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Green Math, Engineering and Technology

An introduction to Middle School Math Curriculum Unit

Secondary, Middle

Description

This ESD unit places mathematics at the forefront of a comprehensive critical thinking project. Students must design a “green” building, applying both math skills and sustainability principles. The goal of the resource is to increase awareness of sustainability while using and applying mathematics in a real-world context.

Students design a 1200 square foot house, keeping their budget under $240,000. Math topics covered include fractions, decimals, percent, central tendency (mean, median, mode), measurement, area of 2-D shapes, spatial relations, scale, estimation, unit conversions, graphing, and financial math. Throughout the lesson sequence students analyze the economic, environmental and social implications of their lifestyle choices and of their construction plans. They also learn to calculate interest on a bank loan, practice measuring and converting measurements used in designing floor plans, and analyze the cost of different types of construction materials.  Students create a final budget and build a 3-D model of their house.

Each lesson can be delivered in a “stand alone” fashion to introduce or supplement individual math outcomes or the entire unit can be implemented in sequence throughout the year to support the existing curriculum.  Students can create a “Design portfolio” and collect/compile their project work as the activities relevant to the math curriculum are completed.

Lesson One: Whose House? (3 X 60 min.)

As the first step in designing their “green” houses students view a Power Point Presentation showing the homes of various celebrities.  This activity begins the discussion of sustainability and social equity. 

Students are then introduced to the requirements, expectations and assessment methods of the project. They complete a concept map of their dream home along with a specifications sheet and a math skills concept map.

Lesson Two: Intended Occupants (optional)

This lesson is a quick math literacy activity which asks students to envision and describe the people who will live in the house they design.

Lesson Three: Leave Only - (2 X 60 min)

Students consider how their everyday decisions impact their futures and those of generations to come by analyzing consumption patterns and calculating ecological footprints. After sharing their findings, students illustrate their footprint calculations in graphic format.

Lesson Four: Design Graphic- (1 X 60 min.)

Students use a decision-making graphic to weigh the environmental and economic impacts of two houses, one made of straw bales and one made of wood timber. Students then calculate means for the rating scale on both the economic and environmental criteria.  They communicate this data using their choice of bar graphs, line graphs, pictographs or pie charts.

Lesson Five: All A Loan. Pt. 1- (1 X 60 min.)

Students calculate the percentage of each color of M&M candy found in a bag of M&Ms, and communicate this on a bar graph.

 Lesson Six: All A Loan. Pt. 2- (1 X60 min)

Using the percentage of one color of M&M candy as an interest rate, students calculate the principle interest to be paid on a bank loan to finance their house.

Lesson Seven: Measurement Madness – (1 X60 min.)

After a brief introduction to the ways and means of measuring and converting units using equivalent fractions, students complete a measurement chart which converts inches to ½ inches and ¼ inches.

Lesson Eight: Scale the Wall- (2 x 60 min)

Students brainstorm what tools and skills an architect would use to create a floor plan. They are assigned classrooms within the school to measure.  After first estimating the area of the rooms, the lengths and widths are measured and students create scale floor plans using graph paper.

Lesson Nine: Hit the Deck - (3 X 60 min)

After reviewing how to determine the perimeter and area of rectangles and triangles, students are given floor plans and asked to determine the areas of these composite shapes. They are then asked to draw floor plans for rectangular, triangular, and circular and parallelogram-shaped decks of specified areas.

Lesson Ten: Drafting Bubbles- (2 x 60 min.)

Students develop a series of potential house plans estimating the square footage and spatial layouts of the rooms. Using graph paper and draft design sheets students design their “green’ home.

Lesson Eleven: The Final Floor- (2 X 60 min)

Using proper scale and the skills associated with linear measurement, students draw the final floor plan for t their house, incorporating the required specifications.

 Lesson Twelve: Greenhouse- (2 X 60min)

Students complete a construction estimate list and calculate the cost of required materials. They must research material options for foundations, walls, windows, roofing, and heating and cooling systems in terms of their environmental and economic implications. They then share this information in a jigsaw activity. Finally, students calculate the total cost of their design.

Lesson Thirteen: Thermal Resistance Activity- (1 X60 min.)

In this simple hands-on activity, students will learn what the ‘R=value’ means in energy efficient design.

Lesson Fourteen: Final Budget- (2 x 60 min)

Students calculate their final budget costs, taking into consideration the materials / construction costs and sales tax. They also must write cheques and balance their transaction register.

Lesson Fifteen: Build-A-Math (3 x 60min.)

Students will calculate how much of the building material is needed to create a 3-D structure and then build the structure to scale.

General Assessment

What skills does this resource explicitly teach?

  • Using tools and apparatus to conduct investigations
  • Interpreting patterns and trends in data
  • Analyzing results
  • Evaluating processes used in planning, problem solving, and completing a task
  • Select and use appropriate statistical methods to analyze and represent data
  • Critical and creative thinking strategies
  • Selecting appropriate methods to compute with fractions, decimals and percents
  • Use appropriate formulas, units and measurement tools to determine areas of 2-D shapes
  • Use spatial reasoning and geometric modelling to solve problems
  • Analyzing one's ecologicial footprint

Strengths

  • Resource is interesting and addresses a variety of math outcomes in a "sustainable" mindset
  • Excellent graphic organizers, concept maps, and decision-making charts
  • Applies mathematics in a "real world" context
  • Case studies are included in teacher background information, as well as suggestions for innovative homes. These can be used to "jump start" discussions.
  • A rubric is provided for grading the final house projects
  • Answer keys are given for all assigned work
  • Students calculate their own ecological footprint which brings local focus
  • A social equity component is addressed in housing choice and also a re-examination of "want" versus "need" choices
  • Provides many points of view in the form of lists of advantages and disadvantages of possible student choices in their house design
  • Create and innovative solutions are encouraged.

Weaknesses

  • No authentic action project
  • No suggestions for differentiated math activities for those students working below grade level
  • The metric system is not used in calculating areas or in measuring activities
  • Activities are time intensive
  • There are many paper handouts required which may be seen as a small contradiction to Green Principles.

Recommendation of how and where to use it

This resource can be implemented as either a stand alone unit linking math, science and broad based technology curricula, or as a yearlong math project with embedded skills, supporting the math curriculum taught in the classroom. This second choice is best suited for addressing outcomes in Grade 6 or Grade 7 math classes. This ongoing math portfolio would culminate in the final building project.

Relevant Curriculum Units

The following tool will allow you to explore the relevant curriculum matches for this resource. To start, select a province listed below.

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  • Alberta
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        • Geometry: Shapes are defined and related by geometric attributes
        • Number
        • Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating.
        • Shape and Space
        • Statistics and Probability
        • Statistics: The science of collecting, analyzing, visualizing, and interpreting data can inform understanding and decision making.
    • Grade 7
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        • Number
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        • Knowledge and Employability: Number (Number Concepts and Number Operations
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    • Grade 10
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        • Math 10-3: Measurement
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        • Mathematics 10C: Measurement
  • British Columbia
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    • Grade 6
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      • Math
        • Step 4Relevant matches
        • Data from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret
        • Mixed numbers and decimal numbers represent quantities that can be decomposed into parts and wholes
        • Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles
    • Grade 7
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      • Math
        • Step 4Relevant matches
        • Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers
    • Grade 8
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      • Math
        • Step 4Relevant matches
        • Analyzing data by determining averages is one way to make sense of large data sets and enables us to compare and interpret
    • Grade 9
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Computational fluency and flexibility with numbers extend to operations with rational numbers
        • Similar shapes have proportional relationships that can be described, measured, and compared
    • Grade 10
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      • Math
        • Step 4Relevant matches
        • Workplace Mathematics: Representing and analyzing data allows us to notice and wonder about relationships
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        • Essential Mathematics : 2-D Geometry
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        • Number
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        • Math 1201: Measurement
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        • Number
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        • Math 10-3: Measurement
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        • Mathematics 10C: Measurement
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        • Geometry
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        • Knowledge and Employability: Number (Number Concepts and Number Operations
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        • Statistics & Probability
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      • Math
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        • Knowlege And Employability: Number
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        • Patterns and Relations
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        • Statistics and Probability
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        • Apprenticeship & Workplace Math: Number
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        • Math 10C: Foundations of Math & Pre-Calculus: Measurement
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        • Data
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        • Natural Resources around the World: Use and Sustainability
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        • Structures and Mechanisms: Form, Function, and Design of Structures
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        • Data
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        • Data
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        • Number
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        • Number
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        • Statistics & Probability
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        • Statistics and Probability
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        • Math 421A. Relations and Functions
        • Math 421A: Management and Probability
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    • Grade 6
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        • Arithmetic
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        • The Technological World
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        • Applied Science & Technology: The Technological World
  • Saskatchewan
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    • Grade 6
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      • Math
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        • Mathematics 6 : Number
        • Mathematics 6: Shape and Space
        • Mathematics 6: Statistics and Probability
    • Grade 7
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      • Math
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        • Mathematics 7: Number
        • Mathematics 7: Shape and Space
        • Mathematics 7: Statistics and Probability
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        • Mathematics 8: Statistics and Probability
        • Mathematics 8: Shape and Space
    • Grade 9
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Math 9: Statistics and Probability
  • Yukon Territory
    • Step 2Select a grade level
    • Grade 6
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Data from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret
        • Mixed numbers and decimal numbers represent quantities that can be decomposed into parts and wholes
        • Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles
    • Grade 7
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers
    • Grade 8
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Analyzing data by determining averages is one way to make sense of large data sets and enables us to compare and interpret
    • Grade 9
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Computational fluency and flexibility with numbers extend to operations with rational numbers
        • Similar shapes have proportional relationships that can be described, measured, and compared
    • Grade 10
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Workplace Mathematics: Representing and analyzing data allows us to notice and wonder about relationships

Themes Addressed

  • Citizenship (2)

    • Ecological Footprint
    • Sustainable Consumption
  • Land Use & Natural Resources (1)

    • Sustainable Urbanization
  • Science and Technology (1)

    • Analysing Conventional Science

Sustainability Education Principles

Principle Rating Explanation
Consideration of Alternative Perspectives Good

This resource increases the awareness of sustainability issues by asking students to use data sets to investigate the world around them. Students use math skills to solve problems, reach conclusions, and come to new understandings.

Consideration of Alternative Perspectives:
  • Satisfactory: absence of bias towards any one point of view
  • Good: students consider different points of view regarding issues, problems discussed
  • Very good: based on the consideration of different views, students form opinions and  take an informed position
Multiple Dimensions of Problems & Solutions Very Good

Students analyze their own lifestyle preferences and the economic, environmental, and social implications of non-sustainable housing choices.

Multiple Dimensions of Problems & Solutions:

Effectively addresses the environmental, economic and social dimensions of the issue(s) being explored.

  • Satisfactory: resource supports the examination of  these dimensions
  • Good:  resource explicitly examines the interplay of these dimensions
  • Very Good:  a systems-thinking approach is encouraged to examine these three dimensions
Respects Complexity Good

This resource clearly demonstrates the complexity of environmental issues associated with sustainable lifestyle choices.

Respects Complexity:

The complexity of the problems/issues being discussed is respected.

Acting on Learning Poor/Not considered

There is no action project .

Acting on Learning:

Learning moves from understanding  issues  to working towards positive change — in personal lifestyle, in school, in the community,  or for the planet

  • Satisfactory: action opportunities are included as extensions 
  • Good: action opportunities are core components of the resource
  • Very Good: action opportunities for students are well supported and intended to result in observable, positive change
Values Education Good
Values Education:

Students are explicitly provided with opportunities to identify, clarify and express their own beliefs/values.

Empathy & Respect for Humans Satisfactory
Empathy & Respect for Humans: Empathy and respect are fostered for diverse groups of humans (including different genders, ethnic groups, sexual preferences, etc.).
Personal Affinity with Earth Satisfactory

Sustainable choices (needs vs wants) are paramount in this resource. The promotion of these attitudes are important first steps for planet stewardship.

Personal Affinity with Earth:

Encourages a personal affinity with -the natural world.  

  • Satisfactory: connection is made to the natural world
  • Good: fosters appreciation/concern for the natural world
  • Very Good: fosters stewardship though practical and respectful experiences out-of-doors 
Locally-Focused Learning Good

Students calculate their ecological footprints, complete their own design and carry out serveral  learning tasks in a real-world context.

Locally-Focused Learning:

Includes learning experiences that take advantage of issues/elements within the local community. 

  • Satisfactory: learning is made relevant to the lives of the learners
  • Good: learning is made relevant and has a local focus
  • Very Good: learning is made relevant, local and takes place ‘outside’ , in the community 
Past, Present & Future Good

Present day situations are evaluated and students are asked play a role in implementing solutions for a future of sustainable housing.

Past, Present & Future: Promotes an understanding of the past, a sense of the present, and a positive vision for the future.

Pedagogical Approaches

Principle Rating Explanation
Open-Ended Instruction Good

The resource provides "real world" data and statistics for students to analyze. Students are encouraged to consider this information, make sustainable choices, and create their own solutions.

Open-Ended Instruction :

Lessons are structured so that multiple/complex answers are possible; students are not steered toward one 'right' answer.

Integrated Learning Satisfactory

Although the activities are varied and creative, the resource addresses, for the most part, math and science outcomes.

Integrated Learning:

Learning brings together content and skills  from more than one  subject area

  • Satisfactory: content from a number of different  subject areas is readily identifiable
  • Good:  resource is appropriate for use in more than one subject area
  • Very Good:  the lines between subjects are blurred 
Inquiry Learning Good
Inquiry Learning:

Learning is directed by questions, problems, or challenges that students work to address.   

  • Satisfactory: Students are provided with questions/problems to solve and some direction on how to arrive at solutions.
  • Good: students, assisted by the teacher clarify the question(s) to ask and the process to follow to arrive at solutions.  Sometimes referred to as Guided Inquiry
  • Very Good:  students generate the questions and assume much of the responsibility for how to solve them.  . Sometimes referred to as self-directed learning.

 

Differentiated Instruction Satisfactory

The resource teaches to both the cognitive and affective domains. There are no suggestions given for differentiation of the math lessons for students working below grade level.

Differentiated Instruction:

Activities address a range of student learning styles, abilities and readiness.

  • Satisfactory:  includes a variety of instructional approaches
  • Good: addresses  the needs of visual, auditory &  kinesthetic learners
  • Very Good: also includes strategies for learners with difficulties
Experiential Learning Good

Students are given opportunities to gather and record measurements in a real-world context. There is also a "hands-on" learning opportunity associated with heat loss.

Experiential Learning:

Authentic learning experiences are provided

  • Satisfactory: learning takes place through ‘hands-on’ experience or simulation
  • Good: learning involves direct experience in a ‘real world context’
  • Very good: learning involves ‘real world experiences’ taking place’ beyond the school walls.
Cooperative Learning Satisfactory

There is a jigsaw activity in one of the lessons.

Cooperative Learning:

Group and cooperative learning strategies are a priority.

  • Satisfactory:  students work in groups
  • Good: cooperative learning skills are explicitly taught and practiced
  • Very Good: cooperative learning skills are explicitly taught, practiced and assessed
Assessment & Evaluation Good
Assessment & Evaluation: Tools are provided that help students and teachers to capture formative and summative information about students' learning and performance. These tools may include reflection questions, checklists, rubrics, etc.
Peer Teaching Satisfactory
Peer Teaching:

Provides opportunities for students to actively present their knowledge and skills to peers and/or act as teachers and mentors.

  • Satisfactory: incidental teaching that arises from cooperative learning, presentations, etc.
  • Good or Very Good: an opportunity is intentionally created to empower students to teach other students/community members. The audience is somehow reliant on the students' teaching (students are not simply ‘presenting')
Case Studies Good

Case studies are provided in the teacher background information, which can be shared with students.

Case Studies:

Relevant case studies are included.  Case studies are thorough descriptions of real events from real situations that students use to explore  concepts in an authentic context.

Locus of Control Good

Students have entire control over their final housing project, including design, and choice of construction materials.

Locus of Control: Meaningful opportunities are provided for students to choose elements of program content, the medium in which they wish to work, and/or to go deeper into a chosen issue.