## Friday, October 09, 2009

### Linear Word Problems

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.

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?

2. Anonymous1:07 PM

Definitely. Send me e-mail:

math_mambo@yahoo.com

I didn't feel comfortable posting it on scribd since I adapted problems from the text.

3. I would like the problems too! I am just finishing solving linear equations also. Somehow I ended up ahead of all the other algebra I teachers so I need to do some activiites this week and let everyone catch up with me.

I'll shoot you an email.

4. I have been following your blog for sometime... though this is my first comment here.

Thought would drop by and send you this site for your opinion before I start using it with my class.

5. Anonymous8:20 PM

Judy,

I've never seen that site before. After glancing at it, I like that it is one that the students have to create their own material. It looks like the details have been thought out nicely.