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## Design a Better Classroom Workplace

By Leonard Beqiraj, October 4, 2009

• High School

• Architecture

• Mathematics

### Lesson Time

Minimum: 300 minutes for classroom activities and 100 minutes for homework

### Introduction

In this project students will design a new classroom workplace. The existing desks are too small and inconvenient to hold books and be moved around the classroom. Students will be required to use area formulas (curriculum) to identify the problem with the existing desks and to defend the new choice. If they design their own solution volume formulas might be used to calculate the weight and/or cost. Students will work on something they are using everyday so their engagement is highly probable.

### National Standards

Mathematics

Standard 1. Level IV. Uses a variety of strategies in the problem-solving process

1. Uses a variety of strategies (e.g., identify a pattern, use equivalent representations) to understand new mathematical content and to develop more efficient solution methods or problem extensions

Standard 3. Level IV. Uses basic and advanced procedures while performing the processes of computation

4. Uses a variety of operations (e.g., finding a reciprocal, raising to a power, taking a root, taking a logarithm) on expressions containing real numbers

Standard 4. Level IV. Understands and applies basic and advanced properties of the concepts of measurement

4. Solves real-world problems involving three-dimensional measures (e.g., volume, surface area)

Common Core Standards

Key Ideas and Details:

Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.

Craft and Structure:

Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

Assess how point of view or purpose shapes the content and style of a text.

Integration of Knowledge and Ideas:

Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

Range of Reading and Level of Text Complexity:

Read and comprehend complex literary and informational texts independently and proficiently.

Text Types and Purposes:

Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details and well-structured event sequences.

Research to Build and Present Knowledge:

Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation.

Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.

Draw evidence from literary or informational texts to support analysis, reflection, and research.

Anchor Standards for Writing:

Anchor standards for Speaking and Listening:

Comprehension and Collaboration:

Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others' ideas and expressing their own clearly and persuasively.

Presentation of Knowledge and Ideas:

Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.

Anchor standards for Language:

Conventions of Standard English:

Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Knowledge of Language:

Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

Vocabulary Acquisition and Use:

Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference materials, as appropriate.

Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.

### Objectives

Students will be able to:
• use the surface area formulas to find the area of different shapes
• use volume formulas to find the cost or the weight of different materials
• compare and contrast different design options and come up with an optimal solution

### Materials

• project handout
• measuring tapes
• calculators
• LCD projector or SmartBoard
• Post-It large white sheets

### Vocabulary

• area: the extent of a 2-dimensional surface enclosed within a boundary
• base: the bottom side of a geometric figure from which the altitude can be constructed
• height: the vertical dimension of extension; distance from the base of something to the top
• altitude: the perpendicular distance from the base of a geometric figure to the opposite vertex (or side if parallel)
• apothem: a line segment from the center to the midpoint of one of its sides; equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides; the word "apothem" can also refer to the length of that line segment

### Procedures

1. Identify the problem -- Take a survey: How many students like the existing workplace? How many students dislike it? Can it be improved? Who are the customers (students, teacher, custodian)?

2. Quantify the problem -- Area too small, desks non-stackable, books falling off, etc. Quantification of the problem will be done by using the area formulas. Students in this step will find the area of the desk, the area of the books (open and closed) the area of the notebooks (open and closed) and the area of the empty space on the desk needed for a student to work comfortably.

3. Research the problem -- Internet/Library.  During this phase of the lesson students will use any available resource to learn about desks in general and especially the desk they are using. They will get information about the purpose of every part of a desk and why it was designed in a certain way. If possible students will find information about alternative designs that were considered and how the benefits of the final design outweighed the disadvantages.

4. Restate the problem (mathematically support it) -- In this phase of the lesson students will have a lot of information about the workplace (desks) in use and how the workplace satisfies or does not satisfy the goals of the designer and the goals of the users (clients). The major part of this step will be comparing the surface area that is needed for working comfortably with the actual area of the desk.  Other concerns like weight, space, portability, “eye pleasing design,” etc., will also be addressed.

5. Design a new workplace or propose a replacement (mathematically support the design and solve all or most of the issues with the existing one) -- In this phase of the lesson students will use area and volume formulas to calculate the amount of materials needed to build their ideal desk and the co st of each unit. If they decide to replace the desk with another desk from the market then a spreadsheet to compare the existing desks and at least three alternative ones will be required.

6. Present the project to a panel of designers and investors to convince them to buy/build the new workplace.  (These can either be real designers and investors from the community, or students playacting as such.)

### Assessment

During presentation the “quantification” part of each phase of the project will help to determine whether students achieved the objectives. Another form of assessment will be a chapter test with area problems. An alternative project where students find the amount and cost of paint needed to paint their house would be available for students who have trouble completing this project.

### Enrichment Extension Activities

In this project students will use higher order thinking. Completing all the phases of the project will require students to use application, analyses, syntheses, and evaluation categories of cognitive domain. After students learn the design process they will have the option to solve a problem in their community and based on the complexity of the problem it may qualify as their senior project.
1. One way I try to foster innovation during a design project is to emphasize empathy through listening to and sharing narratives. When students can actively listen to the stories of the people they are interviewing, then the opportunity to generate more ideas increases. I like this lesson because of its very relevant and practical application to the student. I do think that the students should be encouraged to collect as many narratives as they can from different people.

As I was reading this lesson, I was thinking about the student who cannot sit at a desk. This project could really help these kinds of students. However, their stories would need to be collected so that the student-designers can use math to design for a specific set of needs.