A Lumber Expert's Word Problem Expedition

As a result of pulling my head slightly above water and of many discussions with the 8th grade math teacher at my school, I've decided to adjust the way I teach my math class. She is a 2008 TFA member who successfully taught two full grades in her first year of teaching and is the department chair in her second. She is encouraging and understanding, but relentless and unwilling to compromise expectations. In short, she's a very good teacher.

So far this year I've been fighting to reteach skills that my students have been building for the last several years. Adding and subtracting decimals, converting fractions, comparing positive and negative integers, and on and on... I've slightly empowered some who had already mastered these things, slightly improved some who hadn't, and slightly annoyed the rest. The never-ending battle with differentiation.

But where was I? Oh yes, new direction. The knowledge and skills that my students must leave 7th grade with haven't changed, but I am now going to approach them through the mysterious and dangerous jungle of word problems. I still need to spend plenty of time teaching how to do things like dividing decimals, but I am going to start spending much more time teaching recognition of when and why to do what.

My students DO NOT know how to solve problems. The extent of their problem solving skills are to pull each number out of the problem and then choose an operation at random - like spinning some sort of Wheel of Arithmetic. Here are three reasons why I think this is important:

1. Being unable to think critically about two sentences sets a dangerous precedent for thinking critically about any number of scenarios that my students may be faced with in the future, academically or otherwise.
2. Seeing these skills used in as many contexts as possible will give the most students the greatest chance of internalizing the big mathematical picture. Being able to visualize these numbers and operations is something I take for granted. But a 7th grader has a hard time seeing that a 20% tip is the same as 1/5 of the bill, which is the same as $0.20 for every $1. Once they can visualize it and connect it to the real world, they're golden.
   
3. For better or worse, the one measuring stick that anyone in Texas can easily use to judge these children is by standardized test scores. The TAKS (Texas Assessment of Knowledge and Skills) Test is full of word problems, so knowing how to convert or subtract simply isn't useful unless you know when to. These test scores determine which students get put in which classes, which students pass, which teachers get stipends, which schools get money, and on and on. An imperfect situation? Of course. But it is what it is.
   

I feel a little sheepish for just now landing on these obvious and basic conclusions, but hey - better late then never, right?

On Friday, each student entered my classroom and followed a protocol that will occur at least 3 times a week from now until the end of the year. They each took a half-sheet of paper from the back table and spent 5 minutes beginning the word problem that you will see below while I took attendance. Then we spent 10-15 minutes discussing the problem, where they got stuck, the different strategies they used, and why some did or didn't work.

We've been learning how to multiply, divide, add, and subtract fractions, so my students would all know how to solve this problem once they decided what to do, but no one did.

A piece of lumber is 4 1/4 feet long. If you need a piece of lumber that is 2/3 this size, how long of a piece do you need?

In addition to the above problem, each half-sheet contained a problem solving grid that I adopted with spaces for:

• Question - What are you looking for?
• Data - What do you know?
• Devise a Plan - How will you know you're right?
  
• Answer - Show your work
• Write a complete sentence
• Expression - How did you get there?

On Monday, I'll share the answer and some humorous results of our class discussions. But take a stab at it... are you smarter than a 7th grader?