Arrays and Introduction to Multiplication

Grade 2 · Math · Study Guide

Discover how arrays help us understand multiplication as repeated addition.

An array is a way of arranging objects into equal rows and columns. Arrays help us see multiplication in a very clear way.

Imagine you have 3 rows of stars with 4 stars in each row. That is an array! We can count all the stars by adding: 4 + 4 + 4 = 12. We can also write this as 3 x 4 = 12. The multiplication sign (x) means 'groups of.' So 3 x 4 means 3 groups of 4.

Every array has rows (going across) and columns (going up and down). The number of rows times the number of columns tells us the total. A 2 x 5 array has 2 rows and 5 columns, for a total of 10 objects.

A cool thing about multiplication is that you can switch the order and get the same answer. 3 x 4 = 12 and 4 x 3 = 12. This is called the commutative property.

Arrays are all around us in real life. Egg cartons, chocolate bars, and windows on a building are all arranged in arrays. Next time you see things in rows and columns, you are looking at an array!

Key terms

Array: A set of objects arranged in equal rows and columns
Row: A horizontal line of objects going across
Column: A vertical line of objects going up and down
Multiplication: A fast way to add equal groups together
Repeated addition: Adding the same number over and over, like 5 + 5 + 5
Product: The answer to a multiplication problem

Flashcards

What is an array?: Objects arranged in equal rows and columns
2 x 3 array total: 6 (2 rows of 3)
4 x 5 array total: 20 (4 rows of 5)
Row: Goes across (horizontal)
Column: Goes up and down (vertical)
3 + 3 + 3 as multiplication: 3 x 3 = 9
5 + 5 as multiplication: 2 x 5 = 10
Commutative property: 3 x 4 = 4 x 3 (order doesn't change the product)

Questions

An array has 3 rows and 5 columns. How many objects are there in total?
1. 8
2. 15
3. 12
4. 20
Show answer
Answer: 15
3 rows x 5 columns = 3 x 5 = 15 objects total.
The array 4 x 2 and the array 2 x 4 have the same total number of objects.
Show answer
Answer: True
4 x 2 = 8 and 2 x 4 = 8. Switching the order gives the same product.
2 + 2 + 2 + 2 = 4 x ___
Show answer
Answer: 2
Adding 2 four times (2+2+2+2) is the same as 4 groups of 2, or 4 x 2.
Which repeated addition matches the array 3 x 6?
1. 3 + 3 + 3
2. 6 + 6 + 6
3. 3 + 6
4. 6 + 6
Show answer
Answer: 6 + 6 + 6
3 x 6 means 3 groups of 6, so the repeated addition is 6 + 6 + 6 = 18.
In an array, all rows must have the same number of objects.
Show answer
Answer: True
For something to be an array, every row must have the same number of objects.

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