# GeoMetric Collage Maker

This lesson combines the artistry of Mondrian with the Mathematics of Geometry. Students create a doodled collage of geometric shapes, resulting in crayon rubbings used to calculate area and perimeter of combined shapes.

**Note:**Any links outside of the3doodler.com are optional resources. We can’t ensure their upkeep or accuracy.

### Knowledge

had practice calculating area and perimeter in centimeters.

practiced drawing quadrilaterals and triangles with rulers.

measured shapes in centimeters.

had practice with the 3Doodler.

### Objectives

innovate, design and create a doodled collage composed of quadrilaterals and triangles.

create crayon rubbings from their doodled shape collages.

calculate area and perimeter of 2-3 combined shapes in centimeters

### Materials

3Doodler START (1 per group)

pencil (2 per group)

ruler (1 per group)

scrap paper (1 per student)

white copy paper (2 per student)

small box of crayons (1 per group)

### Lesson Plan

#### Instructions

Whole group: Review calculation of area and perimeter in centimeters. Practice calculating area and perimeter of 2-3 combined shapes. Note: Find the composite area of two or more shapes, by determining the area of each shape and adding them together.

Share the goal: Students will create shape collages composed of quadrilaterals and triangles, resulting in crayon rubbings used to calculate the area and perimeter of four sets of 2-3 combined shapes.

Model how to create a shape collage of quadrilaterals and triangles using a ruler, pencil and copy paper. Fill the whole paper with shapes.

Demonstrate how to use the 3Doodler to trace over lines in shape collage. Note that it is necessary to weld the adjacent sides of shapes together.

Place another sheet of copy paper over the doodled shape collage. Use crayons to create a crayon rubbing. Use multiple colors to create an artistic piece.

Select 2-3 shapes from crayon rubbing to combine. Calculate area and perimeter in centimeters.

Divide students into groups of 2-3. Hand out copy paper, pencils, 3Doodlers, crayons and scrap paper to record calculated area and perimeter of four combined shapes.

Prompt students to compromise and collaborate on the design of their shape collage.

Circle to assist and assess as students work together.

#### Wrap Up

#### Assessment

#### Possible Extensions

Explore the Four Color Theorem: Students determine how many different colors are sufficient to color all of the shapes in their collage, so that no two adjacent shapes have the same color. Example: Mathforum.org

Explore Angles: Students measure each of the angles in individual and combined shapes from collage.

Open PIC COLLAGE app on tablets. Upload photo images to create photo collages and calculate area and perimeter of individual and combined shapes.

#### Resources

#### Vocabulary

**Doodle**- An object we “draw” using a 3Doodler.**Extrude**- The act of plastic being melted and then ejected from the 3Doodler as a steady stream, similar to a thread until stopped.**Retracing**- The fine and delicate lines created with the 3Doodler are great, but sometimes you want your creation to be a little stronger or you didn’t get it exactly right the first time. Retracing is exactly what it sounds like. You simply extrude back over the lines you've already created to make welded sections stronger or reinforce thinner areas, or just make some small adjustments.**Stencil**- A stencil is a guide that you can draw or print on regular paper and then trace over the lines with the 3Doodler. Stencils can be of simple shapes or very complicated ones. Stencils are useful for making more than one of the same shape.**Welding**- Freshly extruded plastic can be used to weld two already finished pieces. The hotter the plastic used to weld two pieces, the better they will stick together. Touching the hot nozzle of the 3Doodler to the two pieces being joined just before beginning to extrude can remelt the pieces and help create an even stronger connection.

#### Educational Standards

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Students will calculate area and perimeter of 2-3 combined shapes in shape collage.

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measuremen

In Possible Extensions, students will measure angles of individual and combined shapes in collages.

Define a simple design problem that can be solved through the development of an object, tool, process, or system and includes several criteria for success and constraints on materials, time, or cost.

Students will work in small groups to brainstorm, design and construct their shape collage according to the selected criteria of this task.

Plan and create a design document to illustrate thoughts, ideas, and stories in a sequential (step-by-step) manner (e.g., story map, storyboard, sequential graphic organizer).

Students will sketch a shape collage that covers a whole paper using quadrilaterals and triangles to use a stencil for doodling with 3Doodler and creating a crayon rubbing.

Decompose (break down) a larger problem into smaller sub-problems with teacher guidance or independently.

Students will break down the process of creating a crayon rubbing of combined shapes.

Use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

Students will use the 3Doodler to create a shape collage that covers a paper, incorporating tactile skills to enhance learning.

Exhibit a tolerance for ambiguity, perseverance and the capacity to work with open-ended problems.

Students will demonstrate willingness and competency within an open-ended task with more than one possible outcome.

Create original works or responsibly repurpose or remix digital resources into new creations.

Students will create shape collages with 3Doodler.

Use collaborative technologies to work with others, including peers, experts or community members, to examine issues and problems from multiple viewpoint

Students will seek feedback from group members as they create their shape collages.