About Daily Head Problems

The Daily Head Problem is the first of 2 content strategies we recommend using as part of your regular mathematics program. Daily Head Problems are oral presentations of standards based math problems which students must compute mentally. The problems should include the appropriate math vocabulary and concepts found in the California mathematics standards and textbooks. (For second language learners please remember to use SDAIE techniques. Sheltering techniques are offered in the sample problems for each grade.)

The use of "Mathematical Number Generators" (# of sides on a triangle, # of degrees in a right angle, days in a week) conceptually enhance the Daily Head Problem and also have the added advantage of making use of math vocabulary.

Ideally the Daily Head Problem should range in length from 2-4 steps, and generally should take up no more than 3-5 minutes of class time and as the name suggests, should be done on a daily basis. Daily Head Problems are to be replayed one step at a time with the appropriate answer generated for each step. (Examples of the replay are given with the first sample problem at each grade.) The more complex math computations occur at the end of the problem. Daily Head Problems can also be cross-curricular in nature (that is they can be used in Language Arts, Science, Geography, etc.)

Making Head Problem Grids

There is a way to write three to five head problems in such a way that the parts can be mixed and matched to create many more head problems. "But my students will get bored," you might think. Surprisingly, there are so many variations available to you this way that no two head problems will be quite the same, yet students will have multiple opportunities to hear the same mathematical language. Repetition provides for increasing student success, but in an interesting way.

The grid writing shared here is just one way. If it gives you ideas of your own, all the better. What you develop for yourself will be best suited to how you think and plan.

A great place to begin thinking about your head problem grid is to gather some vocabulary you would like students to learn. You might draw words and phrases from the standards, or you might draw them from your math curriculum. In the samples available on the right, vocabulary was drawn from a whole unit.

The next thing to do is to write five head problems (I did mine from left to right). You'll notice the boxes have numbers or letters in them. That is to help keep track of different combinations to use. You can combine step 1 with A on one day, B on another and so on. The last column is the "final Mode of Response." You will want to choose that so that it works best with the final number answer of the particular combination of steps you used. So here's a math problem for you: how many possible head problems have you written once a grid is complete?

Kindergarten teachers, please note that your grids will look a little different than the other grades. The grids can still be useful for getting head problem ideas, but may not provide interchangeable parts in the same way as the grids for other grades.

Sample Head Problem Grids

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K:	A B
1st:	A B
2nd:	A B
3rd:	A B
4th:	A B
5th:	A B
6th:	A B

Here is another way to get the most from your head problem creation. Take a look at a single head problem. We'll just look at the mathematical steps for now, leaving off the final Mode of Response.

In your head, think of the number of edges on a cube.

Multiply that by the number of quarts in a gallon.

Now we'll highlight words or phrases that might be changed to something else without changing the whole head problem.

In your head, think of the number of edges on a cube.

Multiply that by the number of quarts in a gallon.

The last thing we need to do is make lists of words we might substitute for the highlighted words.

for edges: vertices faces or for flat figures: sides

for cube: triangular prism rectangular prism square pyramid triangular pyramid triangle square parallelogram pentagon How many more can you think of?

for quarts in a gallon: pints in a quart pints in a gallon inches in a foot feet in a yard For interest, you might even ask for the number of yards in a foot. What you do will depend on your grade level.

Here's one of my new head problems:

In your head, think of the number of vertices on this square pyramid.

Multiply that by the number of feet in a yard.

How many different head problems can you find?