## Saturday, November 2, 2013

### International call costs x¢ per min for 1st n min, then y¢ for...

I can't believe I'm actually posting again. This won't last!

OVERVIEW
Developing abstract reasoning needs to start early and often and it's founded on a strong foundation of arithmetic/quantitative reasoning. That is, children normally learn to generalize from several concrete numerical examples before patterning takes place. Seems too obvious? Well, at what point would you expect a majority of your algebra students to do this successfully?

THE PROBLEM
Phone carrier charges for an international call are x¢ per minute for first n minutes, then y¢ per min for each additional minute or part thereof. Write an expression for the cost, in dollars, of a call lasting z minutes, z>n. Assume n,z are positive integers.

REFLECTIONS
Appropriate level of difficulty for Algebra 1? Algebra 2? Only for the 'honors' kids?
Too much expense of time to get students to be able to do this? Not worth the effort?
How many of this type are your algebra students normally exposed to? From the text? From teacher-constructed materials?
How many of these would most students need to practice to be proficient?
What % of your 'average' middle schoolers could solve this quantitatively, i.e., if all variables were replaced by numbers?
What are some of your favorite instructional strategies for these kinds of 'literal' word problems? By the way, this is the primary reason for my posting this!
What do you see as the main challenges to student performance on these kinds of assessment questions? Do you place 'understanding the question' high on this list?
Which of the 8 Common Core Mathematical Practices come into play here? By the way, do you have your own 'laminated' copy of these practices in front of you at all times! Here's the link:
http://www.corestandards.org/Math/Practice
Sorry, the 'answer' will have to come from someone who comments! I always assumed one of my students or a group would solve the problem...