Head Problems -- A little extra math thinking

A few years ago (well, more like 5 or 6), our math coach introduced us to the concept of "Head Problems" and I immediately knew that this was something I wanted to incorporate into my classroom.   Head problems are three step oral math problems which students compute in their head.  Sounds simple right?  What takes head problems to the next plane is the level of vocabulary, thinking, and discussion that must be done by the students.

Click to enlarge for the complete "script"

The basic routine of Head Problems is simple.  I give the students three steps in which they need to compute mathematical problems.  For example,

Step 1:  Add the number of degrees in a right angle and the number of sides on a pentagon. 
Step 2:  Subtract the digit in the ones place from the digit in the tens place.
Step 3:  Multiply by the number of quarts in a gallon.


You then debrief the problem with the students EVEN BEFORE THEY SHOUT OUT TO CONFIRM THE ANSWER.  You lead them through each step of the problem, having them talk to their neighbor, discussing each step one by one.  The entire class confirms the answer to each step before moving on.  This allows those students who have completely followed along to get validation that they were right, and those students who weren't quite sure to get it straight in their head.  The added benefit is that the stronger math students are able to express their math knowledge to the not so strong students, helping them both in the end.

Head problems are also great because of the level of vocabulary in them.  I am using words like "vertices", "degree in an angle", "gallon", "digit", "square root", etc...instead of normal, everyday math words.

In my class, I do one head problem twice a week.  The independent thinking, use of vocabulary, and problem solving skills become ingrained within a few weeks.   The 5 - 7 minutes it takes to do these problems is WELL worth the time and effort.

Click the text here to download the blank "form"