Any foundational math skill that should have been learned, but has not yet been learned is a gap in math. Let's look at an example.

Students who reach grade 8 or higher who find math more difficult all of the sudden may have one or more math gaps. As frustration grows, they ask themselves: "Why has math become so difficult?" Maybe they are studying really hard, but it is just not enough. Since math concepts are cumulative, there may be some concepts that are missing from past math training not yet mastered to the level needed at this point to successfully progress forward.

To give you a better understand of this, I have brought the following a common math gap example to show you. Consider working with negative numbers.

**1. Adding and Subtracting Integers When One is Negative**

While tutoring and teaching high school students over the years, I noticed a common gap around adding and subtraction integers when one integer is negative. Here are four exercises with the answers. You may want to test your student's knowledge and/or your own knowledge here. Try these (or have your student try these) *without a calculator*.

Write down the answer and compare it with the following solution.

Did the student get the following answers?

When I first noticed how much many students struggle with this, I was puzzled, then I became concerned. Now, I help those who struggle so they can thrive, shine and success.

Another math gap that causes students to stumble is multiplying an integer with a fraction.

**2. Multiplying an Integer With a Fraction**

Here are four exercises to try. Do these *without a calculator*.

Again, write down the answer before comparing your answer with the following answer.

Did you get the correct answers?

You may be thinking "What does it matter? I can always use a calculator."

Consider trying to the the following Algebra 1 problem without having mastered these two math skills.

You can do this with a calculator; however, it will take much longer than it would when the prior two skills are mastered. Do you see how the burden becomes greater with missing necessary skills?

Try the problem *without a calculator*. Did you write down your answer?

Did the student get the following answer?

Are these the only gaps in math? No. There are more common math gaps. Are you familiar with one-step equations?

**3. One-Step Equations**

Try these one-step equations. Write down your answer and compare with the solutions given below.

Did you get the correct answer?

One-Step equations can be solved using one operation in one step. To solve this the student would use one of four operations (addition, subtraction, multiplication and division) to solve. First determine which operation is being used in the problem. Let's call that operation "A". Next, determine the operation that is the *opposite* of operation A.

The opposite of addition is subtraction. The opposite of subtraction is addition. The opposite of multiplication is division. The opposite of division is multiplication.

Apply this opposite operation to both sides of the equation and you are done! It is solved!

Next comes Two-Step Equations.

**4. Two-Step Equations**

Are you ready for these? Try the following four two-step problems. Solve for x.

Compare your answers below.

Did you get the right answer?

The thing that trips student up about the two-step problems is that they think back to the order of operations. Did you learn this mnemonic for remembering the order of operation: PEMDAS (Please Excuse My Dear Aunt Sally). Well for these, we use the order of operations in *reverse*.

Further, can you see how Two-step equations are going to be difficult if the process for solving One-step equations has not been mastered?

__Contact__ me for a free consultation if you need help or want more information about how to fill in math gaps.

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Thrive Math Tutoring, LLC

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