by Qiaochu (Joy) Xu and Michelle Li
Theme: Creating a series of papercraft through paper cutting
Goal: Appreciate the beauty of patterns and symmetry while creating crafts
Materials: colored paper, scissors, coloring materials, and these handouts printed
Curricular Competencies:
- Model mathematics in contextualized experiences (Grade 3)
- Use reasoning to explore and make connections (Grade 4)
Content Objectives:
- Spatial sense in terms of play and reasoning
- Critical thinking and problem-solving skills
- Learn geometric vocabularies
Description:
Joy and Michelle both found it fascinating for people to be able to cut such intricate designs and wondered about the mathematics behind this activity. We wanted to provide an experience that linked symmetry while paying respects to our culture. Inspired by the “春” character, meaning spring and symbolizing the arrival of the new year, we designed an activity to explore the mathematical concepts of patterns and symmetry while linking the themes of exploration, play, and families.Getting Started:
Problem 1: Warm-up – have students explore the relationship between the number of folds and the number of cut-outs through patterning.
Question: How is the pattern growing?
Try It Yourself!
Problem 2: Symmetry Chain – have students explore cutting out a chain of people through the use of symmetry and linking the number of folds to the number of people in their chain.
Question: How many folds do you need in order to cut out 4 people in a chain? The challenge is that they must remain connected.
Try It Yourself!
Follow Up:
How do you get repetitive patterns in paper cutting?
What would you do to maintain connected patterns without cutting the inside all off?
What are the patterns you observe when you open the paper? Is that what you planned before cutting?
How many times you folded the paper, how many repetitive patterns you get?
Would you be able to cut a given shape without tracing and folding the paper before cutting?
Video:
1. Paper snowflake tutorial – learn how to make snowflakes in 5 minutes – EzyCraft
https://www.youtube.com/watch?v=YeR5p8OocUE
2. Making Chinese Paper Cut Art For Spring Festival | 春节剪纸
https://www.youtube.com/watch?v=yKSYQy8M2og