Thanks for posting this plan. I tried this when starting a unit on systems of equations with my special ed Algebra class today and things went well, at least until it came time to write the equations. They struggled with this, we need to work some more on it. I think the fact that the first dog included a per dog fee and and an initial dog fee threw them.
Anyway, I thought you might like to know your plan was put to good use.
Thanks for posting this plan. I will use it next year in my math 8 and algebra I classes. I especially like the last question on the worksheet that asks them to write a situation to match the systems of equations given.
I was wondering about the fact that the 'initial value' in this application is for one dog (not zero dogs ). Did you have your students graph the problem as written and then extend the line back to the y-axis when they were ready to write the equation? If so, how did that work? And do you think that is an important part of the activity?
I was thinking that I might make the problem more like they charge a 'paperwork' fee of $5 and then $3 per dog. The only other change I would make is to just give them a 1st quadrant grid to work with.
Thank you for posting this lesson.
When I have taught systems of equations in the past, I started out with solutions on a graph. I always picked equations with nice solutions so students could easily read them from the graph paper.
Next I would solve systems in tables. The answers would get a little less nicer, maybe having decimal parts, but nice decimal parts.
Then I would move on to algebraic solutions. Here's where any answer would work out. I would do this in three separate lessons.
As I think about this, it would be nice to attack systems with a graphing calculator. We could graph two equations simultaneously. Then use the trace command to find the point of intersection. This could lead to a class discussion on the meaning of the intersection.
I could even connect it to a real life situation like renting a snowmobile for a weekend from two different companies. This could lead to further discussion about what happens after the point of intersection or before the point of intersection.
It seems to me that this would lead to a better understanding of systems prior to looking at the different ways to solve a system.
I will be working on systems in early April. This is definitely worth a try. So in the lesson above, I could come up with a real life problem first, explore it on the graphing calculators, and then solve it the old fashioned way—by hand.
I am adding a document which describes shows how to solve systems of equations
in " y=" form
from the Y=
by graphing--1 using trace
2 using the graph table
3 using the calc menu #5 Intersect
in standard form (ax = by = c)
4 using RREF in the Matrix menu
5 and by writing and using a program to solve the equations for x and y
when all else fails there is always the old fashioned way ...by hand
This is a nice lesson where students look at a linear system by making a table, making a graph and writing an equation for a real world problem about a dog walking business.