Geometry and Spatial Sense
Identify and describe the 2D shapes that can be found in a 3D figure (compose and decompose shapes)
Identify and compare various polygons and sort them by their geometric properties
Compare various angles, using concrete materials and pictorial representations, and describe angles as bigger than, smaller than, or about the same as other angles
Identify flips, slides, and turns, through investigation using concrete materials and physical motion, and name flips, slides, and turns as reflections, translations, and rotations
Demonstrate an understanding of composition, using principles of design to create art
Demonstrate an awareness of a variety of works of art and artistic traditions from diverse communities, times and places
Whole class and small groups.
- Picture Book: Sadako and the Thousand Paper Cranes
- Model Origami (see Appendix for instructions)
- One Origami Paper per student: if not available cut coloured paper into 8 x 11 squares
- Origami shape instruction per student (see Appendix) Various coloured markers for students
*Download lesson plan for appendices.
Students will have the opportunity to make connections between mathematics, history and visual arts, through origami. Students will be able to connect their understanding of two- and three-dimensional geometric properties and relationships in a real-world application. This activity will allow students to interact with shapes and angles in a different representation, which will guide them along in their learning of angles and shape composition (Sarama & Clements, 2003). This activity can be used as an introductory, exploratory or closing activity, and to assess for learning.
Introduction (20 minutes): whole class
• Read “Sadako and the Thousand Paper Cranes”
• Discuss origami, cultural history and its representation (see Appendix for details)
• Connect origami with mathematics using model. Discuss geometric shapes, two-dimensional and three-dimensional shapes and relations and the role of symmetry.
Activity (50 minutes): Whole group activity, students organized into small groups of 4 – 5
1. Provide each student the materials. Place instruction sheets on overhead/Smartboard and lead instructions to form same origami structure. Model the use of appropriate mathematical language.
2. Allow students who have successfully completed one fold to assist other students to encourage collaborative learning. Make landmarks on the paper with a pencil for students who are having difficulty forming spatial representations.
3. Facilitate discussions during the process of making the origami structure (see Possible Questions/Prompts). This will encourage students to identify different 2D shapes, compare their geometric attributes and decompose/compose shapes.
4. Complete making the structure and explore the different shapes and its attributes. Highlight the relationship between 2D shapes and 3D figures.
Closing Remarks (15 minutes): whole group
• Ask students to unfold their work and have the class discuss results.
• Encourage students to independently colour-in the different 2D shapes, angles and lines they can see on their paper (extended into a later visual arts activity).
• Facilitate a whole class discussion about the interesting shapes that did not exist before and their attributes, shape/line patterns, creases/folds and angles that were created through the activity.
• End the activity by highlighting the relationship between smaller and larger shapes.
Questions to Extend Student’s Thinking
- What new shapes have been formed? How does this shape compare to the shape we had before? It is interesting that these two lines are connecting. What kind of shapes do we see in this 3D shape? Do you see the same shapes now that we used to make this structure? After attending this shape, I wonder if we will find shapes we did not use before. There are so many lines and shapes here. Do you see shape patterns? Let’s look at the shapes that are close together.
- Introduce the concept of fractions (Number Sense strand) using appropriate terminology (e.g. half, quarter): Compare the original size of the shape/paper with the previous: How does this shape/paper compare to the shape/paper we had before?
- Are students able to accurately name their geometric shapes? Can students identify and compare attributes (e.g. side length, number of sides) of two-dimensional shapes? Are students able to correctly identify and compare different angles? Do they recognize angles in shapes?
Do students recognize that large 2D shapes are composed of smaller 2D shapes? Are they able to identify this relationship between 2D shapes and 3D figures?
Do students use appropriate spatial sense vocabulary when describing the position of shapes and folds (e.g. reflection, rotate, translate)? Are they able to independently follow verbal/written instructions?
- Do students understand the importance and representation of origami? Are they able to describe their artwork using different principles of design (line, shape, colour, space, pattern)?
Baicker, K. (n.d.). Origami Math – Scholastic.com. Retrieved November 24, 2015, from http://www.scholastic.com/ teachers/lesson-plan/origami-math
Sarama, J. & Clements, D. (2003). Building blocks of early childhood mathematics. Teaching Children mathematics, 9(8), 480-484.