Standards
  • ISTE NETS for Students:
    • 1 - Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology
    • 2 - Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others
    • 3 - Students apply digital tools to gather, evaluate, and use information
    • 4 - Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.
  • NCTE/IRA Standards for the English Language Arts:
    • 4 - Students adjust their use of spoken, written, and visual language (e.g., conventions, style, vocabulary) to communicate effectively with a variety of audiences and for different purposes.
    • 7 - Students conduct research on issues and interests by generating ideas and questions, and by posing problems. They gather, evaluate, and synthesize data from a variety of sources (e.g., print and non-print texts, artifacts, people) to communicate their discoveries in ways that suit their purpose and audience
    • 8 - Students use a variety of technological and information resources (e.g., libraries, databases, computer networks, video) to gather and synthesize information and to create and communicate knowledge.
  • NJCCCS for High School Mathematics:
    • SRT.A.2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
    • MG.A.1 - Use geometric shapes, their measures, and their properties to describe objects
    • MG.A.2 - Apply concepts of density based on area and volume in modeling situations
    • MG.A.3 - Apply geometric methods to solve design problems

Keywords
  • Architecture
  • Greenhouse
  • Blueprints
  • Scale Factor
  • Similarity
  • Wiki
  • SketchUp
  • Environmentally Friendly
  • Modeling

Objectives - Students will be able to:
  • Use similarity to create scale models and blueprints
  • Develop skills for how to work cooperatively with others
  • Prepare persuasive presentations
  • Research, observe, reflect, and react to the content that is developed and presented by their peers
  • Integrate technology into the creation of scale models
  • Relate concepts from mathematics and environmental science to a real-world application problem
  • Construct accurate and realistic scale drawings and models
  • Research and explain what makes a good greenhouse through the use of a Wiki or similar technology
  • Develop the construction of an environmentally friendly greenhouse

Unit Description

This unit plan is intended to show students the importance of math and how it can be used to help benefit the environment. Intended for a high school Geometry class, students will be asked to use the math they know to create plans for building a greenhouse for their school. The lesson encompasses what the students know about scale models, scale drawing, and similarity. They must work in groups to research the various components of what it takes to make a good greenhouse, then come up with their own plans which will be represented in a variety of ways. Finally, they will be asked to make a presentation to the administration of the high school to persuade them and their peers to vote for their greenhouse to be built. The activities are structured in a way that the students will gradually incorporate what they know with new ideas. There are also modifications included for struggling students and excelling students. Attention to the use of technology, social literacy and the participatory culture through affinity spaces is what makes this unit so valuable for a high school Math class.

Technology

  • Computers
  • iPads
  • Internet
  • Wikis
  • Word Processors
  • Presentation Creators - Powerpoint or Prez
  • Jing
  • Google Hangout
  • Small Blue Printer

Resources

Additional Resources for Teachers

Activities

Week 1

The school has commissioned this High School Geometry class to come up with the plans to build a greenhouse for the school. The school has wanted to do this for some time, but now sees the benefits of student involvement. The class must come up with several options, make blueprints and models of the greenhouses, and make presentations to the administration and their peers to decide which of the students’ plans will be selected and constructed. Construction of the greenhouse will be done by the school’s shop class. All necessary funds and materials will be donated by the school’s Home and School Association.

Through an assembly, the administration and the Home and School Association will present the project to the students. They will explain what they want the students to do, their expectations, and that in the end, there will be a winner chosen that will get to have their greenhouse built and named after the group.

In order for students to understand how to make a blueprint, they will need to know about similar objects and scale. Students will be given a variety of objects, and rulers, and must use what they have already learned about the definition of similarity to determine if the objects are similar or not. If the objects are similar, students will calculate the scale factor between the objects. A discussion will follow of what they have found. Students will talk about where similarity can be used in real life - topic of blueprints will come up. Once they have done that, they will be given a model of a house/building, will determine the scale factor they are going to use, and create a blueprint of the building. Students will perform a gallery walk to see one another’s work.

Using Geogebra, free downloadable software available on the students’ laptops, they will work with a partner to create figures that are similar and find the scale factor. This will help the students develop the technical/computer skills which will help them later on to create the blueprint using technology. They will find that they can make the drawings using this program much more easily and accurately than by hand, which will be important.

Class discussions about what kinds of information we need to know about blueprints and architecture in order to complete the project. They will write down three questions that they want to ask the architect, which will be looked at by the teacher before the Hangout session. Google Hangout session with local architect where students can ask questions and hear how he uses scale in his career. He can talk about the aspects of good construction, such as accuracy of drawings and models, and how to ensure that the blueprint will turn into a realistic construction when actually built. Students will ask questions that they have written in order to get a better understanding of what they will need to know about making blueprints and scale drawings. This will be included in the rubric.

Students will each create a Google Group for their groups project and presentation. They will watch the How to Video seen here http://screencast.com/t/75qQXIXj6Cxt (Made by Lauren Truncale) to learn how to make a Google Group. The group will allow them to participate in a discussion board with their group to bounce ideas off of one another and share content on the Drive with each other. Students put into groups of 3 or 4 decided upon by the teacher to encourage understanding that student distribution will make sense given the makeup of the class - they will create a Google Document that they will share with one another in preparation for the following week where they will be collaborating.

Students will begin a Pinterest page devoted to pictures of greenhouses or blueprints that they find inspiring. This page will be kept throughout the entire unit.

Differentiation:

Remediation - Investigation steps will be more outlined to guide students through the process of discovery about similarity. For example, step by step instructions of what to measure and what to compare can be written and given to students who may need it.

Extension - students research models that exist in real life (statues, buildings, etc) and determine the scale factor of the model to the real life figure.

Week 2

Students will now begin preparations in their groups to develop blueprint plans to build a greenhouse for the school. They will need to use their knowledge of scale models and scale drawing to develop plans for an actual greenhouse, so dimensions and construction must be accurate for real life.

In order to know what components make up a good greenhouse, students will conduct research online with their groups. They can use the resources listed above as ways to start research. Conversations will be had about determining good resources from online resources with false information. What students find will all be compiled in the Google Document that the groups created with the members so they can all contribute to the same document, editing it as they go along. Important features should include that it is environmentally friendly, easy to maintain, uses limited additional resources, location in relation to the sun or rain, what materials will be needed to actually construct the greenhouse, etc.

Students will be encouraged to email architects or draftspeople from around the world to inquire about the methods they use to create good blueprints. Students will also email companies that specialize in greenhouses to find out the important features that they should include in their greenhouse plan development.

When students feel that they have gathered enough information about what components should go into a greenhouse, a class Wiki will be made. All students will be members, and participate in adding information to the Wiki. The content will include the research that they have found and conversations they had with various companies. The Wiki will also include links to the resources they have found for future reference.

Differentiation:

Remediation - Resource lists will be provided for students to choose from to start research. Students can work with the school librarian or media specialist who can further help them learn how to perform research, what search engines to use, what to type in to obtain a good search, etc.

Extension - Students will share with the companies their process so far, ask if they may be able to look at what they have done and provide constructive criticism.

Week 3

This week begins the actual time that the students will be making the plans for their greenhouse.

Students will use SmallBluePrinter either on their laptops or on their iPads to begin making their plans. Their scale must be realistic and plans feasible. They must be cognizant of the features they researched the previous week in order to make sure their greenhouse will work and do what is expected of it. Students will also be expected to make a greenhouse that has visual appeal, as they are trying to convince others that theirs is the one that should be built.

Modifications will be made throughout the week as necessary to their plans.

Continuing Activity:
Students will continue to update the class Wiki with any new features they find, or additions they feel are important to include.

Students will continue to update their Google Document with their group based on what they have done with their blueprint, and what modifications they are planning to make on it over the course of the unit.

Differentiation:

Remediation - Students will observe sample creations and tutorial videos from SmallBluePrinter to see how to use the source and how they can apply it to what they are creating.

Extension - Students will make their own tutorial video for how to use their iPad and SmallBluePrinter to create a blueprint for future classes or others to use.

Week 4

To get a better visual for what their plans will translate into when viewed in three dimensions, students will use SketchUp to translate their two dimensional plans into 3D. In the 3D model, they can add various features including color, design, and include plants to simulate what the actual greenhouse would look like. This will be used later on as a part of their presentations.

Continuing Activity:
Students will continue to update the class Wiki with any new features they find, or additions they feel are important to include.

Students will continue to update their Google Group and Google Document with their group based on what they have done with their blueprint, and what modifications they are planning to make on it over the course of the unit.

Students will begin a Pinterest page devoted to pictures of greenhouses or blueprints that they find inspiring. This page will be kept throughout the entire unit.

Differentiation:

Remediation - Students will receive guidance on 3D models and their construction using the various resources. Templates can be used to help start construction of 3D models

Extension - Students will share the 3D models that they have made on SketchUp’s 3D Warehouse (http://sketchup.google.com/3dwarehouse/) or other similar sites.

Week 5

Students will begin work on their presentations to the administration to persuade them to pick their greenhouse design.

Students will research what makes a good presentation (see resources above). They will share this in a new Google Document with their group members so they can continue to update that with the information that they will need to complete the presentation.

To make their presentations, student groups can choose from various means of presentations including PowerPoint and Prezi. Their presentations should be engaging and convey all of the information that they feel the administration would benefit from knowing about their plan. They should include their blueprint, 3D model, and rationale in their presentations.

Continuing Activity:
Students will continue to update the class Wiki with any new features they find, or additions they feel are important to include.

Students will continue to update their Google Document with their group based on what they have done with their blueprint, and what modifications they are planning to make on it over the course of the unit.

Students will begin a Pinterest page devoted to pictures of greenhouses or blueprints that they find inspiring. This page will be kept throughout the entire unit.

Differentiation:

Remediation - Students can use a template in PowerPoint, Prezi, and the like, to help format their presentations in an orderly manner.

Extension - Students will re-contact the companies/architects they had previously emailed to let them know of their progress and to ask for more constructive criticism. Google Hangouts or Skype can be used to more easily transfer information.

Week 6

At the beginning of the week, students will finalize their presentations for the administration. In order to make their presentations available for others who cannot attend the meeting, students will make a video recording of their presentation using resources such as Jing. The video should also convey all of the key information of the presentation, and will be posted to the greenhouse wiki. Video will be posted on Youtube.

Administration and student peers will attend presentations. Student groups will get up and present their projects and rationale. At the end of the presentations, administration and peers will fill out a survey about which group’s presentation they have picked and why.

The resulting surveys will decide which group’s plan will be the blueprint for the construction of the actual greenhouse.

Survey to be filled out by administration and peers after presentations:

Rate the following on a scale of 1-10, where 1 is the lowest/strongly disagree and 10 is the highest/strongly agree

1) The group made a convincing argument for why their greenhouse should be built.
2) The group seemed knowledgeable about the subject
3) The blueprint and model presented by the group was appealing
4) The blueprint and model presented by the group would go well with the
school structure
5) I would pick this group’s greenhouse as the one to be built

Assessments/Rubric

Participation Rubric

4 Points
3 Points
2 Points
1 Point
0 Points
Overall Participation
Actively and constructively participated in all components of the project
Constructively participated in project, with moderate activity
Participated in project with moderate activity and minimally constructive
Participated in project with minimal effort
Did not participate
Group Contribution
Participated greatly to the group, providing constant guidance and feedback that pertained to the learning
Participated greatly to the group, providing guidance and feedback
Participated with the group providing occasional guidance or feedback
Participated minimally to the group with little guidance and feedback
Did not actively participate in group
Participation in Google Group and Google Docs
Frequently contributed to the Google Group and Google Docs. Contributions were very valuable.
Often contributed to the Google Group and Google Doc. Contributions were valuable
Occasionally contributed to the Google Group or Google Doc. Contributions were mildly valuable
Minimally contributed to either the Google Group or the Google Doc
Did not participate in Group or Docs

Presentation Rubric

4 Points
3 Points
2 Points
1 Point
0 Points
Spelling, Punctuation, Grammar
Spelling, punctuation, and grammar used throughout the project was correct with few to no errors
Spelling, punctuation, and grammar used throughout the project was correct with a few errors
Spelling, punctuation, and grammar used throughout the project had a moderate amount of errors
Spelling, punctuation, and grammar used throughout the project was full of errors
Grammar was very poor and no attention was paid to it at all
Utilization of Good Research Strategies
Employed the discussed research strategies - effort was put into making sure information was accurate and confirmed
Employed most of the research strategies discussed - effort was put into making sure information was accurate
Employed a few of the research strategies - information was checked but could contain errors
Employed a few research strategies - information does contain errors
No research strategies used - content is inaccurate
Presentation Clarity
Presentation was made in a very clear manner. Information was conveyed in a way that made sense and was cohesive.
Presentation was clear. Information was conveyed in a way that made sense and was cohesive.
Presentation was a bit unclear. Information was conveyed in a way that was cohesive.
Presentation was unclear. Information was not conveyed in a way that made sense.
Did not make presentation
Presentation Content and Coverage
Presentation included description of the greenhouse, presentation of the blueprint, presentation of the 3D model and a well written rationale for why their model should be picked.
Presentation was lacking one of the following: description of the greenhouse, presentation of the blueprint, or presentation of the 3D model. A rationale for why their model should be picked was included.
Presentation was lacking two of the following: description of the greenhouse, presentation of the blueprint, or presentation of the 3D model. A rationale for why their model should be picked was included.
Presentation was lacking two of the following: description of the greenhouse, presentation of the blueprint, or presentation of the 3D model. A rationale for why their model should be picked was not included.
Did not make presentation
Survey Results
Scored very highly with the administration and peers on the survey of their presentation
Scored highly with the administration and peers on the survey of their presentation
Scored moderately with the administration and peers on the survey of their presentation
Scored low with the administration and peers on the survey of their presentation.
Results were very poor

Use of Technology

4 Points
3 Points
2 Points
1 Point
0 Points
Use of Drawing Tools
Used drawing tools thoughtfully and skillfully to construct various creations. Drawings were accurate.
Used drawing tools thoughtfully and skillfully to construct most creations
Use drawing tools well to construct assigned creations
Use of drawing tools was basic and only constructed the minimum of the assigned creations
Did not use drawing tools to create scale models
Contributions to the Wiki
Additions were made to the Wiki that significantly benefitted the groups - content was based on the research done
Additions were made to the Wiki that benefitted the groups
Additions were made to the Wiki
Additions were made to the Wiki that resulted in errors
Did not contribute to Wiki at all
Video of Presentation
Video presentation included a brief but thorough description of their greenhouse, how they made it and why they should be picked
Video presentation included a brief description of their greenhouse, how they made it and why they should be picked
Video presentation included a lengthy description of their greenhouse, how they made it and why they should be picked
Video presentation included a lengthy and unclear description of their greenhouse, how they made it and why they should be picked
Did not make video of presentation
Google Hangout and Architecture Emails
Came up with and asked relevant questions that aided blueprint plans and focus on good construction
Came up with and asked relevant questions
Asked questions that had little to do with the assignment
Asked questions that had nothing to do with the assignment
Did not contribute questions to Hangout or emails

Scale Model and Drawings

4 Points
3 Points
2 Points
1 Point
0 Points
Scale Drawing Creation
Scale drawing was completely accurate, with scale included
Scale drawing was mostly accurate, with scale included
Scale drawing was relatively accurate, with minor errors, and scale included
Scale drawing was full of errors, no scale included
Did not make a scale drawing
Blueprint Design and Execution
Blueprint design included all of the found features that make a good greenhouse. Execution was done in a very thoughtful and creative way.
Blueprint design included many of the found features that make a good greenhouse. Execution was done in a thoughtful and creative way.
Blueprint design included a few of the found features that make a good greenhouse. Execution appeared rushed.
Blueprint design included none of the found features that make a good greenhouse. Execution was poor.
Did not design or execute blueprint
3D Model Design and Execution
3D model was exactly accurate to the original blueprint plans. Execution was done in a very thorough and creative way.
3D model was mostly accurate to the original blueprint plans. Execution was done in a thoughtful and creative way.
3D model was relatively accurate to the original blueprint plans. Execution appeared rushed.
3D model was inaccurate to the original blueprint plans. Execution was poor.
Did not design or execute 3D model

Rationale

One of the most common questions math teachers hear is, “When are we ever going to have to use this?” It can be a source of frustration for both the teacher and the student as content often feels like it is not applicable to their lives. However, this does not need to be the case. With advances in technology and students being more involved in the world than ever before, it is possible to make learning a very powerful experience.
For this unit plan, the intention is to take what was formerly taught in a very mundane way, and have students become much more involved in their learning. The premise behind creating a greenhouse is that we can incorporate math, science, social awareness and technology to help accomplish a goal. Suddenly, learning all of these subjects has become applicable in the students’ lives. Math and science remain topics they are supposed to learn about and become proficient within, but using the social and digital framework, the content have become relevant to the students. These new literacies, which include social and digital awareness, provide the foundation for learning about blueprint drawing, scale models, and constructing a greenhouse (Lankshear & Knobel, 2006).
The greenhouse lays the framework around which all other learning in this unit can occur. The learning objectives are skillfully intertwined in the unit plan so thoughtful learning occurs at all stages of development. Students are able to find out about the environmental impacts and benefits of a greenhouse, and in this unit, why the school would want to construct one. Children who learn about the environment tend to care more about where they live, or in this case, where they go to school (Fishman, 2005). It grounds real-life application in something that will create a positive climate throughout the school. The social aspect of the unit, where students are working with one another in person and through technology, helps show them how to engage in positive and appropriate social practices. Students are already so involved in the participatory culture, where they can share, produce, and create media of their own with others (Jenkins, 2009). The connections that they feel between themselves and those around them, both physically and virtually, are undeniable. By tapping into some of that culture in the classroom, we can help to build the students socially, and engage them in activities that they will want to be a part of.
Technology plays a very significant role in the lives of our students. According to the Pew Research Center, the percentage of teens who use the internet (at least occasionally) has increased from 73% in the year 2000 to 93% by the year 2009 (Pew Research Center, 2013). In education, we can take advantage of their internet usage and their technological skills, and utilize them in the classroom. Students can use the internet for research, use various apps available online to construct blueprints or 3D models, and even use sites like Google Docs or Wikis to keep in touch with one another and make sure their projects are up to date.
Keeping in mind that educators face a variety of students in the classroom, differentiation strategies were included in the unit plan. They take into account both students who may need modifications or students who are excelling and can do something more challenging. Differentiation allows us to reach students who are at all levels of education in the classroom, providing an appropriate challenge for each student (Heacox, 2002).
This unit plan also touches on many key learning principles that are important in the classroom for all learners. They include allowing students to be able to customize their own greenhouse designs, creating a sense of identity by having designs that are unique to their group, being able to create and manipulate knowledge to design their models, and being able to take risks in their designs to attract viewers (Gee, 2007). Students can use technology and social literacies to make meaning of what they are learning, problem-solve, and see that knowledge does not exist in isolation of other knowledge (Gee, 2005). In this unit, students face a challenge that, at the end, would prove to be very rewarding. The input from the administration validates the project showing students that their work is meaningful beyond the four walls of the classroom.
Gee (2005) also discusses how education would benefit from “system thinking,” where students have to think about the whole picture, and not just isolated events. This student-centered activities of this unit pay close attention to developing skills over the course of time, rather than several weeks’ worth of individual, unrelated activities. In addition to that, the students must not only think about how their project is going to develop, but how their group members and contributions will develop over the course of time. They will have to work with one another during allotted class time, and through various technological resources, in a cohesive and productive manner. This is a huge factor in the social literacy that this unit is aimed to promote. Students have to work with their peers to convey information in a new and creative way.
As mentioned before, the unit plan does fit in with the new literacies that have been acknowledged, such as digital literacy and social literacy (Lankshear & Knobel, 2011). Digital literacy plays a significant role in this unit, in that much of the unit cannot be done without the aid of digital technology. Using resources like SketchUp, Wikis, Youtube, Pinterest, Google Docs and Groups, Geogebra, and SmallBluePrinter, students are able to create and share content they have made with others, which is in line with the trends of a participatory culture (Jenkins et al., 2009). Indeed, even 15 years ago, internet pundits were arguing that “[a]s we teach the next generation of Web users about the networks available to them, we are also giving them the opportunity to learn a mindset that can allow them to stretch and explore the potential of this medium” (Gilster & Gilster, 1997, p. 2).
The experiences that a unit plan like this has to offer are not found in traditional classrooms. Using new literacies, important learning principles, and technology, learning takes on a new form. It takes a great deal of effort to create and implement in the classroom. But despite how much work it may make for the teacher, the results in the end will be well worth it.

References

Fisman, L. (2005). The effects of local learning on environmental awareness in children: An empirical investigation. The Journal of Environmental Education,36(3), 39-50.

Gee, J. P. (2005). Good video games and good learning. In Phi Kappa Phi Forum (Vol. 85, No. 2, p. 33). THE HONOR SOCIETY OF PHI KAPPA PHI.

Gee, J. P. (2007). Good video games + good learning: Collected essays on video games, learning, and literacy (Vol. 27). Peter Lang.

Gilster, P., & Glister, P. (1997). Digital literacy. Wiley Computer Pub..

Heacox, D. (2002). Differentiating instruction in the regular classroom: How to reach and teach all learners, grades 3-12. Free Spirit Pub.

Jenkins, H. (2009). Confronting the challenges of participatory culture: Media education for the 21st century. Mit Press.

Lankshear, C., & Knobel, M. (2006). New literacies: Changing knowledge in the classroom. Open University Press.

Lankshear, C., & Knobel, M. (2011). New literacies: Everyday practices and social learning. Open University Press.

Pew Research Center. (2013). Trend Data: Teens. Retrieved from http://www.pewinternet.org/Static-Pages/Trend-Data-(Teens)/Usage-Over-Time.aspx