Early Math · Grade 2

Arrays: Rows, Columns and Equal Groups

Quick answer

An array is a set of objects in rows and columns, with the same number in every row. Its total is a sum of equal numbers: three rows of four is 4 + 4 + 4 = 12. Adding the columns instead, 3 + 3 + 3 + 3, gives the same 12, because it counts the same objects another way. A rectangle cut into rows and columns of same-size squares is an array of squares, counted the same way.

What you'll learn

  • Find the total in an array of up to 5 rows and 5 columns by adding
  • Write the total as a sum of equal numbers
  • Cut a rectangle into rows and columns of same-size squares and count them

Rows and columns

These dots are in an array. They are set out in rows and columns.

Three rows of four Twelve dots in an array of 3 rows and 4 columns.
Three rows of four

A row goes across. There are 33 rows, with 44 dots in each.

A column goes up and down. There are 44 columns, with 33 dots in each.

Add the rows

Every row has the same number of dots. So add the rows:

4+4+4=124 + 4 + 4 = 12

There are 1212 dots. A sum like 4+4+44 + 4 + 4, where every number is the same, is a sum of equal addends.

Why the columns give the same total

You can add the columns instead: 3+3+3+3=123 + 3 + 3 + 3 = 12.

It is the same 1212 dots. Adding rows or adding columns only groups them in a new way. No dot is added and none is taken away. The total of an array does not depend on how you group it.

Squares in a rectangle

A rectangle can be cut into rows and columns of same-size squares. Then it is an array of squares.

A rectangle cut into squares A rectangle cut into 2 rows and 5 columns of same-size squares.
A rectangle cut into squares

There are 22 rows of 55 squares. 5+5=105 + 5 = 10 squares.

To cut a rectangle this way, draw lines across for the rows and lines down for the columns. Space them so every piece is a square, all the same size.

Worked examples

Common mistakes

Practice problems

  1. How many dots are in this array?

    How many dots? An array of 2 rows and 4 columns of dots.
    How many dots?
    Answer

    88

    Full solution

    22 rows of 44: 4+4=84 + 4 = 8.

  2. Write a sum for the rows of this array.

    Write a sum An array of 3 rows and 5 columns of dots.
    Write a sum
    Answer

    5+5+5=155 + 5 + 5 = 15

    Full solution

    There are 33 rows with 55 dots in each. Add 55 three times.

  3. Write a sum for the columns of the array in problem 2.

    Answer

    3+3+3+3+3=153 + 3 + 3 + 3 + 3 = 15

    Full solution

    There are 55 columns with 33 dots in each. Add 33 five times. It is still 1515.

  4. An egg carton has 22 rows of 66 eggs. How many eggs is that?

    Answer

    1212

    Full solution

    6+6=126 + 6 = 12 eggs.

  5. How many squares are in this rectangle?

    How many squares? A rectangle cut into 4 rows and 2 columns of same-size squares.
    How many squares?
    Answer

    88

    Full solution

    44 rows of 22: 2+2+2+2=82 + 2 + 2 + 2 = 8 squares.

  6. A garden has 44 rows of plants with 55 plants in each row. How many plants are there?

    Answer

    2020

    Full solution

    5+5+5+5=205 + 5 + 5 + 5 = 20 plants.

  7. An array has 33 rows and 33 columns. How many objects does it have?

    Answer

    99

    Full solution

    33 rows of 33: 3+3+3=93 + 3 + 3 = 9.

  8. Can 1010 chairs be set out in 22 equal rows? How many in each row?

    Answer

    Yes, 55 in each row.

    Full solution

    5+5=105 + 5 = 10, so 22 rows of 55 make an array of 1010 chairs.

  9. How many squares are in this rectangle?

    How many squares? A rectangle cut into 3 rows and 4 columns of same-size squares.
    How many squares?
    Answer

    1212

    Full solution

    33 rows of 44: 4+4+4=124 + 4 + 4 = 12 squares.

  10. An array has 44 rows and 55 columns. Noah says it has 99 objects. What went wrong?

    Hint

    How many objects are in each row?

    Answer

    He added the rows and columns. It has 2020 objects.

    Full solution

    Each of the 44 rows has 55 objects. 5+5+5+5=205 + 5 + 5 + 5 = 20.

    Adding 4+54 + 5 counts rows and columns, not objects.

Frequently asked questions

What is an array?

Objects set out in rows and columns, with the same number in each row. An egg carton is an array.

How do I find the total in an array?

Add the rows. Three rows of 4 is 4 + 4 + 4 = 12. You can add the columns instead and get the same total.

What is the difference between a row and a column?

A row goes across, from left to right. A column goes up and down.

Why do rows and columns give the same total?

They count the same objects, only grouped another way. Nothing is added or taken away.

How do I cut a rectangle into squares?

Draw lines across to make rows and lines down to make columns, spaced so every piece is a square of the same size. Then count them like an array.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.2.OA.C.4Operations and Algebraic ThinkingUse addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
  • CCSS.MATH.CONTENT.2.G.A.2GeometryPartition a rectangle into rows and columns of same-size squares and count to find the total number of them.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.