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Real World Math-Lessons 7, 9 and 12

Engaging Students Through Global Issues

Middle, Secondary

Description

This three-lesson math package promotes the development of math skills within the context of teaching about global issues and sustainability. Using real data students participate in activities that touch on credit card debt and national budgeting, investigate how our actions contribute to climate change and design an object to maximize economic benefits while minimizing impacts on people and environmental resources. Math topics include changing fractions to decimals (and vice-versa), solving percent word problems and algebraic equations, graphing inequalities and calculating the surface area and volume of cylinders and prisms.

Each lesson has opportunities for group/partner work, word problem assignments, and class discussion.

Rational Numbers-Financial Decisions:

Working in pairs, students examine a credit card offer sheet, come up with two questions or concerns that it raises and share them with the class. A  handout is then given to each pair that focuses on word problems involving budgeting.  A second worksheet compares factors contributing to national debt by investigating the revenues and expenditures of two countries. Math skills required include calculating percentages, decimal/fraction conversions, and solving problems involving more than one step.

Class discussion questions focus on the overuse of personal credit cards and the positive and negative implications of accumulating national debts.

Solving Inequalities- Carbon Emissions

Students complete a carbon footprint survey and then discuss as a class the terms carbon footprint, greenhouse gases, and climate change. They are then asked to express one way that to reduce climate change . A worksheet is completed which focuses on the carbon dioxide emissions of everyday items. Math skills required include writing and graphing inequalities, and solving one-step algebraic equations. Class discussion questions ask students to reflect on actions to reduce carbon footprints.

Volume and Surface Area-Sustainable Design

Students discuss in groups well designed and poorly designed everyday items. After sharing their ideas they are each given a plastic milk jug and a crate. Groups are instructed to re-design the jug so that a maximum number can be put into a crate. Ideas are presented to the class. A problem sheet is completed which highlights how volume and surface area calculations for prisms and cylinders are useful in deciding the most sustainable design for a milk container. Discussion questions focus on the  environmental and economic benefits of materials that are sustainably designed.

General Assessment

What skills does this resource explicitly teach?

  • Communicating mathematical thinking coherently and clearly to peers
  • Representing numbers in a variety of ways- percents, decimals, fractions
  • Applying algorithms in a variety of problem situations involving fractions, decimals and percent
  • Representing patterns and relations using algebraic equations and inequalities
  • Graphing inequalities
  • Representing and solving real-world problems in terms of 3-D models
  • Applying measurement formulas to solve for the volume and surface area of prisms and cylinders

Strengths

  • The resource is interesting, and easy to follow
  • It is up-to-date
  • It reinforces the relevance of mathematical concepts by linking them to the real world
  • Math skills are taught within the context of global issues and sustainability
  • Lessons can be used as "hook activities"to start a unit, as reinforcement for previously learned concepts, or as a real world assessment for learning
  • Group work allows for shared dialogue and incidental peer teaching
  • Possible answers are provided for discussion questions as well as answer keys for mathematical problems

Weaknesses

  • No accommodations or modifications suggested for struggling learners
  • No authentic case studies are included
  • Action plans are extensions rather than an integral part of the lesson
  • SI units are not used in the lesson on Budgeting for Climate Change

Relevant Curriculum Units

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        • Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers
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        • Computational fluency and flexibility extend to operations with fractions
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    • Grade 7
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        • Step 4Relevant matches
        • Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers
        • Linear relations can be represented in many connected ways to identify regularities and make generalizations
    • Grade 8
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • Computational fluency and flexibility extend to operations with fractions
        • Discrete linear relationships can be represented in many connected ways and used to identify and make generalizations
        • Number represents, describes, and compares the quantities of ratios, rates, and percents
        • The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships
    • Grade 9
      • Step 3Select a subject
      • Math
        • Step 4Relevant matches
        • The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed

Themes Addressed

  • Air, Atmosphere & Climate (1)

    • Climate Change
  • Citizenship (1)

    • Ecological Footprint
  • Economics (1)

    • Corporate Social Responsibility
  • Science and Technology (1)

    • Appropriate Technology

Sustainability Education Principles

Principle Rating Explanation
Consideration of Alternative Perspectives Good

As a math resource, it provides adequate information for the students to see the link between the sustainability issues that are discussed and the math skills being used.

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 Good

The resource focuses on the issue of  making sustainable living choices. Good and bad choices will have future environmental, economic, and social impacts.

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 Satisfactory

Although the resource does not examine all aspects of the issues it does promote dialogue and awareness through the carbon footprint, designing the container and examining financial choices activities.

Respects Complexity:

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

Acting on Learning Satisfactory
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 Satisfactory

Students have some opportunities during class discussions and group work to express their own beliefs/values.

Values Education:

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

Empathy & Respect for Humans Satisfactory

Students should see the link between our choices today and having a livable planet for future generations.

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 Good

Although there is no out-of-doors experience, the carbon footprint activity certainly encourages a personal affinity with the Earth.

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

The carbon footprint activity, the examination of credit card offers, and redesigning an everyday item like a milk jug gives local focus and relevance.

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

There are no discussions of the past, but present day situations are examined and evaluated and students are encouraged to play a role in implementing solutions. The future is seen as positive if society continues to work towards changes that will lead to a sustainable future.

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 Satisfactory

A combination of structured and guided inquiry is used.

Open-Ended Instruction :

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

Integrated Learning Satisfactory

This is for the most part, a math resource delivered in the context of promoting choices and behaviors that will lessen negative environmental impacts in the future.

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 Satisfactory
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, but does not suggest any accomodations for those students who are struggling with math. Alternative math activities should be provided for these students.

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 Satisfactory
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
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 Satisfactory

Reflection questions and math problems are provided, complete with suggested solutions and answer keys. Rubrics have not been included.

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 Poor/Not considered

Poor- there are no relevant case studies included

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 Satisfactory

Although the resource is specific with regards to content and materials used, there are opportunities in the extension activities that go deeper into chosen issues.

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.