Whew! In algebra 1 I've finished the initial introducing of solving a variety of linear equations: one-step, two-step, multi-step, weird distributive action, variables on both sides. Now it's just a matter of having them practice their hearts out until most/all of them are successful. Yesterday, I wanted to have them see how these problems could be used in real life, and after scanning through books and such, I saw that a lot of people were fascinated with how many coins someone has, or how much of a certain type of mixture to use, or which 2 consecutive numbers add to another number.
Then, whew! I scanned throught he Hughes-Hallett book of "Functions Model Change" and adapted some of their ideas that were written in table form to use as linear equation problems. There's one problems about carbon-14 dating which I know is not linear, but, boom, call it a "model", and it can become a linear situation. Then there was one about weight of a person vs. calories burned doing various exercises. Finally there was one about the years since 1970 vs population of a town.
I liked my adaptations because I've altered the scales on the variables, so that the kids have to think about what the numbers mean in terms of units. Also, these are in-context types of problems, not "math world" type. Also, the kids didn't need a calculator, since I made the numbers "doable". We had a discussion about estimating. For example, for the fossils, t represented time the tree had been dead in 1000's of years. An answer came up as t=3 & 2/11, and I asked them what that meant. We discussed approximating 2/11 by 2/10 and having t=3.2 and they finally got to the point to see that was 3,200 years. I also liked that in 2c below, they had to think to put in w=1.4 instead of 140, for example.
Here's an example of one problem I adapted:
2. Exercise physiologists tested many people, and have come up with an equation that shows the number of calories used per minute as a function of body weight for various activities. For walking they calculated the equation
b – 4.6 = 3(w – 1.7)
where b represents the calories burned in one minute, and w is the weight in 100’s of pounds of the person.
a. If w is found to be 1.6, what does that person weigh? (don’t solve; interpret w=1.6)
b. If b is found to be 5.4, what does that mean? (don’t solve; interpret b=5.4)
c. Suppose a person weighs 140 pounds, how many calories did they burn walking in one minute? In 30 minutes?
d. Suppose someone burns 5.2 calories a minute, how much do they weigh?