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PSAT Prep: Tutoring Solution17 chapters | 173 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Is it better to learn a math concept rather than a math fact? In this lesson, learn which one will help you more in life. Also explore some math concepts and see how they are applied.

A **math concept** is the 'why' or 'big idea' of math. Knowing a math concept means you know the workings behind the answer. You know why you got the answer you got and you don't have to memorize answers or formulas to figure them out. Because you know why things work, you can figure out the answers and formulas yourself. You understand answers and formulas better and can tell when something isn't quite right.

When you understand a math concept, you have essentially reached an upper tier in math that allows you to think and process abstractly. This takes us to the difference between a math concept and a math fact.

A **math fact** is something that needs to be memorized or written down. For example, the multiplication and addition tables are math facts because they tell you that 1 + 1 = 2 and that 2 * 2 = 4. There are no ifs, ands, or buts about them.

Knowing a math fact allows you to recall the information when you need it, like for a test. However, if you were given a problem that is similar but uses different numbers or arrangements, then you wouldn't be able to do the problem because you only know the fact and not the concept behind it. You don't know how the problem works so you can't solve it because the facts you know don't include that specific problem.

Let's compare a few math concepts and math facts.

- Counting. The math concept for counting tells you that you start at a number and incrementally go up. You can choose your increment to suit your needs. The math fact for counting gives you the number line of 1, 2, 3, 4, etc.
- Addition. The math concept of addition tells you to gather 2 quantities or numbers together and get their total. The math fact is the additional table that tells you 1 + 1 = 2, 1 + 2 = 3, etc.
- Multiplication. The math concept of multiplication tells you to get the total of a certain number or quantity that has been copied or cloned so many times. The math fact is the multiplication table.
- Division. The math concept tells you that to divide means to split fairly. The math fact is the division table or the reverse multiplication table.

The math concept is more general than the math fact. Do you see how the math concept can be applied in so many more areas than the math fact? The concept allows you to solve so many more problems than just the math fact. One math fact lets you solve one specific type of problem, but one math concept covers a whole range of like problems.

Let's see how these math concepts can be used.

- Counting. If you know the math concept of counting, you can count anything. You can count whole numbers, decimals, by twos, by fives, by tens, etc. Using this math concept, you can count 1.1, 1.2, 1.3, 1.4, or 5, 10, 15, 20, etc.
- Addition. You can use this math concept to add any 2 quantities together. You could add 236 + 2 together to get 238 and you can add 2.1 + 3.5 to get 5.6. You understand that adding means combining the two quantities to get the total.

- Multiplication. Just knowing the multiplication table limits you to just those numbers. Understanding the math concept allows you to do problems such as 21 * 3 to get 63. You understand that this problem is telling you to get the total of 3 bunches of 21.

- Division. Because you understand the sharing principle behind division, you can divide anything. You can divide problems that don't split nicely, such as 1 divided by 4. You understand the problem to mean dividing a whole of something. If you only had one pie, how would you split it among 4 people? You would realize that 1 divided by 4 gives a result of a quarter, or 0.25.

**Math concepts** give you the 'big idea' of math. They are general and can be applied to a range of problems. **Math facts**, on the other hand, limit you to very specific problems. Applying math concepts makes your problem solving easier.

**Math concepts**: Math concepts are how math works, in general.

**Math facts**: Math facts need to be memorized or written down.

After viewing this lesson, you should be able to summarize the meaning and general application of math concepts.

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PSAT Prep: Tutoring Solution17 chapters | 173 lessons

- What are the Different Types of Numbers? 6:56
- How to Find the Greatest Common Factor 4:56
- How to Find the Prime Factorization of a Number 5:36
- How to Find the Least Common Multiple 5:37
- How to Find and Classify an Arithmetic Sequence 9:09
- What is a Mathematical Sequence? 5:37
- Mathematical Sets: Elements, Intersections & Unions 3:02
- Critical Thinking and Logic in Mathematics 4:27
- How to Calculate a Permutation 6:58
- What is an Absolute Value? 4:42
- How to Calculate an Arithmetic Series 5:45
- What Are Venn Diagrams in Math? - History, Types & Examples 6:40
- What is a Math Concept? 4:31
- What is a Negative Number? - Definition & Rules
- What is a Square Number in Math? - Definition & Examples 2:41
- What is an Ordinal Number? - Definition & Example 2:46
- What Is Pi? - Number & Usage 4:55
- Postulate in Math: Definition & Example 5:39
- Subtracting Polynomials: Examples & Concept
- Go to PSAT Math - Numbers and Operations: Tutoring Solution

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