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Multiplication as Repeated Addition

Before learning the meaning of multiplication, your child must have mastered counting and adding numbers.

When we think about multiplication, we usually think of the Times Tables. In my opinion, you should not teach your child the Times Tables until he or she understands what it means to multiply two numbers. After your child has understood the concept, then the Times Tables are useful as a short cut to carrying out the calculations. Knowing the concept will allow your child to tackle the complex problem sums found in tests and exams. |

Go to Long Multiplication (multiplication of multi-digit numbers)

Essentially, to multiply numbers is to add groups of a number.

For example, if we have three groups of five flowers and we need to find the total number of flowers, we can either:

- add the flowers within the groups

(5 + 5 + 5) - or we can multiply the number of groups by the number of flowers in one group

(3 groups x 5 flowers) - 5 + 5 + 5 has the same meaning as 3 x 5

(3 groups of 5)

Multiplying means repeated addition of a number. (The number must all be the same before we can use it to multiply.)

When you think of it this way, learning the Times Tables makes sense.

Let's take the 3 times tables, for example. Students usually learn the 3 times tables this way:

1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

and so on.

Using the idea of groups, we have:

1 x 3 = 3 (1 group of 3)

2 x 3 = 3 + 3 = 6 (2 groups of 3)

3 x 3 = 3 + 3 + 3 = 9 (3 groups of 3)

and so on.

So if your child knows the answer to 3 x 4 is 12, but cannot remember the answer to

4 x 4, they will just need to add 4 to 12 to get the answer.

4 x 4 = 12 + 4

During exams, your child will still be able to find out the answer even if they have forgotten some of their times tables.

Thinking in groups help them understand multiplication better. But that is not the only way to look at multiplication.

The other way (some say it is the only correct way) is multiplication as repeated addition.

Now let's look at something interesting:

3 groups of 5 = 5 + 5 + 5 = 15

5 groups of 3 = 3 + 3 + 3 + 3 + 3 = 15

3 groups of 5 has the same answer as 5 groups of 3!

So,

3 x 5 = 5 x 3

This means that when you multiply 2 numbers, the order of the numbers (which number is first and which is second) does not matter, the answer will still be the same.

When we multiply, there is the Multiplier and the Multiplicand.

The Multiplier is the number that tells us how many groups.

The Multiplicand is the number inside each group.

The Product is the answer we get after doing the multiplication.

2 x 7 means 2 groups of 7 or 7 + 7. So 2 is the Multiplier. 7 is the Multiplicand.

2 x 7 = 14 , so 14 is the Product of 2 x 7.

Look at the Repeated Addition Method for another way of understanding multiplication.

Step 1

Start by printing and cutting out this set of Dots Cards.

Use them to teach your child to add and multiply based on the groups of dots as shown in the examples below.

Step 2

After playing with the cards and your child is beginning to understand the concept of multiplication, give him or her physical objects like erasers, paper clips or stickers to form the groups shown in the card.

Remember to say it aloud, for example "3 groups of 5" until your child gets used to thinking like that when it comes to multiplying.

Step 3

Once your child has mastered using the cards, have him form his own groups and write the multiplication statement, without looking at the cards. Make it a family activity and test each other.

Try these worksheets on multiplication.

Another way of looking at multiplication is as repeated addition. Some Math teachers view this as the correct way to view multiplication, but personally, I find the first way easier for my students to understand. After they understand the grouping idea, then I tell them about repeated addition.

In repeated addition, you still have to add groups of numbers.

For example 7 x 3 means add the number 7, 3 times.

7 x 3 = 7 + 7 + 7 = 21

If we apply this method to learning the Times Table, it would look like this:

3 Times Table

1 x 3 = 1 + 1 + 1 = 3 (add the number 1, 3 times)

2 x 3 = 2 + 2 + 2 = 6 (add the number 2, 3 times)

3 x 3 = 3 + 3 + 3 = 9 (add the number 3, 3 times)

and so on.

If your child needs to learn multiplication tables as repeated addition, the following way makes more sense.

3 Times Table

3 x 1 = 3 (add the number 3, 1 time)

3 x 2 = 3 + 3 (add the number 3, 2 times)

3 x 3 = 3 + 3 + 3 (add the number 3, 3 times)

3 x 4 = 3 + 3 + 3 + 3 (add the number 3, 4 times)

and so on.

In Repeated Addition,

2 x 7 means 2 + 2 + 2 + 2 + 2 + 2 + 2

so 2 is the Multiplicand and 7 is the Multiplier.

In 2 x 7 = 14, the Product is 14.

Once your child has mastered using physical objects, you can progress to drawing models.

Tips to remember when drawing multiplication models:

- The size of the boxes must be equal for the same number.
- A bigger number should have a bigger box than a smaller number.
- The boxes are usually drawn horizontally in a row.

Go to Long Multiplication (multiplication of multi-digit numbers)

You can also use this method to teach your child to multiply 2-digit numbers with a 1-digit number. Just think of adding groups of numbers.

For example, let's work this out: 3 x 23

We know that 3 x 23 means 3 groups of 23. We can draw the model.

Now we apply the idea of place value.

23 is (20 + 3) or (10 + 10 + 3)

We draw the model and add the numbers as shown below.

If your child can multiply big numbers by herself, beyond her age level, what a boost to her confidence that will be!

Using an array

Breaking into smaller groups

Using tally marks

After your child understands the concept of multiplying numbers, ask him to write out the Times Tables in a chart. Click here or on the picture to print out the chart.

Let
him find the answers using his preferred method from the previous
examples. The next step is to memorize the Tables to use as a short cut.