✖️ Understand Multiplication - Grade 3
What is Multiplication?
Multiplication is a way to add the same number over and over again quickly!
\(\text{Factor} \times \text{Factor} = \text{Product}\)
Instead of adding the same number many times, we can multiply to find the total faster!
👥 Count Equal Groups
What are Equal Groups?
Equal groups are groups that have the same number of objects in each group!
Example:
Imagine you have \(4\) bags of apples.
Each bag has exactly \(3\) apples.
🍎🍎🍎 🍎🍎🍎 🍎🍎🍎 🍎🍎🍎
This is \(4\) equal groups of \(3\)
How to Count Equal Groups
- Count the number of groups
- Count how many objects are in ONE group
- Use skip counting or repeated addition to find the total
Example:
\(5\) groups of \(4\) stars each:
⭐⭐⭐⭐ ⭐⭐⭐⭐ ⭐⭐⭐⭐ ⭐⭐⭐⭐ ⭐⭐⭐⭐
Skip count by \(4\): \(4, 8, 12, 16, 20\)
Total: \(20\) stars
Key Formula:
\(\text{Number of Groups} \times \text{Objects per Group} = \text{Total}\)
🔢 Identify & Write Multiplication Expressions
Parts of a Multiplication Sentence
- 🔵 Factors: The numbers being multiplied
- 🔵 Product: The answer when we multiply
- 🔵 Times (×): The multiplication symbol
Example: \(4 \times 5 = 20\)
Factors: \(4\) and \(5\) | Product: \(20\)
How to Write Multiplication Sentences for Equal Groups
Step-by-Step Guide:
- Count the number of groups → This is the first factor
- Count objects in ONE group → This is the second factor
- Write: (number of groups) × (objects per group) = total
- Calculate the product
Examples
Example 1:
Picture: \(3\) baskets with \(6\) oranges each
🍊🍊🍊🍊🍊🍊 🍊🍊🍊🍊🍊🍊 🍊🍊🍊🍊🍊🍊
Number of groups: \(3\)
Objects per group: \(6\)
Multiplication sentence: \(3 \times 6 = 18\)
We read this as: "3 times 6 equals 18" or "3 groups of 6 equals 18"
Example 2:
Picture: \(5\) groups with \(2\) flowers each
🌸🌸 🌸🌸 🌸🌸 🌸🌸 🌸🌸
Number of groups: \(5\)
Objects per group: \(2\)
Multiplication sentence: \(5 \times 2 = 10\)
We read this as: "5 times 2 equals 10" or "5 groups of 2 equals 10"
🔗 Relate Addition and Multiplication
Multiplication = Repeated Addition
Multiplication is a shortcut for adding the same number many times!
\(a \times b = \underbrace{a + a + a + ... + a}_{b \text{ times}}\)
How They Connect
Example 1: \(4 \times 3\)
As multiplication: \(4 \times 3 = 12\)
As repeated addition: \(3 + 3 + 3 + 3 = 12\)
(Adding \(3\) four times)
Both give the same answer: \(12\)! ✓
Example 2: \(6 \times 2\)
As multiplication: \(6 \times 2 = 12\)
As repeated addition: \(2 + 2 + 2 + 2 + 2 + 2 = 12\)
(Adding \(2\) six times)
Both give the same answer: \(12\)! ✓
Example 3: \(5 \times 4\)
As multiplication: \(5 \times 4 = 20\)
As repeated addition: \(4 + 4 + 4 + 4 + 4 = 20\)
(Adding \(4\) five times)
Multiplication is faster! ✓
Key Formula:
\(n \times m = \underbrace{m + m + m + ... + m}_{n \text{ times}}\)
First factor = How many times to add
Second factor = The number being added
📐 Arrays for Multiplication
What is an Array?
An array is an organized arrangement of objects in rows and columns!
- 🔵 Rows: Lines that go across (horizontal) →
- 🔵 Columns: Lines that go up and down (vertical) ↓
- 🔵 Arrays help us see multiplication!
How to Read Arrays
Array Formula:
\(\text{Rows} \times \text{Columns} = \text{Total}\)
OR
\(\text{Columns} \times \text{Rows} = \text{Total}\)
Examples with Arrays
Example 1: \(3 \times 4\) Array
⭐ ⭐ ⭐ ⭐
⭐ ⭐ ⭐ ⭐
⭐ ⭐ ⭐ ⭐
Rows: \(3\) rows
Columns: \(4\) columns
Multiplication: \(3 \times 4 = 12\)
Total stars: \(12\) ✓
Example 2: \(2 \times 5\) Array
🔵 🔵 🔵 🔵 🔵
🔵 🔵 🔵 🔵 🔵
Rows: \(2\) rows
Columns: \(5\) columns
Multiplication: \(2 \times 5 = 10\)
Total circles: \(10\) ✓
Example 3: \(4 \times 3\) Array
🟢 🟢 🟢
🟢 🟢 🟢
🟢 🟢 🟢
🟢 🟢 🟢
Rows: \(4\) rows
Columns: \(3\) columns
Multiplication: \(4 \times 3 = 12\)
Total circles: \(12\) ✓
Making Arrays
To make an array for a multiplication fact:
- The first factor tells you the number of ROWS
- The second factor tells you the number of COLUMNS
- Draw the array with objects in rows and columns
- Count all objects to find the product
Important Property:
💡 Commutative Property of Multiplication:
\(a \times b = b \times a\)
Example: \(3 \times 4 = 4 \times 3 = 12\)
You can flip the array!
📏 Multiplication on Number Lines
What is a Number Line?
A number line is a line with numbers in order. We can use jumps or hops to show multiplication!
How to Multiply on a Number Line
Step-by-Step Guide:
- Start at \(0\) on the number line
- First factor = Number of jumps to make
- Second factor = Size of each jump
- Where you land = The product (answer)
Examples with Number Lines
Example 1: \(3 \times 4\)
Multiplication: \(3 \times 4 = ?\)
Meaning: Make \(3\) jumps of \(4\)
Number line:
Start at \(0\) → Jump \(4\) → Jump \(4\) → Jump \(4\)
\(0 \xrightarrow{+4} 4 \xrightarrow{+4} 8 \xrightarrow{+4} 12\)
We land on: \(12\)
Answer: \(3 \times 4 = 12\) ✓
Example 2: \(5 \times 2\)
Multiplication: \(5 \times 2 = ?\)
Meaning: Make \(5\) jumps of \(2\)
Number line:
\(0 \xrightarrow{+2} 2 \xrightarrow{+2} 4 \xrightarrow{+2} 6 \xrightarrow{+2} 8 \xrightarrow{+2} 10\)
We land on: \(10\)
Answer: \(5 \times 2 = 10\) ✓
Example 3: \(4 \times 3\)
Multiplication: \(4 \times 3 = ?\)
Meaning: Make \(4\) jumps of \(3\)
Number line:
\(0 \xrightarrow{+3} 3 \xrightarrow{+3} 6 \xrightarrow{+3} 9 \xrightarrow{+3} 12\)
We land on: \(12\)
Answer: \(4 \times 3 = 12\) ✓
Number Line Formula:
\(n \times m = \) Make \(n\) jumps of size \(m\)
OR
Start at \(0\), add \(m\) a total of \(n\) times
📝 Important Formulas Summary
Basic Multiplication Formula:
\(\text{Factor} \times \text{Factor} = \text{Product}\)
Equal Groups Formula:
\(\text{Number of Groups} \times \text{Objects per Group} = \text{Total}\)
Repeated Addition Formula:
\(n \times m = \underbrace{m + m + m + ... + m}_{n \text{ times}}\)
Array Formula:
\(\text{Rows} \times \text{Columns} = \text{Total Objects}\)
Commutative Property:
\(a \times b = b \times a\)
(Order doesn't matter!)
Zero Property:
\(a \times 0 = 0\)
Any number times zero equals zero
Identity Property:
\(a \times 1 = a\)
Any number times one equals itself
📊 Three Ways to Show Multiplication
💡 Quick Learning Tips
- ✓ Multiplication is repeated addition - a faster way to add!
- ✓ Equal groups must have the same number in each group
- ✓ First factor = number of groups (or rows)
- ✓ Second factor = objects per group (or columns)
- ✓ In arrays, count rows and columns to multiply
- ✓ The order doesn't matter: 3 × 4 = 4 × 3
- ✓ On number lines, count your jumps carefully!
- ✓ Any number times 0 equals 0
- ✓ Any number times 1 equals itself
- ✓ Draw pictures to help you understand!
- ✓ Practice skip counting to multiply faster
- ✓ Arrays can be flipped - rows become columns!
- ✓ Use the method that works best for you