Multiplication and division are challenging subjects to second, third, and fourth graders. They have a lot of facts to memorize, and some children will struggle to understand the concepts. You can use different strategies outlined in this post (from concrete to abstract) to make multiplication and division fun rather than a drudgery. As a homeschool parent, you can pick and choose which multiplication or division strategy works best for your elementary-age child.

## Multiplication and Division

Multiplication and division are two of the four basic operations in mathematics. One adds together, or multiplies, the same number a set number of times, and the other shows how many times a number goes into another number. Without a solid understanding of these operations, a child will not be able to succeed in more advanced math studies. Children who fail to learn the single-digit multiplication facts will remain behind their peers throughout the middle and high school years.

**What grade do you learn multiplication?** Most children begin to learn multiplication in second grade.

**What grade do you learn division? **Children often begin learning division in second or third grade.

**What grade do you learn long division? **Children learn long division in third or fourth grade.

### How are multiplication and division related?

Multiplication and division are inverse operations. That means one undoes the other. Each multiplication equation has a related division equation using the same three numbers. In multiplication, you multiply two factors to get a product. In division, you start with the product (the dividend) and divide by one factor (the divisor), which results in the other factor (the quotient).

#### How to Check Your Division with Multiplication

Because multiplication and division are inverse operations, you can check your division answer by multiplying the quotient and divisor to get the dividend. For example, if you got 3 as an answer to 21 divided by 7, you can check your answer by multiplying 7 by 3.

### Key Concepts Before Learning Multiplication and Division

Since multiplication is repeated addition, your child should understand addition before moving on to multiplication. For example, a student should know that seven is the same as one plus six, two plus five, or three plus four. The commutative property of addition (the property that allows you to reverse numbers you’re adding together and get the same result, such as 3+4=7 and 4+3=7) will also apply to multiplication. Familiarity with using a number line to add will help when it comes time to add the same number repeatedly.

## How to Teach Multiplication and Division

Teaching multiplication and division should start with concrete methods before progressing to abstract equations. Elementary children will gain the most understanding by working with manipulatives and real-life problems to start. In the classroom, a teacher will use most of these strategies to account for different students’ learning abilities, but as a homeschool parent, you can pick and choose which work best for your children. Your goal for your children should be to understand and be able to apply multiplication and division so they can use them as they progress to more difficult concepts.

### Multiplication Strategies and Methods

Here are various strategies to teach multiplication that progress from concrete to abstract.

#### 1. Multiply with Manipulatives

To begin, children should learn multiplication by making groups of items. You can provide them with small Unifix Cubes, pennies, or any object you have. The idea is that they will make a number of equal sized groups, and then be able to physically count the objects in total.

#### 2. Multiply Using a Number Line

Since multiplication is repeated addition, children who are familiar with adding on a number line will be able to add the same number over and over to reach a multiplication product. Progress to using repeated addition without the concrete number line to follow.

#### 3. Use the Array Model

If you have used small cubes, like the Unifix Cubes, as a manipulative to learn multiplication, the transition to arrays is a smooth one. Arrange cubes into rectangular arrays where each side has a length given by the factors in your multiplication problem. For example, the number 12 is a rectangular array of three blocks by four blocks, or two blocks by six blocks. This model also works as an early introduction to finding the area of a rectangle or similar shape.

#### 4. Use a Multiplication Table

A multiplication table is a handy tool for children to use until they have memorized the single digit times tables. It has the numbers 0 through 9 down the left side and across the top (many tables may only list 1 through 9 or will go up to 12). At the intersection of each row and column is the product of the number at the left and top. Children should be able to recognize patterns in the table that will help them in learning the multiplication facts. For example, the products of the nine row all have digits that add up to nine (except for 0 x 9). Children will easily start to learn the commutative property of multiplication by noticing that the product at the intersection of two numbers is the same whether you start at the left or the top.

#### 5. Skip Counting to Multiply

Children usually enjoy the speed and challenge of counting by fives or tens. Skip counting takes you through all the multiples of a number as you go. Try counting by threes or sevens to help children practice remembering their multiplication facts. You can start by using the multiplication table, choosing a row, and counting across all the products in that row. With enough practice, children should start to remember these multiplication facts.

#### 6. Memorize Single Digit Multiplication Facts

After thoroughly understanding the concept of multiplication and how and why it works, it’s often recommended that children memorize multiplication facts for zero through nine. These single digit facts are critical for being able to tackle multiple digit multiplication in the future. If children fail to learn these facts, they may not be ready to progress to fractions and then start to learn algebra. Flashcards may be helpful as children memorize these facts.

#### 7. Use commutative and Distributive Properties

Three properties will support children’ understanding of multiplication and even help them devise tricks along the way. The commutative property says that two numbers can be multiplied in any order. a x b = b x a. Once a child has learned the zeroes and ones facts, he will already know the first two facts of all the other times tables. The distributive property says that multiplying a number by two addends and adding them together is the same as multiplying a number by their sum. a x (b + c) = (a x b) + (a x c). Using this property, children who know the five facts and the two facts can find the seven facts by multiplying each number by 5 and by 2, then adding those together. For example, 7 x 6 = 5 x 6 + 2 x 6 = 30 + 12 = 42.

## Division strategies and methods

#### 1. Divide with Manipulatives

Give children several manipulatives or objects and ask them to divide these into equal groups. Start with basic word problems, like “if you want to share nine apples equally among three friends, how many apples will each friend get?” The concept of equal sharing is the basis of division.

#### 2. Using the Measurement Model vs. Partitive Model of Division

In the partitive (a part of a whole) model of division, a child will partition counters (manipulatives used to count with) evenly into a certain number of groups (the divisor), in a “one for you and one for me” fashion, and then count the final amount in one group to get the answer. In the measurement model, the child will begin making sets of a certain number (the divisor), and the number of sets she has at the end will be the answer. It is useful to have children solve division problems both ways to physically demonstrate that they will get the same result.

#### 3. Division Using a Number Line

Division looks like repeated subtraction on a number line. A child should start at the dividend and make each jump backward on the number line the size of the divisor. The number of jumps will be the quotient. This process is also known as chunking. Once children are confident with using the number line, you can move on to using repeated subtraction without a concrete number line.

#### 4. Division Array Model

As with the multiplication array model, small cubes work well for teaching division. For example, give children 12 cubes, and ask them to create rectangles with even rows. They might first try to make rows of five and discover that there are blocks leftover. Rows of 2, 3, 4, or 6 will work out just right and will give you all the factors of 12.

#### 5. Division Number Model

The division number model uses the multiplication facts a child has learned to derive answers. Children can pull out the multiplication table and search for the dividend on the table in the column or row that matches the divisor.

## The Best Way to Teach Multiplication and Division in Your Homeschool

The best way to teach multiplication and division is to progress through multiple strategies from concrete to abstract. Begin by giving children manipulatives to work with. Putting objects into equal groups creates a physical link between multiplication and division. Eventually children need to have enough understanding of the concepts that they can solve an equation, which is more abstract. Only after children grasp the concept of multiplication should a they start to memorize the single digit multiplication facts. Many curriculum will strongly advise or require memorizing the times tables from 0 to 12 or from 1 to 9. If your children struggle with memorization, give them plenty of practice with their math facts. Being familiar with the math facts, at least with 0 through 9, will be crucial for multiple digit multiplication and long division. Speed drills are available from AfterSchoolHelp for additional practice with multiplication and division.

## How to Teach Multiplication and Division by Grade

### Teaching 2nd Grade Division and Multiplication

In second grade, teach multiplication with very concrete strategies. If children do not progress to memorizing the facts, they will still have a solid foundation for third grade. Begin to introduce division as the concept of sharing equal amounts between groups.

### Teaching 3rd Grade Division and Multiplication

In the third grade, begin again with concrete examples and word problems. Arrays and skip counting are helpful in third grade as well. Children should continue working with multiplication facts. You can also introduce the idea of area with arrays. Give third graders concrete practice with division, like splitting a pizza with 12 slices evenly among 4 family members.

### Teaching 4th Grade Division and Multiplication

Continue using concrete manipulatives with different colors to represent different place values. Use lots of pictures and real life problems. As they multiply and divide multi-digit numbers, provide graph paper to keep children organized. Visualize the problems whenever possible.

#### How to Teach Long Division

Teach long division as a series of steps: divide, multiply, subtract, and drop down the remainder. Start with dividing numbers that have no remainder in any step, such as 84 divided by 2. With no remainders to worry about, the process is simpler. Then use problems with a remainder in the final step, such as 85 divided by 2. Finally, progress to problems with remainders in the tens, such as 96 divided by 4, or in either or both places. Emphasize that the multiply and subtract steps are about finding the remainder to carry to the next place.

### Teaching Multiplication and Division to Special Needs Children

Teaching multiplication and division to special needs children is not that different from the strategies outlined above. Many times, these children will need a longer period in the concrete stage of learning before progressing to more abstract methods. Graph paper might be helpful for children to keep numbers organized. It can also be used to draw arrays while learning multiplication and division. The distributive property trick above may be especially useful to children who struggle with memorization, allowing them to memorize fewer facts but still be able to find answers to the more difficult ones.

## Fun ways to teach multiplication and division

- Give children candy or snack manipulatives that they can eat after practicing multiplication or division.
- Use numbered cards to play a game like go fish, only instead of laying down pairs, lay down numbers where one divides into the other evenly. You might find that everyone is looking for those Aces.
- Roll a pair of dice and write multiplication and division equations that use those two numbers. For example, you roll a 3 and a 4, and you write 3 x 4 = 12, 4 x 3 = 12, 12 ÷ 4 = 3, 12 ÷ 3 = 4.
- Play video or board games that use numbers with your children.
- Introduce math concepts to younger children with educational shows. Recently, my four-year-old demonstrated her learning from a show when making hot dogs with her grandma. When grandma asked her how many she thought she would eat. She divided eight by two in her head and said, “We have eight hot dogs, so you can eat four, and I can eat four.”

## The BJU Press Approach to Multiplication and Division

BJU Press’s approach to teaching multiplication and division has always been a heavily manipulative focused approach. We encourage the use of manipulatives throughout all of our math programs, and provide manipulative packets for Math K5 through Math 4. Our program is designed to introduce students to math concepts with physical manipulatives before moving them on to working equations.

- Shop our Math 2 curriculum.
- Shop our Math 3 curriculum.
- Shop our Math 4 curriculum.

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*Valerie is a wife and a mother to a very busy toddler. In her free time she enjoys reading all kinds of books. She earned a B.S. in Biology from Bob Jones University, minoring in Mathematics, and a Ph.D. in Molecular Genetics from Ohio State University. Valerie has 15 years of experience working in research laboratories and has coauthored 8 original research articles. She has also taught several classes and laboratories at the high school and college levels. She currently works as a Data Analyst and a freelance writer.*

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