What multiplication arrays are, why they’re so helpful for teaching the concept of multiplication, and how to use a multiplication array to help your child master the times tables. Includes a free printable multiplication array that you can use to model multiplication problems from 1×1 up to 10×10.
Hands-on manipulatives help children make sense of math. They make math concrete and help children understand math at a deeper level.
But, when it comes to memorizing the multiplication facts, hands-on materials can become pretty cumbersome. After all, counting out 8 groups of 7 may take your whole math lesson! And, all that time spent counting won’t really help your child remember that 8 times 7 equals 56, either.
That’s why multiplication arrays are so helpful. Instead of counting out piles and piles of little plastic objects, you can model multiplication problems by simply sliding a piece of paper. Even better, multiplication arrays provide an simple visual model that not only helps kids understand the concept of multiplication–it helps kids memorize the times tables faster, too.
What’s a multiplication array?
An array is any arrangement in rows or columns. Cards laid out into rows to play Memory, seats arranged in rows for a recital, or numbers arranged in an Excel spreadsheet are all examples of arrays.
A multiplication array is simply an arrangement of rows or columns that matches a multiplication equation. You can make arrays out of objects or pictures, and you can use any sort of shape. For example, here are 3 different arrays that all show 3 × 4.
(Generally, the first number refers to the number of rows, and the second number refers to the number of columns. So, all of the above arrays are considered 3 × 4 arrays, not 4 × 3, even though the total number (12) would be the same either way.)
What are the benefits of a multiplication array?
1. Multiplication arrays make it easy to visualize multiplication problems.
Hands-on objects are great for introducing multiplication, but they can be a bit of a pain when you’re doing a lot of problems or working with larger numbers. With a paper dot array, you can slide an L-shaped cover over the top of the array and show any multiplication fact you want from 1×1 up to 10×10. Here’s what the dot array and L-cover look like.
Here’s how you use them. For example, let’s say we wanted to help your child understand what 6 × 8 looks like. 6 × 8 means “6 groups of 8,” so slide the L-cover so that the dot array looks like this.
Each of the 6 rows has 8 dots, so there are 6 groups of 8 dots. So, the total number of dots in the array is the answer to 6 × 8. There are 48 dots showing, so 6 × 8 = 48.
2. Multiplication arrays help kids use strategies–not rote memorization–to find answers.
Let’s take 6 × 8. It’s one of the toughest facts for kids to memorize, but most children find it quite easy when they use 5 × 8 as a stepping stone.
Here’s how you teach your child to do this:
5 × 8 is 40. (5 × 8 makes a nice stepping stone, since children’s familiarity with 5s from their early years of arithmetic usually make the ×5 facts easy to learn.)
6 × 8 is just one more group of 8 than 5 × 8.
So, you can just add 40 + 8 to find the answer: 6 × 8 = 48.
This strategy works for all of the ×6 facts. And the good news is that there are similar strategies for all the multiplication facts!
3. Multiplication arrays make it easy for kids to see the commutative property in action.
The commutative property says that you can multiply numbers in any order and still get the same answer. For example, 2 × 7 and 7 ×2 both equal the same answer: 14.
To show your child this fact, use the dot array to show a multiplication fact. Then, turn the array 90 degrees. Now, the dot array shows the related multiplication fact–but the total number of dots didn’t change.