Curricular Objectives
Students will be able to:
1. demonstrate an understanding of the energy crisis (motivating factor) and the role of biofuels in potentially alleviating that crisis in a written communication.
From the first day, students will be exploring the energy crisis. Initially, we will show them an introductory video that discusses the basics of the energy crisis
and the role of biofuels within sustainable energy sources. They will then have time to research the energy crisis and biofuels, and will demonstrate their
understanding of the role of biofuels within the energy crisis in a two paragraph summary.
2. identify the factors that make biomass a good or bad crop to grow.
Students will research biomass in the context of farming for a considerable portion of the unit. They will have to create a list of factors relating to profitability
in economic and environmental terms of economic farming, and then rank those factors in terms of importance. In a presentation to a panel of experts,
students will have to demonstrate their knowledge of those factors and sound mathematical reasoning in a convincing argument on whether or not farmers should
consider growing biomass.
3. determine which plants can be grown for biofuels.
Students will do research on a variety of plants which can be used as biomass for
biofuels. Based on that research, groups will be created according to their
selection of biomass crops. In the first days of the project, they will be
required to write several paragraphs on biofuel crops and typical Indiana
crops.
4. identify the difference between types of biofuels.
In determining the crops that they would suggest farmers plant for conversion to biofuel, they will need to be able to distinguish between types of biofuels and
the sources of those biofuels. If students struggle during days of research on biofuels, they will be guided back to this question to direct them in their path
to answering the guiding question.
5. perform a cost benefit analysis.
Students will be presenting their ideas on the profitability (in economic and environmental terms) to a panel of experts. They will need to perform a cost
benefit analysis based on several constraints as a benchmark of the unit; and the final rubric for the presentation will have a section devoted to sound
mathematical reasoning in their cost benefit analysis.
6. identify constraints on farmers when they determine crops to plant.
Students will need to create a list of factors that would contribute to a farmer’s decision whether or not to plant a crop for conversion to biofuel. They will
have an opportunity to consult a group of farmers about these factors. Based on the answers they receive and research they undertake, they will determine the
important constraints. They will need to select two or three of these as the most significant and create a cost benefit analysis based on those constraints.
1. demonstrate an understanding of the energy crisis (motivating factor) and the role of biofuels in potentially alleviating that crisis in a written communication.
From the first day, students will be exploring the energy crisis. Initially, we will show them an introductory video that discusses the basics of the energy crisis
and the role of biofuels within sustainable energy sources. They will then have time to research the energy crisis and biofuels, and will demonstrate their
understanding of the role of biofuels within the energy crisis in a two paragraph summary.
2. identify the factors that make biomass a good or bad crop to grow.
Students will research biomass in the context of farming for a considerable portion of the unit. They will have to create a list of factors relating to profitability
in economic and environmental terms of economic farming, and then rank those factors in terms of importance. In a presentation to a panel of experts,
students will have to demonstrate their knowledge of those factors and sound mathematical reasoning in a convincing argument on whether or not farmers should
consider growing biomass.
3. determine which plants can be grown for biofuels.
Students will do research on a variety of plants which can be used as biomass for
biofuels. Based on that research, groups will be created according to their
selection of biomass crops. In the first days of the project, they will be
required to write several paragraphs on biofuel crops and typical Indiana
crops.
4. identify the difference between types of biofuels.
In determining the crops that they would suggest farmers plant for conversion to biofuel, they will need to be able to distinguish between types of biofuels and
the sources of those biofuels. If students struggle during days of research on biofuels, they will be guided back to this question to direct them in their path
to answering the guiding question.
5. perform a cost benefit analysis.
Students will be presenting their ideas on the profitability (in economic and environmental terms) to a panel of experts. They will need to perform a cost
benefit analysis based on several constraints as a benchmark of the unit; and the final rubric for the presentation will have a section devoted to sound
mathematical reasoning in their cost benefit analysis.
6. identify constraints on farmers when they determine crops to plant.
Students will need to create a list of factors that would contribute to a farmer’s decision whether or not to plant a crop for conversion to biofuel. They will
have an opportunity to consult a group of farmers about these factors. Based on the answers they receive and research they undertake, they will determine the
important constraints. They will need to select two or three of these as the most significant and create a cost benefit analysis based on those constraints.
Curricular Standards
In the mathematics classroom, there are certain standards that need to be addressed. These are stated on the Indiana Department of
education (IDOE) website (2010). This Problem-Based-Learning (PBL) unit contains Algebra I and Algebra II standards. The following indicates
which mathematical content and practice standards will be addressed.
Indiana Common Core State Standards:
F.BF.1 Write a function that describes a relationship between two quantities.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the
quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels
and scales.
A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable
or non-viable options in a modeling context.
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and
graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Note: Because we are not requiring students to use a specific mathematical strategy to answer our driving question, it is impossible to determine
exactly which content standards will be used in students’ solutions. However, the above list details some mathematical skills and competencies we
expect students to use. For example, students might create an equation for profits in two or more variables (A.CED.2) and use that equation as part
of the mathematical reasoning behind their answer to the driving question.
Mathematical Practice Standards:
1. Make sense of problems and persevere in solving them.
Students will have to understand the multiple variables that farmers consider when deciding what crop to plant in their fields. While the question is seemingly
simple, it will require students to understand a complex system and persevere to formulate a solution.
2. Reason abstractly and quantitatively.
Students will need to reason abstractly in order to decontextualize research they find on biofuels and farming to make their mathematical model to solve the problem.
After they have manipulated their model to find the answer they were searching for, they will have to take the numbers and contextualize them to make them
meaningful for the farmers whom they will be trying to persuade.
3. Construct viable arguments and critique the reasoning of others.
Students will be required to justify their recommendations for which biofuel crops (if any) to plant with mathematical arguments, because they will be presenting their
recommendations to a panel of farmers. In addition, they will have to critically evaluate the soundness of other groups’ reasoning.
4. Model with mathematics.
Students will need to develop some kind of mathematical model in order to answer this question. Some might develop a model to analyze the financial viability of
planting a certain biofuel crop. Others might develop a model to show the environmental impact that growing a biofuel crop might have. Whatever argument
students choose to make, a mathematical model must be at the heart of their argument.
5. Use appropriate tools strategically.
While working on their projects, students will have mathematical tools available to them--graph paper, pencils, computers, graphing calculators, etc. They will have
to determine how to best utilize these tools for their purposes.
education (IDOE) website (2010). This Problem-Based-Learning (PBL) unit contains Algebra I and Algebra II standards. The following indicates
which mathematical content and practice standards will be addressed.
Indiana Common Core State Standards:
F.BF.1 Write a function that describes a relationship between two quantities.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the
quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels
and scales.
A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable
or non-viable options in a modeling context.
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and
graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Note: Because we are not requiring students to use a specific mathematical strategy to answer our driving question, it is impossible to determine
exactly which content standards will be used in students’ solutions. However, the above list details some mathematical skills and competencies we
expect students to use. For example, students might create an equation for profits in two or more variables (A.CED.2) and use that equation as part
of the mathematical reasoning behind their answer to the driving question.
Mathematical Practice Standards:
1. Make sense of problems and persevere in solving them.
Students will have to understand the multiple variables that farmers consider when deciding what crop to plant in their fields. While the question is seemingly
simple, it will require students to understand a complex system and persevere to formulate a solution.
2. Reason abstractly and quantitatively.
Students will need to reason abstractly in order to decontextualize research they find on biofuels and farming to make their mathematical model to solve the problem.
After they have manipulated their model to find the answer they were searching for, they will have to take the numbers and contextualize them to make them
meaningful for the farmers whom they will be trying to persuade.
3. Construct viable arguments and critique the reasoning of others.
Students will be required to justify their recommendations for which biofuel crops (if any) to plant with mathematical arguments, because they will be presenting their
recommendations to a panel of farmers. In addition, they will have to critically evaluate the soundness of other groups’ reasoning.
4. Model with mathematics.
Students will need to develop some kind of mathematical model in order to answer this question. Some might develop a model to analyze the financial viability of
planting a certain biofuel crop. Others might develop a model to show the environmental impact that growing a biofuel crop might have. Whatever argument
students choose to make, a mathematical model must be at the heart of their argument.
5. Use appropriate tools strategically.
While working on their projects, students will have mathematical tools available to them--graph paper, pencils, computers, graphing calculators, etc. They will have
to determine how to best utilize these tools for their purposes.
21st Century Skills
According to the Parternship of 21st Century Skill (2009), there are particular skills that students need to have in order to be successful in today's world. All of these skills are demonstrated within this PBL unit. The following indicates how each of these has been implemented.
1. Critical Thinking and Problem Solving
As students construct their final presentation, they will use reasoning to make judgements and decisions to help them find a reasonable conclusion. Students will be able to use their knowledge of graphing and systems of equations to critically think about this situation. In addition, they will be able to use the information that they gain from their research on biofuel crops and the guest speakers to evaluate the situation. Throughout the unit, students will be able to ask significant questions to clarify information and help them create their analysis. They will also be able to reflect upon their learning experiences within the exit ticket and bell ringer activities.
2. Communication and Collaboration
Students will be able to communicate clearly with the farmers, their peers and their teacher. Within each group, they will be able to discuss their research and analysis with their group. They will use communication throughout the entire project. In addition, they will present their analysis to a panel of experts. As students construct the final analysis, they will collaborate with each other. They will be able to utilize any form of media or technology that they choose to present the information.
3. Information Literacy
Students will efficiently access the needed information in class from the internet and the farmers (local experts). They will collect information that is directly related to farming and producing biofuel crop. Then, the students will use the information accurately to analyze the situation.
4. ICT (Information, Communications and Technology) Literacy
Students will be able to use the internet to research information. In addition, they will be able to use technology to present their final analysis. Throughout this unit, group members will have different points of view. They will need to negotiate their differences to compromise and find a common solution.
5. Productivity and Accountability
Throughout this unit, students will have to meet deadlines (checklist) set by the teacher. This will help them manage their time so that they are not behind toward the end of the project. In addition, they will need to be thoughtful and respect of their teammates. Each person in the group will be responsible for their work.
6. Leadership and Responsibility
The focus of this unit makes students responsible for others. They will be answering the question, “Under what conditions (environmental or economical), would you use your farm to produce a fuel crop?” The students will analyze the pros and cons of this situation. Then, they will present their ideas to farmers, who are community members.
1. Critical Thinking and Problem Solving
As students construct their final presentation, they will use reasoning to make judgements and decisions to help them find a reasonable conclusion. Students will be able to use their knowledge of graphing and systems of equations to critically think about this situation. In addition, they will be able to use the information that they gain from their research on biofuel crops and the guest speakers to evaluate the situation. Throughout the unit, students will be able to ask significant questions to clarify information and help them create their analysis. They will also be able to reflect upon their learning experiences within the exit ticket and bell ringer activities.
2. Communication and Collaboration
Students will be able to communicate clearly with the farmers, their peers and their teacher. Within each group, they will be able to discuss their research and analysis with their group. They will use communication throughout the entire project. In addition, they will present their analysis to a panel of experts. As students construct the final analysis, they will collaborate with each other. They will be able to utilize any form of media or technology that they choose to present the information.
3. Information Literacy
Students will efficiently access the needed information in class from the internet and the farmers (local experts). They will collect information that is directly related to farming and producing biofuel crop. Then, the students will use the information accurately to analyze the situation.
4. ICT (Information, Communications and Technology) Literacy
Students will be able to use the internet to research information. In addition, they will be able to use technology to present their final analysis. Throughout this unit, group members will have different points of view. They will need to negotiate their differences to compromise and find a common solution.
5. Productivity and Accountability
Throughout this unit, students will have to meet deadlines (checklist) set by the teacher. This will help them manage their time so that they are not behind toward the end of the project. In addition, they will need to be thoughtful and respect of their teammates. Each person in the group will be responsible for their work.
6. Leadership and Responsibility
The focus of this unit makes students responsible for others. They will be answering the question, “Under what conditions (environmental or economical), would you use your farm to produce a fuel crop?” The students will analyze the pros and cons of this situation. Then, they will present their ideas to farmers, who are community members.
Communicating and Ensuring Standards/Objectives
Communication of Standards and Objectives
Each day, the standards and objectives will be posted in classroom for students view.
How will you ensure that students can explain what and how they learned?
Students will participate in many activities that will ensure that they can explain what and how they learned. Every day, they will complete exit tickets and bell ringers that instruct them to reflect upon their experiences. In addition, students will be creating a final project where they have to explain their research to farmers and their peers. The teacher will also use questioning techniques to verify student learning.
Each day, the standards and objectives will be posted in classroom for students view.
How will you ensure that students can explain what and how they learned?
Students will participate in many activities that will ensure that they can explain what and how they learned. Every day, they will complete exit tickets and bell ringers that instruct them to reflect upon their experiences. In addition, students will be creating a final project where they have to explain their research to farmers and their peers. The teacher will also use questioning techniques to verify student learning.