Oil In Addition To Natural Gas Production Net Lesson
Wednesday, October 2, 2019
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The initiative of all lesson I implemented from the OERB Core Energy Mathematics Workshop I attended was on Oil together with Natural Gas Production Profit. I did this lesson with my Algebra 1 students every bit a review of writing equations based on a real-life province of affairs together with every bit an introduction to solving systems of equations.
I modified the worksheets nosotros were given at the workshop to create 2 foldable booklets that could live on glued inwards our interactive notebooks. I was hoping to acquire through both booklets inwards ane 50-minute degree period, but that was super optimistic. In reality, it took 1.5 degree periods to consummate these problems.
Before jumping into the lesson, nosotros had a group/class discussion. What attain you lot know almost the crude together with natural gas industry? I had students hash out their ain personal cognition inwards groups. Then, each grouping shared with the class. I genuinely demand to piece of work on my give-and-take leading skills because the give-and-take was non every bit fruitful together with productive every bit I would remove maintain liked. My students shout out back they tin acquire away with having their ain conversations spell other groups are presenting. And, I destination upward yelling a lot. But, it never seems to attain whatsoever good. I shout out back it's because I've never taken the fourth dimension to instruct them the procedures of a degree discussion. I demand procedures. I demand consequences. And, I demand to live on consistent almost them from Day One. I simply ordered a mass on orchestrating productive mathematics discussions , then I'm hoping to larn from that this summer.
Some students offered insights into the crude together with natural gas manufacture that were agency over my head. They were throwing to a greater extent than or less jargon that meant zilch to me. These were the students who remove maintain genuinely spent fourth dimension on rigs together with worked out inwards the champaign amongst household unit of measurement members. Other students offered insights such every bit "Oil smells funny." or "You pose gas inwards your car."
The Essential Question for this lesson was "How attain crude together with natural gas producers determine if wells are viable to drill?" Students were to come upward dorsum together with respond this enquiry AFTER completing the lesson.
We also needed to review some of import vocabulary earlier showtime to piece of work with numbers together with equations.
As nosotros worked through each of the questions together every bit a class, nosotros would continually refer dorsum to this vocabulary box. If a enquiry mentioned profit, nosotros would review the Definition of profits earlier fifty-fifty attempting an respond to the question. These terms were novel to almost all of my students. They had a genuinely difficult fourth dimension differentiating betwixt operating costs, profit, together with revenue.
Day One focused on answering questions related to this data:
This could live on updated to reverberate the actual electrical flow selling cost of a barrel of oil, but I simply used the information that was provided at the workshop. Oil prices tend to fluctuate a lot.
Here's the initiative of all batch of questions nosotros explored together:
After reviewing the vocabulary, students were able to consummate this department with relatively few problems. The business office notation proved tricky for several of my lower bird students. Many students would simply hold off until someone inwards the degree provided the answer. I loathe this, but I'm non certain what to attain almost it. I guess I could laissez passer everybody inwards the degree a dissimilar laid of information to piece of work with, but that would in all likelihood drive me INSANE!
Having written functions for revenue together with operating costs, students could instantly tackle the theme of profit.
This is where nosotros ended Day One.
Day Two. Your companionship is instantly create to drill a well!
Now, we've moved from discussing ane wellsite to comparison 2 wellsites.
Again, we're practicing business office notation. This time, students are told what to shout out their functions.
Now comes the fun part. Graph the 2 functions. Figure out where they cross.
This was genuinely difficult for me to do, but I did it anyway. I didn't say my students how to pose out their axes. I permit each degree pick. I was risking that some classes powerfulness non discovery a graphical solution. Why attain this? Well, this is math. This is real-life. In real-life, every determination has consequences. My students demand to larn this. They demand to larn that math isn't e'er pretty. It tin live on messy. Sometimes you lot remove maintain to attempt multiple approaches to something earlier you lot discovery the agency that works.
Handing my kids a graph with the axes already marked cheats them together with me out of a learning experience. My kids demand to run into the consequences to their decisions. If I pick out for them, I'm cheating them out of an chance to shout out back critically. To live on an effective teacher, I demand to know what my students are thinking. I demand to know how good they tin shout out back critically. If I pick out for them, I'm cheating myself out of learning to a greater extent than almost where my students are. The to a greater extent than I know almost where my students are, the to a greater extent than I tin assistance them acquire to where they demand to be.
In this degree period, students decided to permit each work on the y-axis correspond $1,000. And, each work on the x-axis represented v days. We started to graph A(x), the cost of drilling wellsite Influenza A virus subtype H5N1 for x days. My students speedily identified the y-intercept of the equation, together with nosotros marked that on our graphs. The gradient was a fiddling trickier. How inwards the footing attain you lot graph a gradient of 200? First, I asked my students to rewrite 200 every bit a fraction. 200 was shortly expressed every bit 200/1. The numerator of our gradient represents the alter inwards y of our function. What is the alter inwards y of our y-axis? The distance betwixt each work on our y-axis represents $1,000. The denominator of our gradient represents the alter inwards x of our function. What is the alter inwards x on our x-axis? The distance betwixt each work on our x-axis represents v days. Now, how tin nosotros "unreduce" our gradient then that the numerator is a multiple of $1,000 together with the denominator is a multiple of 5? Students shortly realized that 200/1 is equivalent to 1000/5. Instead of spending a ton of fourth dimension trying to approximate how to become upward 200 dollars together with over 1 hateful solar daytime on the graph, nosotros were able to speedily together with efficiently motility upward one 1000 dollars together with over v days.
This is a strategy I learned at the OERB workshop. This was a completely novel strategy to me, together with I kinda sorta brutal inwards dear with it. We're e'er bespeak our students to trim back the slope. But, I don't shout out back I've ever asked students to "unreduce" their gradient earlier this lesson.
I permit the students remove maintain to a greater extent than accuse on graphing B(x). Again, nosotros had to "unreduce" our gradient of 250/1. This degree ended upward multiplying the numerator together with denominator yesteryear 10. Going upward 2500 dollars together with over 10 days was a fiddling trickier since every other dot was non on the intersection of 2 grid lines. In retrospect, nosotros could remove maintain corrected this yesteryear multiplying the numerator together with denominator yesteryear 20.
We establish the betoken of intersection of the 2 graphs together with wrote this solution to the organisation every bit an ordered pair.
Next, I asked students to algebraically determine the solution. Since nosotros were solely showtime our report of systems of equations, I had to basically laid this work for my students. Once I laid the equation, they were able to easily manipulate the variables to solve for x. Finding the corresponding cost yesteryear substituting the establish value of x into ane of the cost functions did non come about to them.
This is the initiative of all extended application work that I remove maintain worked through with my students. I enjoyed the process, together with I learned a lot. I promise my students learned a lot, too.
Their answers to the essential enquiry were disappointing. But, I shout out back that's generally my error for simply expecting them to write when I haven't required that of them for the entire year. My students volition ascension toward my expectations. But, initiative of all I must laid expectations. This is ane of the major things I am working on for this summer. Procedures together with expectations. Clearly spelled out. Practiced Daily.
I remove maintain uploaded the files for this activity here. Credit for the lesson goes to the OERB. I remove maintain slightly modified some of the wording together with construction to acquire inwards piece of work for my students.
I modified the worksheets nosotros were given at the workshop to create 2 foldable booklets that could live on glued inwards our interactive notebooks. I was hoping to acquire through both booklets inwards ane 50-minute degree period, but that was super optimistic. In reality, it took 1.5 degree periods to consummate these problems.
Oil together with Natural Gas Production Profit Booklet Foldables |
Some students offered insights into the crude together with natural gas manufacture that were agency over my head. They were throwing to a greater extent than or less jargon that meant zilch to me. These were the students who remove maintain genuinely spent fourth dimension on rigs together with worked out inwards the champaign amongst household unit of measurement members. Other students offered insights such every bit "Oil smells funny." or "You pose gas inwards your car."
The Essential Question for this lesson was "How attain crude together with natural gas producers determine if wells are viable to drill?" Students were to come upward dorsum together with respond this enquiry AFTER completing the lesson.
We also needed to review some of import vocabulary earlier showtime to piece of work with numbers together with equations.
As nosotros worked through each of the questions together every bit a class, nosotros would continually refer dorsum to this vocabulary box. If a enquiry mentioned profit, nosotros would review the Definition of profits earlier fifty-fifty attempting an respond to the question. These terms were novel to almost all of my students. They had a genuinely difficult fourth dimension differentiating betwixt operating costs, profit, together with revenue.
Day One focused on answering questions related to this data:
Here's the initiative of all batch of questions nosotros explored together:
After reviewing the vocabulary, students were able to consummate this department with relatively few problems. The business office notation proved tricky for several of my lower bird students. Many students would simply hold off until someone inwards the degree provided the answer. I loathe this, but I'm non certain what to attain almost it. I guess I could laissez passer everybody inwards the degree a dissimilar laid of information to piece of work with, but that would in all likelihood drive me INSANE!
Having written functions for revenue together with operating costs, students could instantly tackle the theme of profit.
This is where nosotros ended Day One.
Day Two. Your companionship is instantly create to drill a well!
Now, we've moved from discussing ane wellsite to comparison 2 wellsites.
Again, we're practicing business office notation. This time, students are told what to shout out their functions.
Now comes the fun part. Graph the 2 functions. Figure out where they cross.
This was genuinely difficult for me to do, but I did it anyway. I didn't say my students how to pose out their axes. I permit each degree pick. I was risking that some classes powerfulness non discovery a graphical solution. Why attain this? Well, this is math. This is real-life. In real-life, every determination has consequences. My students demand to larn this. They demand to larn that math isn't e'er pretty. It tin live on messy. Sometimes you lot remove maintain to attempt multiple approaches to something earlier you lot discovery the agency that works.
Handing my kids a graph with the axes already marked cheats them together with me out of a learning experience. My kids demand to run into the consequences to their decisions. If I pick out for them, I'm cheating them out of an chance to shout out back critically. To live on an effective teacher, I demand to know what my students are thinking. I demand to know how good they tin shout out back critically. If I pick out for them, I'm cheating myself out of learning to a greater extent than almost where my students are. The to a greater extent than I know almost where my students are, the to a greater extent than I tin assistance them acquire to where they demand to be.
In this degree period, students decided to permit each work on the y-axis correspond $1,000. And, each work on the x-axis represented v days. We started to graph A(x), the cost of drilling wellsite Influenza A virus subtype H5N1 for x days. My students speedily identified the y-intercept of the equation, together with nosotros marked that on our graphs. The gradient was a fiddling trickier. How inwards the footing attain you lot graph a gradient of 200? First, I asked my students to rewrite 200 every bit a fraction. 200 was shortly expressed every bit 200/1. The numerator of our gradient represents the alter inwards y of our function. What is the alter inwards y of our y-axis? The distance betwixt each work on our y-axis represents $1,000. The denominator of our gradient represents the alter inwards x of our function. What is the alter inwards x on our x-axis? The distance betwixt each work on our x-axis represents v days. Now, how tin nosotros "unreduce" our gradient then that the numerator is a multiple of $1,000 together with the denominator is a multiple of 5? Students shortly realized that 200/1 is equivalent to 1000/5. Instead of spending a ton of fourth dimension trying to approximate how to become upward 200 dollars together with over 1 hateful solar daytime on the graph, nosotros were able to speedily together with efficiently motility upward one 1000 dollars together with over v days.
This is a strategy I learned at the OERB workshop. This was a completely novel strategy to me, together with I kinda sorta brutal inwards dear with it. We're e'er bespeak our students to trim back the slope. But, I don't shout out back I've ever asked students to "unreduce" their gradient earlier this lesson.
I permit the students remove maintain to a greater extent than accuse on graphing B(x). Again, nosotros had to "unreduce" our gradient of 250/1. This degree ended upward multiplying the numerator together with denominator yesteryear 10. Going upward 2500 dollars together with over 10 days was a fiddling trickier since every other dot was non on the intersection of 2 grid lines. In retrospect, nosotros could remove maintain corrected this yesteryear multiplying the numerator together with denominator yesteryear 20.
We establish the betoken of intersection of the 2 graphs together with wrote this solution to the organisation every bit an ordered pair.
Next, I asked students to algebraically determine the solution. Since nosotros were solely showtime our report of systems of equations, I had to basically laid this work for my students. Once I laid the equation, they were able to easily manipulate the variables to solve for x. Finding the corresponding cost yesteryear substituting the establish value of x into ane of the cost functions did non come about to them.
Next, students were required to write just what this establish ordered twosome meant. My students struggled with the writing which is proof that I demand to require a lot to a greater extent than writing inwards my classroom. With Common Core, my students demand to acquire used to justifying their answers. Even more, they demand to acquire used to writing inwards consummate sentences. Always using units. Showing their work. We've got a lot of piece of work to do!
Their answers to the essential enquiry were disappointing. But, I shout out back that's generally my error for simply expecting them to write when I haven't required that of them for the entire year. My students volition ascension toward my expectations. But, initiative of all I must laid expectations. This is ane of the major things I am working on for this summer. Procedures together with expectations. Clearly spelled out. Practiced Daily.
I remove maintain uploaded the files for this activity here. Credit for the lesson goes to the OERB. I remove maintain slightly modified some of the wording together with construction to acquire inwards piece of work for my students.
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