# Common Math Pitfalls: Geometry

Geometry is the odd ball of high school math…you either love it or hate it. Many “non-math” students find it is a refreshing break from the equations and formulas of algebra. But others do struggle. I spent a year teaching nothing but geometry back to back in Philadelphia. That experience and multiple tutoring jobs helped me pinpoint these main trouble areas.

Measuring Angles with a Protractor: It seems so simple. But most students don’t understand the concept of what an angle is and then don’t understand what they are measuring. In my high school classes we dedicated an entire day to learning how to use a protractor.

Understanding the parts of a triangle: This is another big one. When it comes to the Pythagorean Theorem the most common mistake is that students mix up the legs and the hypotenuse. If they don’t correctly identify them they misuse the formula.

This becomes an even bigger issue in trigonometry when they need to identify adjacent and opposite sides.

Correctly Using the Order of Operations in Formulas: There are lots of formulas in geometry and all you really need to do is substitute the values and evaluate. But lots of students do not correctly follow the order of operations when they evaluate.

# Common Math Pitfalls: Negative Numbers

The minute negative numbers show up in a math problem things get confusing fast. I started every school year with a quick review of negative numbers because they would trip up even my 11th graders. A student would solve a complex quadratic equation and then get the whole thing wrong because they didn’t correctly calculate $-7-3$.

So here are some tips on how to handle negatives:

1. When your child is first learning about negative numbers or reviewing them don’t be afraid to slow down. Take two days on that section or add in some reinforcement from Khan Academy.
2. Make sure they understand the concept and aren’t just memorizing a saying. Lots of students will tell me “a negative and a negative makes a positive.” That is not true. That would mean

$-7-3=10$

Instead a negative number multiplied by a negative number gives you a positive product. To correctly solve the problem above it can be helpful to use a number line or different colored chips.

3. Practice, practice, practice. In my last post I talked about the importance of memorizing math facts. That includes facts about negative numbers. So incorporate those into your flash cards or mad math minutes.

These tips and a little extra effort and time will save your student from so much frustration down the road.

# Common Math Pitfalls: Not Knowing Your Math Facts

In the elementary grades a lot of time is spent on students learning their math facts. But some kids never quite master the multiplication table or still have to draw a picture (or use their fingers) to calculate $17-9$.

This issue snowballs in high school. These facts need to be memorized and automatic so all their brain power is dedicated to the problem solving or algebra skill. A ten-step problem because laborious if you are still pulling out a calculator for each little step.

But it is easy to remediate. In my high school classes I used this book. We started with subtraction believe it or not and progressed through multiplication, division, and eventually fractions. You only give yourself one minute to do all the facts. It is only possible to get them all right in time if you have them completely memorized.

Try it for a month and you will see a big difference.