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"


  1. THAT sounds like a great idea! I've been looking for ways to get my 3rd graders more fluent in problem solving. They've been taught with VERY traditional methods their whole lives and now that our school has picked up Everyday Math, they're a little rusty in their problem-solving. This is a great scaffold for my 3rd grade thinkers. Thanks, Stephanie!

  2. I've awarded you a Versatile Blogger Award. You can pick it up at Making It As A Middle School Teacher.

  3. I can tell that you teach upper grade just by the title of this post! :) This sounds awesome!
    A Teeny Tiny Teacher

  4. You say "head problem" and my mind immediately goes to"lice"...you can tell I am an elem. school teacher! lol
    First Grade Blue SKies

    The reorganisation of my school's timetable has created a slot we are calling "Mental Maths" and I wasn't entirely sure what I was going to do with that time. I KNOW NOW! This is perfect for the class I will be teaching.

    ✪ Liam ✪
    Twist of Liam

  6. This is cool...another thing to try for math

  7. Great idea! Thanks for sharing. I will adapt this for my 7th graders and let you know how it goes.

  8. I am so glad everyone is finding this useful! This idea is used in Kindergarten all the way to 5th grade at my site (we only go up to 5th grade...it can DEFINITELY be used higher up). Let me know how it goes for you all!

  9. This was just posted by "Teacher's Bag of Tricks" on her blog that showed up on Facebook. Is this still available? I am not able to get to the blank form. I would love to use it in my classroom


  10. I clicked on it but the page that opens says Error... ! Help, this looks awesome and I want to use it!

  11. Be sure you click on the TEXT, and not the picture. For some reason, the picture won't link but the text underneath will.

  12. Do you have a set of "head problems" you do year to year, or do you come up with them as you go?

  13. This is fabulous! We do the mental math at our school, but not consistently. Any third grade teachers have some example problems?


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