Student will complete the Mondrian Inspired Art Challenge and engage in substantive experiences with multiplication and geometric measurement. Through the challenge and the follow on lessons, the mathematical purpose is to develop deep foundational understandings of area — square units, covering a plane, (3.MD5.a&b) counting units, (3MD.6), relating area to addition and multiplication (3.MD7.a&b), use the area model to represent the distributive property (3.MD7c, 3.OA7), recognizing area as additive and using it to solve real world problems (3.MD7.d) and distinguishing between linear and area units of measure (3.MD.8).

Building a maker mindset (link)

This cycle would be best after students have had initial experiences with multiplication, but they do not need to be proficient with the facts. (Fluently multiplying within 100 the year end expectation, 3.OA5).

Students will collaboratively create a painting inspired by Piet Mondrian, while studying multiplication and geometric measurement. Each project will will be completed on grid paper, up to 18” x 28”, and will have specific mathematical constraints, but all will be unique works of art. As part of the challenge, students will analyze their art mathematically — building spatial reasoning (e.g., simultaneously visualizing rows and columns in a rectangular array) and foundational geometric measurement concepts (e.g., using rows/columns to determine the area of a rectangle through repeated addition or skip counting; conservation of area, awareness that area is additive) and more advanced geometric measurement and multiplication concepts (multiplying length and width to find the area of a rectangle, using the distributive property in an area context). Students will also have substantive opportunities to practice their basic multiplication and addition skills throughout the challenge cycle.

Students first cut their sheet to the size they like, within given parameters. Then, they determine the area of their work in square inches. They tape their perimeter and determine the length of tape needed in inches. After a brief whole class discussion of strategies and the difference between linear measurement units and area measurement units, students begin to plan to create their art by pre-determining a few characteristics of their piece, including which colors will fill up the most and least area in their piece. An aesthetic challenge is to design their project so not all line segments go edge to edge on the paper. Students can scout to see how classmates address this challenge. They sketch their draft, indicating which colors go where, then determine the area of each of the rectangles in their project. Students then compute the sum of areas of each color. And then sum of the color totals. This total should be equal to the area of their project. If not, they need to work to find their discrepancies. A whole class discussion follows to discuss strategies, as well as emphasizing concepts including conservation of area. Strategies include “shortcuts in adding”. For example, if you have three 3x5 rectangles, you could think about that as (3x3) x 5 which is the associative property. Or, if you had 3x5 and 4x5, you could think of that as (3+4) x 5 which leverages the distributive property. Emphasizing that these shortcuts are useful and algebraic thinking supports students growth.

Once all the mathematics work is analyzed, students paint their work. Finally, they tape their work, using ½” tape on the border lines. A final math exploration is to determine the length of tape required for each project.

### Prior Experience:

This cycle would be best after students have had initial experiences with multiplication, but they do not need to be proficient with the facts. (Fluently multiplying within 100 the year end expectation, 3.OA5).

### Credits and Sources:

Gena Richman, 2nd/3rd Grade teacher Mary Collins School, Petaluma City School District

Richman, G. (2007). Mathematics through Art, CMC ComMuniCator, California Mathematics Council.