# Origami geometry

Students apply their knowledge of geometric terms to follow directions while folding an origami sculpture. Students then solve math problems which relate to the project with follow-up discussions about the project relating to geometric terms such as symmetry, faces, edges, square, triangle, plane, etc.

**A lesson plan for grades 3–5 Mathematics**

## Learning outcomes

Students will:

- produce an origami sculpture.
- use the appropriate vocabulary to describe the origami sculpture and explain the sequence followed in its development.
- solve related math problems upon completion of the sculpture.

## Teacher planning

### Time required for lesson

50 minutes

### Materials/resources

#### Physical Resources

- Paper precut to the appropriate size for the origami sculpture
- A copy of the directions for the chosen origami sculpture (one for each student, pair, or group)
- Paper, pencil, calculator for solving follow-up mathematics problems

#### Classroom Environment

- Table space large enough for all students to fold individual sculptures
- Computer with access to the Internet for all students

#### Set-up of lesson

- Computer ready for group presentation of selected websites
- Review vocabulary including simple fractions 1/2, 1/3, 1/4, and the geometric terms symmetry, faces, edges, triangle, rectangle
- Paper should be arranged on a central table for easy access by all students or ready for teacher distribution.

### Technology resources

- Computer with Internet access
- Optional: computer projector, SmartBoard, or any available mode of group Internet presentation, computer lab for individual Internet site exploration, digital camera for recording process

## Pre-activities

- The teacher should have previous experience of folding the selected origami sculpture.
- Teacher should pre-select related websites, either bookmarking or creating a desktop folder containing these sites.
- Optional: Read Sadako and the Thousand Paper Cranes by Eleanor Coerr prior to this math lesson.
- Lead-in depends upon student background information; such as a discussion of the book Sadako and the Thousand Paper Cranes.
- Students should already be familiar with simple fractions 1/2, 1/3, 1/4, and the geometric terms symmetry, faces, edges, triangle, rectangle, square, rhombus.
- Introduce origami (an ancient Japanese art form)

## Activities

Introduce Origami via Internet. (On a preceding day, I did this as a 50 minute pre-activity using a projector to provide a teacher directed overview and site exploration. Then in the same lab setting, students accessed the site on individual computers for self-exploration.)

- Orally review fractional parts 1/2, 1/3, 1/4, and geometric terms: symmetry, faces, edges, triangle, rectangle, square, rhombus.
- Distribute Origami paper and instructions (swan and shirt attached). Students may work as individuals, pairs or in small groups as best fits your class. Use the instructions for a swan or for a Hawaiian shirt.
- Optional: Record folding process via digital camera, still shots or video. These can be published on class/school webpage or newsletter.
- Forum - Have students describe the folding process using geometric terms, e.g., faces, symmetry, edges, rectangle, triangle, etc. as they apply to your chosen Origami.
- Solve math problems related to the projects; e.g., elapsed time, geometric shapes, lines of symmetry, cost of project, etc. These questions depend on the abilities of the students in the class and may be posted on an overhead, chalkboard, handout, or HyperStudio teacher created test stack.
- Open discussion follow-up - Have students discuss pros and cons of verbal, oral, pictorial directions, self-evaluate procedure and resulting sculpture.
- Teacher scores using rubric and math problems.

## Assessment

- Creation of an origami sculpture scored by the attached rubric.
- Students explain the sequence of folding the sculpture (orally for my group)
- Correct solution(s) of the follow-up math questions

## Supplemental information

Math in Motion: Origami in the Classroom K-8 by Barbara Pearl

### Comments

Permission for the RTF Swan and Hawaiian Shirt Origami instructions granted for educational, non-profit purposes by creator Emma Craib, Manchester Public Schools, Manchester CT. She is an elementary art teacher.

- Common Core State Standards
- Mathematics (2010)
#### Grade 3

- Geometry
- 3.G.2Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

- Operations & Algebraic Thinking
- 3.OAT.3Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

- Geometry
#### Grade 4

- Geometry
- 4.G.3Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

- Operations & Algebraic Thinking
- 4.OAT.3Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown...

- Geometry

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 3

**Goal 3**: Geometry - The learner will recognize and use basic geometric properties of two- and three-dimensional figures.**Objective 3.01**: Use appropriate vocabulary to compare, describe, and classify two- and three-dimensional figures.

**Goal 5**: Algebra - The learner will recognize, determine, and represent patterns and simple mathematical relationships.**Objective 5.01**: Describe and extend numeric and geometric patterns.

#### Grade 4

**Goal 1**: Number and Operations - The learner will read, write, model, and compute with non-negative rational numbers.**Objective 1.05**: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

**Goal 3**: Geometry - The learner will recognize and use geometric properties and relationships.**Objective 3.03**: Identify, predict, and describe the results of transformations of plane figures.- Reflections.
- Translations.
- Rotations.

#### Grade 5

**Goal 3**: Geometry - The learner will understand and use properties and relationships of plane figures.**Objective 3.01**: Identify, define, describe, and accurately represent triangles, quadrilaterals, and other polygons.**Objective 3.02**: Make and test conjectures about polygons involving:- Sum of the measures of interior angles.
- Lengths of sides and diagonals.
- Parallelism and perpendicularity of sides and diagonals.

**Objective 3.03**: Classify plane figures according to types of symmetry (line, rotational).