There are two ways you can have you students write algebraic models for a set of points.
1. Give them step-by-step directions of abstract coordinates, master the steps, and then work on applying the new skills to word problems.
2. Give and define a structure (in this week's case, the exponential form), then lead them through stories, putting the pieces in place.
You may have more success with writing equations from a given graph if you follow the first method, but how connected will that learning be the logs lesson you're going to have in a few days? How applicable will that knowledge be (which is where you get to have some fun)? Last Friday's quiz had several growth/decay questions, 3 graph to equation matchings, and then one equation modeling word problem that was really half of a context pieced around 2 chunks of data.
Results on the first section were great, but we fell off in the middle, and really lost it at the equation modeling. Last week's modeling examples and practice mostly consisted of a given set of points to be plugged into the general form to find a growth rate of initial value. Granted, we really only did it for a day, but I wouldn't say any memorable learning was going on.
This week, without anymore modeling instruction, I've seen more success (and certainly interest) in involving my students in the problems (that are still even mostly contrived).
Students are looking forward to the next day to see who gets to be in the story and how they are involved, and they're snapping pictures of the notes so they can think about it later.
You may remember two days ago when you worked through the example for exponential decay with points (0,9) and (5, .4), but "The day Sam and her friends were the beginnings of an E. Coli outbreak" or "The day Dani ate the radioactive taco" is the kind of things remember (at the very least until next week.) :)
EXTENSION BONUS:
By modeling the process for writing and working through stories, you can segue way easily into students doing the same for their own assessments. #student-becomes-the-teacher
Student created assessments and demonstrating understanding through a story would be a great item to include in student portfolios if you and/or your school have student-led conferences.
1. Give them step-by-step directions of abstract coordinates, master the steps, and then work on applying the new skills to word problems.
2. Give and define a structure (in this week's case, the exponential form), then lead them through stories, putting the pieces in place.
You may have more success with writing equations from a given graph if you follow the first method, but how connected will that learning be the logs lesson you're going to have in a few days? How applicable will that knowledge be (which is where you get to have some fun)? Last Friday's quiz had several growth/decay questions, 3 graph to equation matchings, and then one equation modeling word problem that was really half of a context pieced around 2 chunks of data.
Results on the first section were great, but we fell off in the middle, and really lost it at the equation modeling. Last week's modeling examples and practice mostly consisted of a given set of points to be plugged into the general form to find a growth rate of initial value. Granted, we really only did it for a day, but I wouldn't say any memorable learning was going on.
This week, without anymore modeling instruction, I've seen more success (and certainly interest) in involving my students in the problems (that are still even mostly contrived).
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| Monday: Real basic information scenario-wise, but it gave us a reason to put in a value for y and solve for x.. "When will 1,000,000 St. Louisans be infected?" |
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| Tuesday: Andre asked at the last second to be in the story, so, there he is. :) It actually helped with my setting when we did this problem the next hour. |
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| Dani chose Taco Bell, which worked well with the radioactive mutation scenario here, LOL |
Students are looking forward to the next day to see who gets to be in the story and how they are involved, and they're snapping pictures of the notes so they can think about it later.
You may remember two days ago when you worked through the example for exponential decay with points (0,9) and (5, .4), but "The day Sam and her friends were the beginnings of an E. Coli outbreak" or "The day Dani ate the radioactive taco" is the kind of things remember (at the very least until next week.) :)
EXTENSION BONUS:
By modeling the process for writing and working through stories, you can segue way easily into students doing the same for their own assessments. #student-becomes-the-teacher
Student created assessments and demonstrating understanding through a story would be a great item to include in student portfolios if you and/or your school have student-led conferences.
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Thanks for sharing!