Overall the "problem" is not so hard for students. The tricky part is communication and attention to detail. Two not so strong skills for high school students! But it's also fun for students because it has role playing and some creativity. And if you have students who are far better in English than in math, then this is their time to shine!
The Premise
Students are given a letter from a business that contains a problem that can be solved using a system of equations. They take on the role of the business person who received the letter. They solve the problem and write a letter back to the business clearly communicating the solution including an attachment with all the algebra details. Here is a sample letter that a student might receive:
Teacher Prep
I have a whole bunch of letters at varying levels of difficulty. Prior to handing out the student letters I determine who should get what letter (here is the differentiation) with my advanced class all receiving a more complicated problem (mixture). I personalize the letters, typing each student's name where it says "your name". And then I print them all out on the only color copy machine in the school. Since I want a really nice polished letter back from the students I think it's important that what I give them is full color.
The Process
Students receive their letters in class. They are given general instructions on what their task is. With an average level class I then have them solve the problem at home and come in the next day with their solution. As students are doing class/group work on some other task I go around the room and check their solution. You could also collect them and hand them back the next day after checking.
I then go over the whole business letter concept. Stressing that they are playing a role and need to be professional. They are not writing this letter to a friend (so they should not have pleasantries such as "how are you doing?" in the letter). Spelling and grammar should be perfect, they want to make a good impression.
A tricky bit for students is understanding the whole address placement and general format of greeting and closure. For example the letter above has the address header for"Gourmet Boutique" and they need to understand that that address now goes under the date in the place of "Coffee Distributors". Basically the two addresses switch places. I point out that they should have the same format with the address blocks, the date, the salutation ("dear....the person who wrote them the letter they got - but don't include their title here) and the closure ("sincerely....their name and title - they make up a title).
The creativity comes in now with a cool header with a fun typeface and a graphic at the end of the letter.
Another formatting comment - the letter is single spaced and in English classes they are used to doing essays in double space.
After we go over the general formatting I talk about content. They should see that a letter has a general format in its paragraphs.
There should be three paragraphs in their letter.
The first paragraph has a professional greeting of some sort and restates the problem that the student received. They can lay on the schmooze pretty thick because they are wooing a client. (I am honored that you have chosen Coffee Distributors for your coffee needs. I am sorry that I was not clear on the correct mixture quantities for your premium South American blend. I am happy to provide the details regarding the exact quantities of Brazilian
coffee and Colombian for your personalized blend.) I would not write out a correct first paragraph but would definitely "say" it for students so they can hear how it might sound. Students are told that this paragraph is similar to an introduction sentence in an English class essay.
The second paragraph is the "meat" of their letter. Here they state the question (again!) and communicate the answer. They comment on how they solved it in a general way with a reference to the attachment. (This result was calculated by using an algebraic system of equations, see the attachment for full details and mathematical explanation).
The third paragraph just wraps things up - there are professional pleasantries, possibly a direct reference to the problem and reassurances that if they have any other questions they just need to ask.
(Thank you again for your interest in working with Coffee Distributors. I assure you that we have only the highest quality product and our blends are extremely well rated. If you have any additional questions please do not hesitate to contact me. Thank you again, and we look forward to working with you in supplying all your coffee needs.)
Sadly, in general, I find that students are not especially good writers. And this professional business letter format is so foreign to them. So it's important to stress that they are not writing an email or a text to a friend. They are trying to grow their business and develop trust and respect. So they must be very professional and have impeccable spelling and grammar. One error could lose a client for them.
I also talk about the attachment. This shows all the "algebra details". It should not just be work, it needs to have some words explaining the set up and implementation of their method. I am looking for the variables being defined. the system of equations clearly shown with some rationale for where it came from. The method used in solving should be stated (the linear combination method was used to solve this system). When the value of a variable is found state clearly what that represents. A short explanation of finding the other variable (that value is substituted into either original equation and then the other unknown is solved for). There should also be a full sentence stating the solution with respect to the problem originally posed. (you will need 80 pounds of the Brazilian coffee and 120 pound of the Colombian coffee).
With all that in mind, I would have all the students in my average classes do a rough draft (of both the letter and the attachment). In the past I've had students work together on some peer editing. This sounds all wonderful and cooperative and collaborative. But I hate to say this, I find peer editing to be a waste of time. Their peers are going to say that their letter sounds great. They often do not see grammatical errors and don't recognize if something sounds unprofessional. So I would usually collect the rough drafts, make general comments on them and hand them back. If a rough draft letter needs a lot of work I make the general comments but then urge the student to come for one-on-one help.
I've been working with advanced students for the last few years and the peer editing can be productive with them. They should work with a checklist when editting. And have a short amount of time (10-15 minutes). And I offer to those classes if they want direct teacher input on their rough draft to come during my extra help times and I will work with them.
Then students have the final task of creating their letter and their attachment. The final version of the letter must be typed and have an interesting header and a graphic/picture. The attachment does not need to be typed. I give them a few more days to get this completed and turned in.
Resources
Here are all my materials for this project:
Acknowledgment
Where does this project come from? I don't think I have ever had a truly original idea. Everything comes from something I've read or seen elsewhere. This project resulted from my experience in a session at an NCTM or ATOMIC convention in the 1980s. It was a very similar project but not so detailed and all the letters are mine.
I think this is a great project! I will probably adapt to fit the needs of my middle schoolers... You have so many options for the letters and I can definitely use that to help differentiate based on student interests.
ReplyDeleteThank you for making this available! This is such an awesome project. All students at every age always need more practice writing. I love bringing writing in to my math class. THANK YOU
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