Fact Families Game

What is a Number Fact Family?
A number fact family (or arithmetic fact family) is a set of related math facts (equations) using the same three numbers. It shows the inverse relationship between two mathematical operations:

• Addition and Subtraction (Inverse Operations)
  
• Multiplication and Division (Inverse Operations)
  The three numbers in a fact family are always the same, but the order and the operation change.
  Scroll down the page for a more detailed explanation.
  

How to play the Fact Families Game?

1. Select the operations: + and - or x and ÷
   
2. Select the conditions for the operands.
   
3. You will be given three numbers and two operators. Select the numbers and operators to form four different family fact equations.
   
4. Click “Check” to submit your answers.
   indicates correct.
   indicates error.
   indicates that equation is repeated.
   
5. Click “Try Again” to correct your errors.
   
6. Click “Continue” to get another set of numbers.
   
7. Click ⚙️ to restart the game.
   
   

 

Addition and Subtraction Fact Families
In an addition/subtraction fact family, the three numbers are related by two addition facts and two subtraction facts.
The Rule
The largest number is always the sum (the answer in addition) and is always the number you start with in subtraction.
The two smaller numbers are the addends (the numbers being added) and are the numbers you subtract from the sum.
Example: The Family of 3, 5, and 8
The three family members are 3, 5, and 8
Addition
3 + 5 = 8
5 + 3 = 8
Subtraction
8 - 3 = 5
8 - 5 = 3
The fact family demonstrates that if you know 3 + 5 = 8, you automatically know three other related facts.

Multiplication and Division Fact Families
Similarly, in a multiplication/division fact family, the three numbers are related by two multiplication facts and two division facts.
The Rule
The largest number is always the product (the answer in multiplication) and is always the number you start with in division (the dividend).
The two smaller numbers are the factors (the numbers being multiplied) and are the numbers you divide the product by.
Example: The Family of 4, 6, and 24
The three family members are 4, 6, and 24.
Multiplication
4 × 6 = 24
6 × 4 = 24
24 ÷ 4 = 6
24 ÷ 6 = 4

How to Use Fact Families in Learning
Fact families are a powerful tool for building number sense and algebraic thinking early on:

1. Mastering Inverse Operations: They clearly illustrate the relationship between addition/subtraction and multiplication/division. This is the foundation for solving equations later (e.g., if x + 5 = 8, you subtract 5 from 8).
   
2. Memorization: By learning the four facts as a group, students can memorize them more quickly and understand why they are related, rather than just rote memorization of 4 separate equations.
   
3. Checking Work: You can use the inverse operation to check an answer. For instance, if you solved 15 - 7 = 8, you can verify your answer using the fact family: 8 + 7 = 15.
   
4. Solving for Missing Numbers: If a student sees a problem like __ × 7 = 42, they know they can use division (42 ÷ 7 = __) to find the missing number.
    
   

Free Addition Games
One More, One Less	1-Digit Addition	Addition (Maximum Sum)
Add Doubles	Number Bonds (Missing Addend)	Add 3 or more single digits
Fixed Addend	Understand the Equal Sign	Fact Families Game
2-digit + 1-Digit (no regrouping)	2-Digit + 2-Digit (no regrouping)	Add Multiples of 10
2-digit + 1-digit Column Addition	2-digit Column Addition
3-digit + 2-digit Column Addition	3-digit Column Addition
2-digit + 1-digit (with regrouping)	2-Digit + 2-Digit (with regrouping)	3-Digit Addition

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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