Shape and Size
Mathematics - Grade 10
This unit of inquiry is not a recipe book but rather a launchpad to inspire new BIG IDEAS. We encourage you to use and/or modify one, or several of the BIG IDEAS below. Adapt it to the grade/ ability level of your students.
Measurement and shape are interdependent with design and purpose.
How does measurement and shape relate to the packaging and distribution of food? What are the effects of shape and size of canned foods to the economy, trade and the environment?
Choose or devise practices to encourage students to be open to new experiences and ways of thinking in your classroom. For example, the MindUP in-school program.
Discovery and Inspiration:
Launch the Project
• Introduce the Theme: Present the Enduring Understanding and Guiding Questions using vocabulary that is appropriate for your grade level.
• About Vancouver Biennale: Play a short video.
• Create Project Space: Brainstorm ideas to make the project theme visual and visible using bulletin boards, and/or a project corner to share relevant materials and inquiry questions and processes.
• Introduction to Sculpture and Public Art Unit Plan for information on how art has evolved over time and the unique experience sculptures and/or public art brings.
• Vancouver Biennale 2014-2016 Exhibition Theme: Open Borders / Crossroads Vancouver,
• Ceramic Forms (Yee Soo Kyung, Korea) from Vancouver Biennale 2009 – 2011 Exhibition.
Learning to Learn:
Project images of Ceramic Forms and encourage students to explore the art piece at different angles individually and in groups. This Art Inquiry process enables the students to practice observing, describing, interpreting, and sharing visual information and personal experiences. Use the Art Inquiry Worksheet (PDF) to guide and capture their ideas and impressions. Customize or create your own Art Inquiry Worksheet as appropriate for your project and class needs.
• Sharing Art Inquiry Experience: Ask students to share the Art Inquiry Worksheet responses in class.
• Artist Themes – Research: In small groups students rotate between information stations detailing the artist’s life and work. Station topics include: (1) education and training; (2) lifetime of artwork; (2) materials and processes; (3) beliefs and values. At each station, students answer questions and complete a task. For example, at the station “life’s work” students might plot the artist’s various installations on a map of the world
• Artist Themes – Recycle and Environmental Impact: Facilitate a class discussion relating Yee Soo Kyung’s Ceramic Forms ‘recycled’ sculpture to recycling of food cans. Students can share what and how they are recycling at school and home and the environmental impact with the increased effort to recycle.
What is inside a can?
Ask students to bring a sample of large, medium and small size cans for this unit of measurement inquiry. Students can inquire into the following questions and contrast the type of products they contain.
- What size and shape are the most commonly used cans?
- What are the categories of products packaged in cans? Compare the size and shape of the product and the container.
- Investigate the size, shape and weight of a canned product and how that relates to the bulk packaging for distribution, and shelf storage in a supermarket.
- Do companies produce different size cans for the same product? Why?
Measuring a Can
Purpose: Students are to describe the activity and how it is connected to the current measurement unit of study by addressing the following challenges:
- Do you think food cans are created with specific measurements for a reason? Explain.
- What are you going to determine from this investigation?
- How is this investigation related to the current unit of study?
Students are to plan the steps during the investigation process using diagrams and ensure the steps are clear to any reader
Students are to record the following data:
- Radius (using C=2πr)
- Surface Area formula in terms of radius and height
- Surface Area formula in term of radius and volume
- Surface area (solely a function of the radius)
- Graph the domain and range of cans investigated
Once investigations for individual food can companies are completed, students across groups can create a class summary chart comparing each of the above questions for each company. The instructor can then facilitate a class discussion on what the students observed and any surprises, confusions or further inquires.
Ask students to reflect on connections to life outside the classroom, new questions you may investigate in the future and improvements to the investigation process.
Create: Designing a Can
Using the students’ knowledge about cans, (e.g. looks, size, types), the students are asked to design ‘the best can’ for a specified product. In addition to visual appeal, the students must be able to describe and explain their personal strategy used to determine any measurements (i.e. circumference and diameter of the top/base, length of a curve, perimeter of the base of an irregular 3D object). Students should be able to refer to their measurements using both imperial and standard international (SI) units. The students must justify why they believe their design is the best.
Student Creations and Taking Action
Students and teachers can determine the platform at which they would like to present their inquiry. The use of posters, videos, PowerPoint, blogs, essays, stories, etc. may be considered. While the project may be displayed in various ways, the students must be able to articulate their discoveries in a presentation to the class.
Students can collect cans as a school-wide project or competition to accumulate as many cans possible for a charity of their choice.
• Teacher and students can reflect on their entire learning process by revisiting the Enduring Understanding and relevant Guiding Questions.
• How did the unit of study open inquiry, create cross–curricular learning opportunities and/or apply learning to real life situations? Has this unit of inquiry changed your opinions, values and world view? In what ways, if any, has it helped you grow as a learner?
Ideas of Cross-Curricular Access
• Business Education – Data Analysis: Investigate how the use of canned food has changed/not changed over time. Graphically show where (i.e. countries) canned foods are consumed the most and provide logical explanations to support the data. Compare the cost of a food product made by a company that produces canned food (e.g. Cream of Mushroom by Campbell’s) and the cost required to create the same product using fresh produce.
• Foods and Nutrition: Compare and contrast the ingredients used in a canned product versus the same product made with fresh produce. How might ingredients found in canned foods affect our health?
• Industrial Education – Metal Work: In groups, students can research the process of how food cans are made. The research can include a description of the material(s) used to make a can, the tools used and a description of each tool, and an understanding of how food can production has changed over time. Students can create a ‘how to’ manual that outlines the materials, tools and steps that are used to create a can. The teacher can facilitate a class project on creating a can, or organize a class field trip to a cannery.
• Social Studies – History: Have students research and inquire into the history and development of canning. What role did canning play in different countries? In different major historical events? Relate canning to offer forms of food preservation during the historic period of study.
Written by Vanessa Tam; Inspired by Grade 10 mathematics project by Kelly Skehill, Mathematics Teacher at West Vancouver Secondary School
©2013 Vancouver Biennale