Multiplication Facts for 2, 5, and 10

Children always enjoy shortcut methods for finding numerical answers. Multiplication is the shortcut operation that empowers them to find fast answers for repeated addition. It is a topic that will be carried forward for years to come.

We say multiplication and division are inverse operations because one operation can "undo" the other operation. Multiplying 3 and 5 to get 15 is related to dividing 15 into 3 equal groups, with 5 items in each group.

 3 5 = 15 and 15 3 = 5 factors product dividend divisor quotient

This explains why the two operations are taught together. It provides an easy way to practice and reinforce fact families.

As you develop the operation of multiplication, it is important for children to connect concepts they learned last year to concepts they are learning this year. Last year, they solved problems involving skip-counting by 2's, 5's, and 10's. This year they will advance to multiplication, solving problems by using skip-counting, arrays, and repeated addition. Next year, they will multiply 2, 3, and 4-digit numbers by a 1-digit number and solve multi-step multiplication problems. See Grade 3: Multiplication.

Multiplication usually starts with skip-counting. As students learn this skill, they are reinforcing the products for that particular number:

 Skip-counting 2 4 6 8 10 12 14 Multiplication 2 1 2 2 2 3 2 4 2 5 2 6 2 7

Using repeated addition to show multiplication offers a sure way of connecting the two operations.

 2 + 2 + 2 + 2 = 8 2 4 x 2 = 8 2 2 + 2 8

At first, multiplication is expressed as "3 fives" or "5 tens." This implies the idea of a number of equal groups. One number tells how many groups; the other number tells the size of each group. As you introduce the word times, be sure to review this explanation.

For many children, a visual picture frequently offers the opportunity for instant recognition. This will help those children memorize the basic facts. Below is a pictorial array, drawn on grid paper, that easily shows why 3 5 is 15. Children can count the boxes singly, use skip-counting by 5's, or learn the multiplication fact.

It is essential to make multiplication both fun and meaningful. Encourage children to participate actively in your lessons by drawing pictures, offering explanations, and investigating patterns. Collections of bottle caps or postcards can be used to show the basic facts.

To strengthen multiplication skills, have children investigate special properties. Tell them to pretend they are detectives, searching for patterns as they work with multiplication. They may notice the following:

Any number times zero is zero.
Any number times one is that same number.
Changing the order of factors does not change the product.
Grouping factors in different ways does not change the product.
All these patterns are given special names as students advance in mathematics. See Grade 3: Multiplication.