one of the challenges.”
• “Once you are happy with your design, trace it with a black marker or crayon.”
• 13–15 minutes: independent work time
• Monitor for students who attempt or accomplish one or more of the challenges.

• “Compare your work with a partner. What is alike or different about your outlines?” (They are alike because they show only rectangles, but the way they are arranged and their sizes are different.)
• “How can you determine if any of the rectangles have the same area?” (See if the sides are factor pairs of the same number. Use the side lengths and multiply them to see if the product is the same number.)

In this activity, students use their understanding of factor pairs, prime, and composite numbers to analyze their peers’ artwork. They look for rectangles that have the same area and those with a prime number or a composite number for their area. Students practice communicating with precision as they identify rectangles and how they know the rectangles meet these conditions (MP6). 

After students share their analyses with their partner and a brief class discussion, give students time to color their artwork and to prepare it for display.

• Groups of 2
• “Switch artwork with your partner.”
• “Look at your partner’s work and try to find three kinds of rectangles: rectangles with the same area, rectangles with an area that is a prime number, and rectangles with an area that is a composite number.”
• “Then, if your partner completed a challenge from the first activity, see which one they did.”

• 5–7 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for students who consider factor pairs of a number as they look for rectangles with the same area in their partner's artwork.

• Invite 1–2 previously selected students to share how they found rectangles with the same area. (The sides are factor pairs of the same number.)
• “Now, take a moment to color your artwork with 3–4 colors. Later, you'll display your work for others to see.”
• Give students colored pencils, crayons, or markers.
• 8–10 minutes: independent work time
• Give students materials needed for the gallery walk: glue or tape for displaying their artwork and sticky notes for writing comments or questions.