I found a nice group of “linear function” word problems today (answers included - pdf file).
The kids in Math A are doing these problems. They aren’t classic Algebra 1 word problems, so if your child needs extra practice they’re not easy to come by.I'm curious about people's reaction to this shift in content. One of our regulars is skeptical; he sees this as a move to turn algebra into statistics. Another sees this as another instance of pushing advanced topics lower down in the curriculum. Functions used to be introduced in calculus; now kids see "function machines" in 3rd grade. (And, of course, both motivations could be involved - both and more.)
As I understand it, algebra 1 used to be focused on setting up and solving linear equations. The classic Algebra 1 word problems were number problems, consecutive integer problems, distance problems (2 trains leave a station), coin & age problems, & mixture & work problems.
Today algebra 1 tends to be focused on the idea of linear functions. That’s why our kids did all those “function machine” problems back at the Main Street School. In a linear function problem you are given a pair of “solutions” and asked to write an equation to model the situation. My favorite linear function word problem thus far is the Celsius – Fahrenheit conversion:
The graph of an equation to convert degrees Celsius, x, to degrees Fahrenheit, y, has a y-intercept of 32°. Given that water boils at 212°F and at 100°C, write the conversion equation.
To write the equation you use the two coordinated pairs you already know:
When Celsius is 0 degrees, Fahrenheit is 32
When Celsius is 100 degrees, Fahrenheit is 212
These two points are coordinated pairs on the graph of the function:
(0,32)
(100,212)
You derive the slope of the linear equation from these two points; then you plug in one of the coordinated pairs and derive the y-intercept; et voila.
y = 9/5 x + 32
Or:
F = 9/5C + 32
I've never been able to remember how to convert from Celsius to Fahrenheit, and knowing how to use the two known conversion points to produce the formula is great.
Any thoughts?
