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BASIC FACTS are the facts that are memorized and then used to figure out the facts that are not memorized. They are basic because they are the basis for all the other facts. For each operation, 100 facts are generally considered to be basic facts.

A CURRENT ISSUE in elementary mathematics education is: When teaching basic facts, what should we be emphasizing? strategies? or relationships?

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Now, we will examine some fact strategies for the hard basic addition facts. Although there are many strategies for finding answers to hard basic addition facts, the strategies that are most successful in resulting in memorization of those facts all have two common characteristics.

The two common characteristics of successful strategies for finding answers to hard basic facts are:1. They are mental strategies (not pencil/paper or mechanical strategies.2. They always require the child to use facts that are already memorized.

As we consider selected strategies, look for these two characteristics.1. They are mental strategies (not pencil/paper or mechanical strategies.2. They always require the child to use facts that are already memorized.

Three successful strategies for figuring out answers to hard addition facts are: One More Building on Doubles Make TenWe will examine each of these strategies.

The easiest strategy for children to use is the One More strategy.This strategy requires the lowest level of knowledge and skills. It is also very easy for children to visualize.

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Although this strategy is easy, it requires that the child already know a specific fact before finding the answer to the target fact. If the child does not know the required fact, then the child cannot use this strategy to find the target fact.

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Although the One More strategy is easy for the children, it is not easy for a teacher to use with a group of more than 2 or 3 children.When using this strategy, it is necessary for the teacher to be aware, precisely, which facts each child has already mastered. Otherwise, the teacher cannot know which facts the child is ready to figure out.With a full class of children, it is virtually impossible for a teacher to keep up with which facts the individual children have mastered. This strategy is not recommended for classroom teachers.However, this strategy is recommended for individuals of small groups, particularly in a remedial setting.

A strategy that many teachers have found to be effective is the Doubles strategy.Since the doubles are typically among the facts the children master early, this strategy requires children to use the doubles to figure out other hard basic addition facts.

For each target fact, the child thinks of a double that is close to the target fact.

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The Doubles strategy has been a relatively successful strategy for the hard basic addition facts. It is a generally easy strategy for facts that are within one or two of a known double (for example, 6+5, 7+9, or 8+7). However, it is not an easy strategy for facts that are more than two away from a double (for example, 5+8, 4+8, or 9+6).Consequently the Doubles strategy is often used together with several other strategies and children choose the best strategy for each specific fact. This often results in confusion at that point in the process where the child must choose a strategy.

A strategy that many teachers feel may be most effective is the Make Ten strategy.Since the tens are typically among the facts the children master early, this strategy requires children to use the tens to figure out other hard basic addition facts.

In this strategy, the child will make ten and see how many are left over. Teachers often use a device called a Ten-Frame to help children visualize the process.

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The Make Ten strategy is very successful strategy for several reasons. It is a universal strategy (it will always work) for all hard basic addition facts. The children only need to learn a single strategy.The Make Ten strategy is directly related to the base-10 numeration system. Numbers less than one hundred are always named as tens and ones.Finally, the Make Ten strategy lays groundwork for regrouping in addition, that children will learn to use when adding multi-digit numbers.

We will now examine three strategies that have proven to be effective for figuring out answers to hard subtraction facts: Think of Related Addition One More Subtract from Ten

The first of these strategies is the Think of Related Addition strategy.This strategy requires the child to think of an addition fact that is related to the target subtraction fact.Of course, this will only be helpful if the child knows that related addition fact.

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The Think of Related Addition strategy is popular among many teachers because it emphasizes the very important relationship between addition and subtraction. It is a universal strategy (it will always work) for all hard basic subtraction facts. The greatest drawback of this strategy is that children who are having difficulty with 15 - 8 = 7 usually do not know 7 + 8 = 15 either. Children who are having difficulty with 12 - 5 = 7 usually do not know 7 + 5 = 12 either. Remember that this strategy will only work if the child already knows the related addition fact.

The next strategy that we will consider is the One More strategy.This strategy requires the child to think of a known subtraction and then take away one more.

Do you already know 12 - 3 ?

Then, to find 12 - 4, take away one more.

15 - 9 is easy if you already know 15 - 8 ?

15 - 9 is 15 - 8 minus one more.

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The One More strategy is a very easy strategy for children. The process is easy to understand, and it is easy to subtract 1. The strategy’s greatest drawback is that children who are trying to figure out 15 - 8 must already know 15 - 7 = 8, to find the answer to 15 - 7 the child must already know 15 - 6 = 9, etc.A child is able to work only on facts that are 1 away from facts the child already knows. Children master facts at different speeds and in different orders, two children will seldom have already mastered the same facts. The teacher must be aware of what facts each child knows in order to know what facts they should be working on. This is very difficult for a classroom teacher to manage.

A strategy that is a general strategy for hard basic subtraction facts is the Subtract from Ten strategy.This strategy requires the child already to know the subtraction facts having 10 as the subtrahend (10-7, 10-4, 10-6, etc.).

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The Subtract From Ten strategy is very easy to teach. It is easy for children to visualize and understand. Some teachers object to the child having to do two steps to get the answer instead of just memorizing the fact. Keep in mind, however, that this strategy is not to be used instead of memorizing the facts. This strategy is an effective vehicle for helping the child commit the facts to memory.If the child does not already know the fact, the strategy provides a quick way for the child to figure out the correct answer. Without an effective strategy, the child’s only options are to guess or to say “I don’t know.” It is far better for the child to have a way to find the answer.

Next, we will now examine two effective strategies for figuring out answers to hard multiplication facts: One More Partial Products

The first strategy for figuring out hard basic multiplication facts that we will consider is the One More strategy.This strategy requires the child to build on a known multiplication fact.

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The second strategy for figuring out hard basic multiplication facts that we will consider is the Partial Products strategy.This strategy requires the child to break a hard fact that the child doesn’t know into two easier facts that are known.

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The Partial Products strategy is a very good strategy to teach. It is easy for children to visualize and understand. Not only does it help the child to figure out hard basic multiplication facts, but it also provides a strong background for the use of partial products in multi-digit multiplication.

ASSIGNMENT 2:Most commercially published elementary textbook series include the development of strategies for figuring out the hard basic facts..With a partner, search for a strategy that is developed in a textbook series for the hard basic facts for the operations, addition, subtraction, and multiplication. You should expect to find both hard addition facts and hard subtraction facts taught late in grade one and early in grade two. Look for the teaching of hard multiplication facts in grade three.After finding the textbook development, with your partner, present to the class the strategies that are developed and explain to the class how it is accomplished on the textbook pages.

Author: Dr. Benny Tucker

Email: btucker@uu.edu

Home Page: http://www.uu.edu/personal/btucker/index.htm

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