Math Background

Multiplication and Division: Overview

Children always enjoy shortcut methods for finding numerical answers. Multiplication can be thought of as a shortcut operation that allows them to find fast answers for repeated addition.

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.

Factors, product, dididend, 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 that children connect the concepts they learned last year to the concepts they are learning this year. Last year, they solved problems involving skip counting by 2s, 5s, and 10s. This year they will advance to multiplication, solving problems by using skip-counting, arrays, and repeated addition. Next year, they will multiply two-, three-, and four-digit numbers by a one-digit number and solve multistep multiplication problems. See Grade 3: Using a Multiplication Table.

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 x 1 2 x 2 2 x 3 2 x 4 2 x 5 2 x 6 2 x 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

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 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 clearly shows why 3 x 5 is 15. Children can count the boxes singly, use skip counting by 5s, or memorize the multiplication fact.

fifteen boxes: three rows of five boxes

It is essential to make multiplication and division 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 post cards can be used to model 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:

Whenever you multiply by zero, the product is always zero.
When you multiply a number by 1, the product is always the other 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, which children will learn as they advance in mathematics. See Using a Multiplication Table.

Houghton Mifflin Math Grade 2