FREQUENTLY ASKED QUESTIONS ABOUT BASIC MATH FACTS

Doesn’t my child need to learn the basic facts?

Yes! But not in isolation. It is important to remember that knowing one’s addition facts is not the same as knowing addition. Many children memorize facts and do not understand that addition is putting things together, subtraction is taking apart, multiplication is taking groups of things, and division is putting things into groups.

Facts (particularly addition and multiplication) are tools that children use to solve other problems and to estimate. However, they are useless to children if they do not have meaning or if children do not know when to use them. If children understand the relationships between addition and subtraction as well as multiplication and division, they can use their addition and multiplication facts to solve subtraction and division problems too.

At TPS, we expect students to learn their facts, but it is equally important to us that students understand the four operations. We believe that understanding of the operations will support them in learning their facts as well as knowing how to use them.

How do children learn their facts?

The general sequence we use to help students understand operations and learn facts is:

1. Understanding the meaning of the operations.
2. Developing number composition (the knowledge that numbers are made up of other numbers)
3. Lots of experience using number combinations to solve problems
4. Reflection on and talk about what they know and don’t know.
5. Developing strategies to use what they do know to figure out what they don’t know.
6. Repetition, repetition, repetition.

This sequence takes a significant amount of time and begins right away. Even though children are not expected to have their facts memorized until much later, the early grade teachers are building the foundations students will need to learn and understand their facts.

At what points should my child have his/her facts memorized?

Addition: Midway through 3rd grade, children should know combinations up to 20.
Multiplication: Midway through 4th grade, children should know the 1-10 facts. By the end of 4th grade, they should also know 11-12 facts.

What should I as a parent do?

Here are some things you might try (depending on the age of your child):

•Find out what your child knows about the operations.
•Play number composition games (how many ways can you make 15?).
•Play the games your child brings home for homework. (Most of these are designed to give them practice.)
•When your child gives you an answer, regardless of whether it is right or wrong, ask, “How did you get that?”
•Encourage your child to visualize the numbers in the problems.
•Help your child keep track of the combinations he knows and encourage him to use what he knows to solve those he doesn’t know.
•If your child is close to the grade level where memorized facts are expected, give her repeated practice, but put her in charge of keeping track of her learning and when she gets stuck, encourage her to figure it out.

Try to avoid:

•Drilling the facts too early.
•Emphasizing memorization over strategy development.
•Equating knowing math with having facts memorized.

Here are some frequently used addition strategies:
•Near doubles—Many children learn double combinations early. They can use these relationships to derive facts close to doubles. (E.g., 6 + 6 = 12, 6 + 7 = 13 because 7 is one more than 6 and 13 is one more than 12.
•Fast tens—As children get good at making tens, they can use this strategy to solve figure out addition combinations. (E.g., 8 + 5 = 13 because 8 + 2 = 10 and 3 more is 13.)

In both cases above, the student used number composition (the knowledge that 7 = 6 + 1 and 5 = 2 + 3) to solve the problem.

Here are some frequently used multiplication strategies:
•Skip counting—Since 6 x 3 can be seen as 3 six times, children often count 3, 6, 9, 12, 15, 18.
•Adding strategies—For 6 x 7, a child might say 6 + 6 is 12, 12 + 12 is 24, 24 + 12 is 36 and 7 more is 42.
•Using well-known facts—Children learn their 2’s, 5’s and doubles very quickly. If they understand that multiplication is repeated addition, they can use this knowledge to derive facts close to these. If a child knows that 5 fours are 20, 6 fours are 20 plus another 4.
•Doubling the small numbers—Once children learns the 2’s-4’s, they can use their knowledge of doubles to derive 6’s and 8’s. If 3 x 7 is 21, 6 x 7 is 42 (because in the 6 x 7 we have twice as many 7’s as we do in 3 x 7).

How can I help my child learn to think?

When your child sees a problem and does not know how to solve it, you might ask:

What is going on in this problem?
Can you draw a picture of what is happening in the problem?
What information do you know?
What do you need to figure out?
What’s the first thing you need to do to figure it out?

Remember that people see and solve problems differently. Children usually see problems and solve them differently than adults because they are still formulating their knowledge. It is important to let your child use a strategy that makes sense to her because you are allowing her to build on and practice what she knows. By having the students talk about their strategies in class, teachers are helping students learn about alternative strategies and relate them to their own.

When your child produces an answer to a problem (regardless of whether it is right or wrong), you might ask: How did you get your answer? How do you know it makes sense?

If the child’s answer is incorrect, try to get him/her to determine this. Kids are empowered and learn more when they can figure out whether their answers make sense. Or you might say, “That’s not the answer I got. Let’s look at what you did?”

Before a child performs a bare computation problem (a problem that just involves numbers and is not in a story context), ask her about what will the answer be. A child should know that 23 + 48 is going to be more than 60, but less than 75. Or that 16 x 3 will be between 45 and 60.

This will help him/her develop number sense and will give her something to check her computation against.

This material was developed by Janine Remillard, Assoc. Professor of Mathematics Education, University of Pennsylvania. Janine recommends an article about math education at http://nctm.org/news/president/2004_10president.htm.