Seven Steps to Solving a Geometry Problem

Geometry requires a lot of big picture thinking that is based on previous Algebra 1 knowledge.  Luckily, many of the details of Algebra 1 are unnecessary in Geometry.  Instead, Geometry provides the reason for algebraic concepts in a visual manner.

As I was working through several geometry problems with one of my students this month, I developed a pedagogical tool that can be used to solve virtually any geometry problem, excluding proofs.  Additionally, this same method will work extremely well in any type of SAT, physics, or engineering problem solving.  After mastering this seven step process, any student will be able to approach and solve any problem with confidence.

1. Identify the question. Find out what the problem is actually asking, and then circle that question. For questions with multiple parts, underline each part.   Many students get easily bored with math because it is too passive, and for these students, I try to make the subject much more physical.  Questions should be attacked from the beginning by identifying and then circling what the problem actually is asking for.

2. Draw a picture.   The picture does not have to be perfect, but it should be an accurate representation of the problem.  Problems will always give enough information that a student can draw a picture.  Sometimes this step is not necessary if a picture is already present.

3. Label your picture.  Step 2 is literally useless without this step.  Accurately labeling a picture will help students see the whole problem in the grand scheme of geometry.   Any information explicitly stated in the problem or information that can be immediately inferred is important enough to label on the picture.

4. Write down all formulas. Any formula a student thinks might be relevant should be written down. Make sure to check that you have the formula written down correctly by checking your formula sheet (if one is given). This step will often times help a student see the big picture of the problem.

5. Write down any other information. From the given information in the problem.  Not all information can be put on the picture, so put that extra information here.

6. Solve for what you can. Problems will often have intermediate steps or variables between the information given and the final answer.  Solve for any variable you think might be relevant.

7. Make sure you answer the question.  If you followed all the steps, the question will be circled and easy to find.  If the test is scantron multiple choice, make sure you enter the correct answer onto the answer sheet.

These steps are a great way for any student to approach even the most difficult geometry problems.  On the other hand, knowing these steps will never be enough.   Practicing the steps by solving a variety of problems is the way to truly learn how to solve any geometry problems.  I try to emphasize the importance of practice to my students by making an analogy depending on what extracurricular activity they are involved in.  For athletes, I tell them that they would never show up to a game without months of preseason conditioning, practice, and scrimmages.  For musicians, I point out that they would never show at a recital without having practiced their pieces for hours on hours.  In the same way, a student should never show up to a math or science test without having practiced all types of problems many times.

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