Basic Arrays

An array is a way to arrange objects in equal rows and columns to show multiplication and addition.

Reading is good — doing is better. Practice Basic arrays as an interactive lesson.

Definition

An array is a group of objects, pictures, or numbers arranged in rows (going across) and columns (going up and down) so that every row has the same number of objects and every column has the same number of objects.

Remember the rule

Rows × Columns = Total (or add the same number of rows together to get the total)

Key words

Array: Objects arranged in equal rows and columns, like a rectangle made of dots or items.
Row: A line of objects that goes across, like reading a sentence left to right.
Column: A line of objects that goes up and down, like a tall stack.
Equal groups: Groups that all have the same number of things in them.
Repeated addition: Adding the same number over and over, like 3 + 3 + 3.
Multiplication: A fast way to add equal groups, written with a times sign, like 3 × 4.
Total: The answer you get when you count or add everything together.
Factor: One of the two numbers you multiply — in an array, the number of rows and the number of columns.

Worked examples

Draw an array with 2 rows and 4 columns. How many dots are there in all?

→ 8 dots total. Think of it as 2 rows of 4: 4 + 4 = 8, or 2 × 4 = 8. · Each row has exactly 4 dots, so you just add 4 two times.

An egg carton has 3 rows and 4 columns. How many eggs fit inside?

→ 12 eggs. 3 rows of 4 eggs: 4 + 4 + 4 = 12, or 3 × 4 = 12. · Real-life objects like egg cartons are perfect arrays!

Look at this array: * * * * * * * * * * * * How many rows? How many columns? How many stars?

→ 3 rows, 4 columns, 12 stars total. 4 + 4 + 4 = 12. · Count one row first, then count how many rows there are.

Write two different repeated addition sentences for a 5-row, 2-column array.

→ 5 + 5 = 10 (reading across 2 columns, five times) OR 2 + 2 + 2 + 2 + 2 = 10 (reading down 5 rows, two at a time). · You can flip an array on its side and get a different addition sentence with the same total.

A classroom has chairs set up in 4 rows with 3 chairs in each row. How many chairs are there?

→ 12 chairs. 3 + 3 + 3 + 3 = 12, or 4 × 3 = 12.

Make an array for 5 × 3. How many rows and columns? What is the total?

→ 5 rows, 3 columns, total = 15. Add: 3 + 3 + 3 + 3 + 3 = 15. · The first number in multiplication usually tells you the number of rows.

Common mistakes

Mixing up rows and columns — remember: rows go ACROSS (like a horizon), columns go UP and DOWN (like a column on a building).
Making unequal rows — every row must have the exact same number of objects or it is not a true array.
Forgetting that you can flip the array — a 2 × 4 array and a 4 × 2 array have the same total (8), just turned sideways.
Counting objects one by one every time instead of using repeated addition — look for the pattern in the rows to add faster.
Writing the repeated addition wrong — for a 3-row, 5-column array, each row has 5, so the sentence is 5 + 5 + 5 = 15, not 3 + 3 + 3 + 3 + 3 (that would be reading the columns instead).

FAQs

What is the difference between a row and a column?

A row goes left to right across the page, like a row of seats in a movie theater. A column goes from top to bottom, like the columns holding up a porch roof.

Why do we learn arrays in 2nd grade?

Arrays help you see why multiplication works. Instead of memorizing facts blindly, you can picture them as a rectangle of dots and figure out the answer by adding equal groups.

Can an array have just 1 row or 1 column?

Yes! A single row of 6 dots is a 1 × 6 array, and the total is just 6. It still follows all the rules of an array.

Is a 3 × 4 array the same as a 4 × 3 array?

The total is the same — both equal 12 — but they look different. One has 3 rows of 4, and the other has 4 rows of 3. Flipping an array is called the commutative property.

How is an array different from just a pile of objects?

In a pile, objects are jumbled and it is hard to count them. In an array, every row has the same amount, so you can count quickly by adding or skip-counting.

How do I find the total if the array is big and I lose count?

Count just one row to find how many are in each row, then count how many rows there are, and add that number again and again. You only need to count one row carefully!

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