Is learning the basic facts important?

YES! I would even say it is critical.  One of the most important skills our students need in Math is the quick and accurate recall of basic facts. The addition and subtraction facts are important, but the multiplication facts may be even more important.   Students should be able to recall a basic fact (and an extended fact such as 300 times 40 which can be solved with the basic fact of 3 times 4) in three seconds or less.  While we realize this is but one small part of the work we need to do with students in Mathematics, quick recall of basic facts is critical for success.  So many tasks require this ability to quickly and accurately recall facts including estimation, finding equivalents, evaluating the reasonableness of answers, and doing work with ratios

1. Children explain that addition is putting items together.  They can model addition problems with cubes or other manipulatives.
2.  Children can explain that one model of subtraction is taking away.  They can model subtraction problems with drawings, cubes, or other manipulatives.
3.  Children can explain that one model of subtraction is comparing two groups to find the difference.  They can demonstrate this with manipulatives.
4. Children employ various methods to arrive at correct sums for addition fact exercises and correct answers for subtraction facts.  Methods may include counting on fingers, using manipulatives, counting on, and relating the exercise to one that is similar and using number sense to find the unknown answer.
5. Children understand relationships of numbers 0 to 20.  Given two numbers under 20, they immediately know which number is greater than or less than the other.
6. Children can construct and deconstruct numbers.  They demonstrate that 1 + 3, 1 + 1 + 2, and 2 + 2 are equal in value.
7. Children have an intuitive understanding of the commutative property of addition.  Children can match facts with the same addends in different order without having to find the sums.  They can explain that x + y has the same answer as y + x.  After finding a sum, for example 4 + 9, they can immediately tell the answer to 9 + 4.

These ideas were taken from the following two books:

Facts that Last by Larry Leutzinger Creative Publications.  (ISBN: 0-7622-1211) and

Practice Worth Repeating: Activities, Puzzles, and Games for Subtraction Facts by Janet Pittock, Creative Publications (ISBN: 0-7622-1202-0)

In their book, Young Mathematicians at Work Constructing Multiplication and Division, Catherine Twomey Fosnot and Maarten Dolk ask the question should children memorize the basic facts or should they become proficient at the quick and accurate recall of the basic facts through relationships in our number system (automaticity).

Memorization or Automaticity?

Memorization of basic facts usually refers to committing the results of operations to memory so that thinking is unnecessary.  Isolated multiplications and divisions are practiced one after another; the emphasis is on recalling the answers.  Teaching facts for automaticity, in contrast, relies on thinking.  Answers must be automatic, produced in only a few seconds; counting is not sufficient.  But thinking about the relationships among the facts is critical.  A child who thinks of 9 * 6 as (10 * 6) – 6 produces the answer of 54 quickly, but thinking, not memorization, is at the core (although over time these facts are remembered).  The issue here is not whether facts should be memorized, but how this memorization is achieved:  by rote drill and practice, or by focusing on relationships?

Children who struggle to commit basic facts to memory often believe that there are hundreds of facts to be memorized because they have little or no understanding of the relationships among them.  Children who commit the facts to memory easily are able to do so because they have constructed relationships among them and use these relationships as shortcuts.  The most important strategies are:

1.  Doubling: 2 * 3 * 6 = 6 * 6. 

         2.  Halving and doubling: 4 * 3 = 2 * 6.

         3.  Using the distributive property: 7 * 8 = (5 * 8) + (2 * 8), or

                                                           7 * 8 = (8 * 8) – 8.

         4.  Using the distributive property with tens: 9 * 8 = (10 * 8) – 8.

         5.  Using the commutative property: 5 * 8 = 8 * 5.

Memorizing facts with flash cards or through drill and practice on worksheets will not develop those relationships.  When these strategies are understood and used, there are fewer facts to memorize.  Using the commutative property, almost half of the facts are repeats.  One times a number is of course the number, so these do not have to be memorized.  Square numbers are easy for most children to remember  (pages 85-86).

Strategies for memorizing your Facts:

One of the best ways to foster students understanding is to put the basic facts into simple story problems and have the students act out or model the situation and then write the equation that matches.  Another way is to have the child write out their own story to fit an equation and act it out or model it using a manipulative to make sure they match.

This link has some good ideas for learning addition and subtraction facts:

http://www.busyteacherscafe.com/units/add_sub_unit.htm

This link gives strategies for developing fluency with basic facts.  It is written for students with Learning Disabilities but the strategies apply to all students.

http://www.ldonline.org/ld_indepth/math_skills/garnett_ldrp.html

Fact Triangles -

The benefit of Fact Triangles is that they cluster facts into fact families.  Reducing the number of facts you need to master.

Click Here to Download your Fact Triangles                                                                    

Facts may be mastered through the use of triangle fact cards. A triangle fact is pictured to the right. Fact triangles are a more effective device for memorizing the facts than ordinary flashcards because of their emphasis on fact families. The three numbers involved in an addition fact are placed on the corners of a fact triangle. The sum (answer) is at the top, under the asterisk (*). You cover one of the corners of the triangle. Then your child gives an addition/subtraction fact that has the number you are concealing as its answer. For example, in the fact triangle pictured, your child would say either “3 + 4 = 7” or “7 – 3 = 4.”