More about basic facts in math 110...

"Arithmetic is being able to count up to twenty without taking off your shoes." 
~ Mickey Mouse

 

You do NOT need to be fast at math facts to be a strong math student!
You do not need to be tall in basketball to be good at the sport, but it does make it easier.
Same with math facts.
Bonus: It is easier to learn math facts than it is to make yourself grow for your basketball team.


 
What is more important:  understanding math facts or memorizing them?
When students first learn the basic operations it is more important for them to learn HOW the operations work. 
 
Knowing WHY 4 x 3 is 12 by understanding that multiplication is repeated addition or through visual representations (4 groups of 3 objects or a tiled rectangle that is 4 by 3) is more important than pure memorization.  Additionally, it is great if a student can quickly figure out that 9*7 = 63 because they know 10*7 is 70 and 9*7 is one less seven. 
 
However, once they understand the operations, mastering them quickly helps tremendously in so many areas of math.
 

 
If understanding them is more important, why is it important to know the facts QUICKLY?
Think about reading.  It is important to be able to sound out words.  However, in order to read fluently and quickly it would not be ideal to slowly sound out every word.  This would make reading very slow and possibly unenjoyable.
 
Besides the number sense gained from mastering the basics, imagine how long would it take to do a series of problems that contained any of these concepts without quick recall of facts:
 
             (1) Add 93.651 and 12.308

             (2) Subtract $27.00 and 3.47

             (3) Multiply $36.56 and 138

             (4) Divide $134.54 by 3.4

             (5) Is 27 a prime number?

             (6) What are all the factors of 36?

             (7) Simplify the fraction 27/81

             (8) Compare 2/3 and 4/7 using common denominators

             (9) Add, subtract, multiply, and divide fractions

             (10) Area, perimeter, volume
 
That is just a small sampling of concepts that we will work on this year.  The usefulness of mastering facts does not end with arithmatic.  Factoring an algebraic expression like 63x3 + 27x2 + 9x is a whole lot easier if you know basic facts.
 

Students who spend the time mastering facts will save time down the road completing daily homework more quickly. 
 
 
 
What does it mean if I do not know the basic math facts very well?
You can be great at math without knowing math facts, and they are only one small aspect of a huge subject.  However, they are a vital part of a strong foundation in a subject that builds on one concept after another.  Being slow at coming up with the answers to the basic facts does NOT mean you are bad at math.  It just means that you are slow at math facts.
  

Students who spend the time mastering facts will save time down the road completing daily homework more quickly. 

 
Why can't I just use a calculator?

Basic math facts (0-9, +, -, x, /) form a very important foundation for understanding more difficult concepts.  It is hard to simplify a fraction like 27/36 without knowing the factors of each.  Long division requires you to use all four basic facts.  Think about the steps to a  long division problem with a two-digit divisor:

    (1) divide

    (2) multiply  {adding is part of long multiplication}

    (3) subtract

    (4) compare

    (5) bring down

 

Calculators eliminate some need for mental computation, but they cannot instill the kind of understanding of arithmetic that comes from committing math facts to memory.  Think of NUMBER SENSE as "common sense" in math.  Instant recall of basic math facts will help develop number sense, an intuitive understanding of numbers and the relationships they have with other numbers.

 

"Memory, like understanding, is unavoidable in mathematics and everything else. Although mathematics might seem to be a constant process of 'working things out,' the foundation of any kind of mathematical enterprise is memory, and a great deal of learning mathematics involves committing mathematical facts and procedures to memory. Memory eases all of our way through mathematics, and we can't get started without it. The first conventional step is to memorize, in order, the numbers from one to ten. These have to be known."

From the book "The Glass Wall: Why Mathematics Seem Difficult" by Frank Smith


 
 
What is the best way to master facts?
No one has come across the "best" method for mastering facts, because there are so many different learning styles.
Students need to find out what method works for them. I am a big fan of the triangle math facts cards.
There is a list of activities/options on the Basic Facts page (see link on the left sidebar).
 
 


 
 
"Brick by brick, my citizens, brick by brick."
-- Emperor Hadrian of Rome