He Was Right!

The other day, I listened to a talk by Robert Kaplinsky in which he commented that if you gave kids a problem they had to solve using steps, about 80 percent could do it but if you gave them a problem with lots of blanks to fill in and come up with a certain type of problem only about 50% out of the 80% could do it while the 30% couldn't.

I took a simple problem from his Open Middle site.  It had two blank squares + x = two blank squares. The idea was to use digits one to nine only once to come up with the largest value for x.  It was the "Solving one step equations with the greatest solution."

I gave it to all my students from Algebra I to Pre-calculus and about half struggled with the problem and the other half managed to figure something out.  Some students decided their first answer had to be right and looked at me strangely at the idea that a problem could have more than one answer or at least the correct answer might not be the one they got.

I started with this one because it is a standard equation that all students should be able to solve. Honestly, I expected the students in my higher level classes to have no trouble but some did.  The ones who finally got the hang of it, did quite well and came up with some interesting solutions.  I downloaded the sheet from Robert's site that allows students to try multiple times while taking time to explain what they learned from their try.  

I think that some were happy to get an answer and they felt they had an answer so it must be correct.  I had others who made several attempts trying to find the largest value of x while others seemed to aim for the smallest as if they didn't quite understand the objective.  I even ad a couple who got the correct answer after multiple tries who showed me the different possibilities they thought of.

This is a website I'll be using at least once a week to help students learn more about solving problems with one answer but with multiple possibilities of getting their.  Students are so focused on a problem that has all the numbers that lead to the answer that they either have forgotten that there are many ways to get to a single answer.

The great thing about the problems is that they include hints and answers so you know what the answer should be as students work their way towards the solution.  There are problems for grades K on up to high school.  I started with one from 6th grade because I wanted my students to be able to do it without too much frustration.  The ones for Kindergarten require things like completing number sequences with caterpillars while some in high school such as having students create an absolute value equation where      x = -2 is an extraneous solution.

If you haven't used it, check it out.  It is designed to help students understand concepts better so they don't just solve a problem by going through the steps.  Let me know what you think, I'd love to hear.  Have a great day.