Activity Name | Entry Activity | Sorting Biomass Crops | Understanding Correlation | Biofuels Crossword Puzzle | Interpreting Graphs | Collaboration Activity | Linear Programming |
Math Standards | F.BF.1 Write a function that describes a relationship between two quantities. | 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. |
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Biofuel Objectives | 1.demonstrate an understanding of the energy crisis (motivating factor) and the role of biofuels in potentially alleviating that crisis in a written communication -- Students will begin learning about the energy crisis in this activity, where they watch two videos portraying different sides of the biomass to biofuel debate: one positive, one negative. 2. identify the factors that make biomass a good or bad crop to grow.-- The videos discuss both sides of the biofuels debate, students should be able to identify several environmental and global factors that contribute to the discussion of biomass as a good or bad crop. |
2. identify the factors that make biomass a good or bad crop to grow. -- Several factors that are discussed in this activity, such as whether the plant is typically grown in Indiana, might be contributing factors in the student's decision if biomass is a good or bad crop to grow. 3. determine which plants can be grown for biofuels. -- Students will sort a number of crops based on key qualities, such as whether or not they can be grown in Indiana, or which are biomass for biofuel crops. This directly leads them to be able to make the determination in our biofuel content objective. |
This activity builds on a math concept that is necessary or extremely helpful for students in learning about biofuel content objectives. | 1. demonstrate an understanding of the energy crisis (motivating factor) and the role of biofuels in potentially alleviating that crisis in a written communication. -- A greater understanding of the words in the wordsearch will contribute to the students' general understanding of the energy crisis. | This activity builds on a math concept that is necessary or extremely helpful for students in learning about biofuel content objectives. | This activity builds on a 21st Century Skill that is necessary or extremely helpful for students in learning about biofuel content objectives. | This activity builds on a math concept that is necessary or extremely helpful for students in learning about biofuel content objectives. |
Activity Name | Show me the money! | How to research? | Finding Reliable Resources | Systems of Inequalities | Intro to Graphing |
Math Standards | 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.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | |||
Biofuel Objectives | This activity builds on a math concept that is necessary or extremely helpful for students in learning about biofuel content objectives. | This activity builds on a 21st Century Skill that is necessary or extremely helpful for students in learning about biofuel content objectives. | This activity builds on a 21st Century Skill that is necessary or extremely helpful for students in learning about biofuel content objectives. | This activity builds on a math concept that is necessary or extremely helpful for students in learning about biofuel content objectives. | This activity builds on a math concept that is necessary or extremely helpful for students in learning about biofuel content objectives. |
Student Activities
When will the unit be taught and how long will it last?
The unit will be taught after a unit on systems of equations in an Algebra 1 class, which typically falls in the early spring. In Algebra 2, this unit could be
taught at almost any time in the year, and students will have the mathematical preparation they need. We anticipate that the unit will last 12 days in a
standard classroom, and 6-7 days in a class with block scheduling.
How you will prepare the students and the environment?
The students will have the required mathematical knowledge in order to complete the unit. The teacher will prepare the students for group activity and 21st century
skills before the unit occurs. Students will practice working in group settings in a number of roles, familiarizing themselves with the process and giving the
teacher an opportunity to address any concerns and build group work skills. In order to accomplish this, students will complete a variety of team building exercises prior to starting the unit. At first, students will be asked to participate in relatively simple team building activities and slowly work their way to more challenging activities throughout the course of the year in anticipation of this PBL unit. The teacher will reserve computers in either a computer
lab or laptop carts for the required days for research and investigation of the biomass and biofuels.
What entry event will you use to introduce the driving question/unit to the students?
How will you ensure it captures their attention and initiates the inquiry process?
We are planning on using a video about the energy crisis to motivate student interest in biofuels and new energy sources. The video discusses the energy
crisis in terms of current energy sources and possible new sources, in particular corn biomass. The presentation discusses many environmental and
economic factors of the biomass to biofuel contribution to energy. While there are controversial aspects of the video, it is very dynamic and uses strong
statistics to back up their claims about the energy crisis. We will also present a video that has a positive perspective on biofuel production, and gives
more information about biofuels and the types of crops that can be converted from biomass to biofuel. The videos are both dynamic and interesting, with high
production values, which we believe will capture their interest and attention. We will then introduce the driving question to students, telling them that we
will be speaking to farmers in the near future and that our students will be serving as their advisors as these experts consider switching to biofuels. The
combination of video, question, and future presentation will initiate the inquiry process.
Based on your driving question, what kinds of investigations do you expect your
students to propose and/or undertake (provide specific examples)?
Students will have to investigate food crops and biofuel crops. In their research, they will consider price of seeds, price of fuel, double cropping, crops grown in
Indiana, biomass products that can be used in Indiana, any other factors that might lead to the profitability or cost in changing farming of food crops to
biofuel crops.Click on the following links to find sample class activities: arm span and height and sorting biomass and biofuel crops.
How will you ensure that the problem is explored from multiple perspectives?
The students will research on the Internet multiple websites, and they will also hear presentations from several different local farmers in the community. They
will also consider environmental or economical situations, and they will also research a variety of crops that can be used.
What kinds of data will students need to collect and analyze to address the driving
question?
The students will need to collect information about crops and biofuel crops that can be grown in Indiana as well as consider price of seed, fertilizer, fuel,
chemicals, and growing time. They also have to consider the environmental or economical conditions that surround growing food crops and biofuel crops.
What evidence will students have to provide to support their claims?
In addition to the information students learn from researching biofuel crops and talking to the farmer(s), students will be expected to provide a mathematical
argument, complete with visual aids (graphs), to support their answers to the driving question. For most students, this will probably mean optimizing a profit
function subject to constraints. Other students, however, might choose to develop a mathematical model to show how planting a biofuel crop would reduce
carbon emissions. Whatever argument students choose to make, they need to have sound mathematical reasoning to back it up.
How much time will you allot for each required activity (provide a timeline),
including time needed to debrief and reflect, and time needed to revise based on
feedback?
Exit tickets will be used on a daily basis for reflection. These will give the teacher feedback. The teacher needs to be flexible. Just-in-time activities may need to be implemented to assist in the learning process. See the attached timeline document.
What activities will be required of all students? What activities will be optional or
self-determined?
Students will be required to participate in all activities that are on our timeline, except those that are set apart as “scaffolding activities.” These may be
useful for the whole class, in which case, we will gather the students together and require all students to complete them. However, since students have a great
deal of freedom to chose their mathematical route to process and collect this information, students may need entirely separate sets of scaffolding events. We
are trying to anticipate these various needs with the scaffolding activities, and will make some tutorials and refreshers for mathematical concepts students
have covered.
How will these activities create student ownership?
Because student groups will be deciding what math they need on their own, they will have to take ownership of their mathematical reasoning. Students won’t be directed
to a specific approach, making them have ownership of their own mathematics, although the teacher may provide support as students determine which approach
would be most helpful to them. Throughout the class, students will gain ownership of their project by making critical choices for their group about
their project, such as picking a biomass crop they want to examine more closely for the duration of the project.
How will these activities foster engagement and active involvement?
There are several activities which will foster engagement. All of the activities are related to biofuels content or mathematical knowledge they ask for, which should
foster their active involvement. We will maintain a focus on the driving question to foster engagement. We believe that the interactive panel with experts, hopefully farmers from the community, who will answer student questions, will also foster engagement. The community connection to this project, and real life aspects of it, should become quite clear during this panel.
How will these activities engage students in higher order thinking?
The presentation at the end of the unit will engage students in higher order thinking as they are required to defend, recommend, and support their analysis
of whether or not farmers should grow their particular biomass crop. Throughout the course of the unit, they will be asked to analyze different aspects of
raising biomass crops for biofuels, which they then synthesize into a critical presentation. From the start of the unit, smaller activities are planned to
direct students to find the knowledge they need to understand the energy crisis and biofuels role in the energy crisis. The building of knowledge and skills
leading to a synthesized project all scale up to higher order thinking skills in the presentation and research part of the unit.
How will these activities help students learn biofuels content?
All of the activities are directed towards learning biofuels content. Math is used to bolster student analysis of the biofuels content, but in this project the
focus remains on math reasoning in the context of biofuels. While smaller activities will be used to remediate student math knowledge, all the rest of the
class time and activities is focused on biofuels content. They start learning about it from the first day in a multimedia manner, and continue to research
biofuels for the rest of the unit.
How will you use just-in-time instruction (provide a specific example) and how will you know it’s needed?
Just-in-time instruction will be used in the classroom when students need assistance with the mathematics concepts within their analysis. These activities will be assigned
on an individual basis. However, if many groups are struggling with a particular part, then it may be given to the entire class. For example, a group
has found its constraints associated with converting food crop to biofuel crop. They have constructed the equations, but they do not understand how to find the
solution set. The teacher would be able to direct them to a Kahn Academy video and some practice problems to help with their comprehension. The teacher will
know when just-in-time instruction is needed. These activities will be given when students do not know how to use a particular skill or concept, or there is
uncertainty with a particular concept. Click here to view a sample just-in-time acivity.
How will students be involved in decision-making regarding project details and demonstrations of their learning? Provide specific examples of areas in which students will be provided with voice and choice.
Once students do research regarding the crops and biofuel crops, they will discusst the information they found about the food and fuel crops. Once
this list is made, the students will be able to choose the fuel and food crop to continue to investigate as well as they will choose 2 or 3 constraints to
investigate to find out whether those constraints will allow the farmer to make a profitable or detrimental decision.
How will you prepare students to take on project responsibilities?
Before the unit, the students will have been introduced to group work through an activity such as “pass the pencil” or an activity similar to this to help the students learn to work together. Students will also sign a document regarding his/her role as a group member. At the end of the unit, students will also fill
out an anonymous form evaluating each other’s work .
How will you assure that students are learning important content?
There will be different assessments throughout the unit. The students will complete worksheets, exit tickets, as well as other forms of assessment throughout the
unit. Students will also have to include and explain in their presentation the mathematical content that they used in this unit.
The unit will be taught after a unit on systems of equations in an Algebra 1 class, which typically falls in the early spring. In Algebra 2, this unit could be
taught at almost any time in the year, and students will have the mathematical preparation they need. We anticipate that the unit will last 12 days in a
standard classroom, and 6-7 days in a class with block scheduling.
How you will prepare the students and the environment?
The students will have the required mathematical knowledge in order to complete the unit. The teacher will prepare the students for group activity and 21st century
skills before the unit occurs. Students will practice working in group settings in a number of roles, familiarizing themselves with the process and giving the
teacher an opportunity to address any concerns and build group work skills. In order to accomplish this, students will complete a variety of team building exercises prior to starting the unit. At first, students will be asked to participate in relatively simple team building activities and slowly work their way to more challenging activities throughout the course of the year in anticipation of this PBL unit. The teacher will reserve computers in either a computer
lab or laptop carts for the required days for research and investigation of the biomass and biofuels.
What entry event will you use to introduce the driving question/unit to the students?
How will you ensure it captures their attention and initiates the inquiry process?
We are planning on using a video about the energy crisis to motivate student interest in biofuels and new energy sources. The video discusses the energy
crisis in terms of current energy sources and possible new sources, in particular corn biomass. The presentation discusses many environmental and
economic factors of the biomass to biofuel contribution to energy. While there are controversial aspects of the video, it is very dynamic and uses strong
statistics to back up their claims about the energy crisis. We will also present a video that has a positive perspective on biofuel production, and gives
more information about biofuels and the types of crops that can be converted from biomass to biofuel. The videos are both dynamic and interesting, with high
production values, which we believe will capture their interest and attention. We will then introduce the driving question to students, telling them that we
will be speaking to farmers in the near future and that our students will be serving as their advisors as these experts consider switching to biofuels. The
combination of video, question, and future presentation will initiate the inquiry process.
Based on your driving question, what kinds of investigations do you expect your
students to propose and/or undertake (provide specific examples)?
Students will have to investigate food crops and biofuel crops. In their research, they will consider price of seeds, price of fuel, double cropping, crops grown in
Indiana, biomass products that can be used in Indiana, any other factors that might lead to the profitability or cost in changing farming of food crops to
biofuel crops.Click on the following links to find sample class activities: arm span and height and sorting biomass and biofuel crops.
How will you ensure that the problem is explored from multiple perspectives?
The students will research on the Internet multiple websites, and they will also hear presentations from several different local farmers in the community. They
will also consider environmental or economical situations, and they will also research a variety of crops that can be used.
What kinds of data will students need to collect and analyze to address the driving
question?
The students will need to collect information about crops and biofuel crops that can be grown in Indiana as well as consider price of seed, fertilizer, fuel,
chemicals, and growing time. They also have to consider the environmental or economical conditions that surround growing food crops and biofuel crops.
What evidence will students have to provide to support their claims?
In addition to the information students learn from researching biofuel crops and talking to the farmer(s), students will be expected to provide a mathematical
argument, complete with visual aids (graphs), to support their answers to the driving question. For most students, this will probably mean optimizing a profit
function subject to constraints. Other students, however, might choose to develop a mathematical model to show how planting a biofuel crop would reduce
carbon emissions. Whatever argument students choose to make, they need to have sound mathematical reasoning to back it up.
How much time will you allot for each required activity (provide a timeline),
including time needed to debrief and reflect, and time needed to revise based on
feedback?
Exit tickets will be used on a daily basis for reflection. These will give the teacher feedback. The teacher needs to be flexible. Just-in-time activities may need to be implemented to assist in the learning process. See the attached timeline document.
What activities will be required of all students? What activities will be optional or
self-determined?
Students will be required to participate in all activities that are on our timeline, except those that are set apart as “scaffolding activities.” These may be
useful for the whole class, in which case, we will gather the students together and require all students to complete them. However, since students have a great
deal of freedom to chose their mathematical route to process and collect this information, students may need entirely separate sets of scaffolding events. We
are trying to anticipate these various needs with the scaffolding activities, and will make some tutorials and refreshers for mathematical concepts students
have covered.
How will these activities create student ownership?
Because student groups will be deciding what math they need on their own, they will have to take ownership of their mathematical reasoning. Students won’t be directed
to a specific approach, making them have ownership of their own mathematics, although the teacher may provide support as students determine which approach
would be most helpful to them. Throughout the class, students will gain ownership of their project by making critical choices for their group about
their project, such as picking a biomass crop they want to examine more closely for the duration of the project.
How will these activities foster engagement and active involvement?
There are several activities which will foster engagement. All of the activities are related to biofuels content or mathematical knowledge they ask for, which should
foster their active involvement. We will maintain a focus on the driving question to foster engagement. We believe that the interactive panel with experts, hopefully farmers from the community, who will answer student questions, will also foster engagement. The community connection to this project, and real life aspects of it, should become quite clear during this panel.
How will these activities engage students in higher order thinking?
The presentation at the end of the unit will engage students in higher order thinking as they are required to defend, recommend, and support their analysis
of whether or not farmers should grow their particular biomass crop. Throughout the course of the unit, they will be asked to analyze different aspects of
raising biomass crops for biofuels, which they then synthesize into a critical presentation. From the start of the unit, smaller activities are planned to
direct students to find the knowledge they need to understand the energy crisis and biofuels role in the energy crisis. The building of knowledge and skills
leading to a synthesized project all scale up to higher order thinking skills in the presentation and research part of the unit.
How will these activities help students learn biofuels content?
All of the activities are directed towards learning biofuels content. Math is used to bolster student analysis of the biofuels content, but in this project the
focus remains on math reasoning in the context of biofuels. While smaller activities will be used to remediate student math knowledge, all the rest of the
class time and activities is focused on biofuels content. They start learning about it from the first day in a multimedia manner, and continue to research
biofuels for the rest of the unit.
How will you use just-in-time instruction (provide a specific example) and how will you know it’s needed?
Just-in-time instruction will be used in the classroom when students need assistance with the mathematics concepts within their analysis. These activities will be assigned
on an individual basis. However, if many groups are struggling with a particular part, then it may be given to the entire class. For example, a group
has found its constraints associated with converting food crop to biofuel crop. They have constructed the equations, but they do not understand how to find the
solution set. The teacher would be able to direct them to a Kahn Academy video and some practice problems to help with their comprehension. The teacher will
know when just-in-time instruction is needed. These activities will be given when students do not know how to use a particular skill or concept, or there is
uncertainty with a particular concept. Click here to view a sample just-in-time acivity.
How will students be involved in decision-making regarding project details and demonstrations of their learning? Provide specific examples of areas in which students will be provided with voice and choice.
Once students do research regarding the crops and biofuel crops, they will discusst the information they found about the food and fuel crops. Once
this list is made, the students will be able to choose the fuel and food crop to continue to investigate as well as they will choose 2 or 3 constraints to
investigate to find out whether those constraints will allow the farmer to make a profitable or detrimental decision.
How will you prepare students to take on project responsibilities?
Before the unit, the students will have been introduced to group work through an activity such as “pass the pencil” or an activity similar to this to help the students learn to work together. Students will also sign a document regarding his/her role as a group member. At the end of the unit, students will also fill
out an anonymous form evaluating each other’s work .
How will you assure that students are learning important content?
There will be different assessments throughout the unit. The students will complete worksheets, exit tickets, as well as other forms of assessment throughout the
unit. Students will also have to include and explain in their presentation the mathematical content that they used in this unit.
timeline.doc | |
File Size: | 56 kb |
File Type: | doc |
timeline_1.pdf | |
File Size: | 275 kb |
File Type: |