**Fact Family**

This Math video lesson is designed for 6-12 years old children to help them understand the concept of fact families, and how to create different expressions using fact family triangles.

**Fact Family Definition**

In mathematics, a fact family is a group of related facts that express the relation between the same set of numbers. Fact families, also known as “number families,” typically consist of three numbers and are used to teach the relationship between addition and subtraction or multiplication and division. The three numbers in a fact family are related to each other by simple arithmetic operations.

**Fact Family Triangle**

A fact family triangle is an essential graphic tool used in math education to help children understand the interrelatedness of mathematical concepts. It not only provides a visual aid for comprehending the relationship between addition and subtraction facts, and how multiplication and division facts are related. Fact family triangles also help children get better at solving problems and seeing patterns in numbers. By using this tool, students can gain a strong foundational understanding of math concepts that can be built upon as they progress through their academic careers.

This video lesson demonstrates how to form fact families using fact family triangles and perform mathematical operations of addition, subtraction, multiplication, and division. This method paves the way for a fun and creative method of learning and practicing different mathematical operations using the same set of numbers.

**Types of Fact Families**

There are two types of fact families:

- Addition and Subtraction Fact Family
- Multiplication and Subtraction Fact Family

**Addition and Subtraction Fact Family**

In an addition and subtraction fact family, three numbers are related to each other by two addition and two subtraction relationships.

For example, the numbers 2, 4, and 6 can form a fact family because:

- 2 + 4 = 6
- 4 + 2 = 6
- 6 – 2 = 4
- 6 – 4 = 2

In this case, we can see that 2 and 4 are called the “addends,” and 6 is the “sum.” The two subtraction sentences show the relationship between the addends and the sum. In general, the two numbers being added are called addends, and the result of the addition is called the sum. Similarly, the two numbers being subtracted are called the minuend and the subtrahend, and the result of the subtraction is called the difference.

**Multiplication and Division Fact Family**

In a multiplication and division fact family, the three numbers are related to each other by two multiplication and two division relationships. For example, the numbers 2, 4, and 8 can form a fact family because:

- 2 x 4 = 8
- 4 x 2 = 8
- 8 ÷ 2 = 4
- 8 ÷ 4 = 2

In this case, we can see that 2 and 4 are referred to as the “factors,” while 8 is called the “product.” The two division sentences illustrate the relationship between the factors and the product.

**Fun Facts about Fact Families:**

- Increases the understanding of the Inverse Relationship between Operations
- Helps to understand the Commutative Property

**Fact Family Examples**

Fact family of numbers 5, 10, and 15 are:

- 5+10 = 15
- 10+5 = 15
- 15-5 = 10
- 15-10 = 5

Fact Family of numbers 5, 10, and 50 are

- 5×10 = 50
- 10×5 = 50
- 50÷5 = 10
- 50÷10 = 50

**5 Advantages of Learning Fact Families**

- It helps children understand the relationship between addition, subtraction, multiplication, and division, making it easier for them to perform mathematical operations.
- It provides a visual representation of the relationships between numbers and operations, which can help children learn and remember math facts.
- Understanding math fact families can help children develop critical thinking and problem-solving skills, as they learn to apply their knowledge of basic arithmetic to solve more complex problems.
- Learning fact families can help children develop a deeper understanding of numbers and their properties, which can help them as they progress through their academic careers.
- By mastering fact families, children can develop a sense of confidence and competence in mathematics, which can help them in other areas of their lives, both academic and personal.

**Fun Activities Related to Fact Families**

Here are some activities related to fact families:

- Use a fact family triangle to demonstrate how addition and subtraction are related. Have students fill in the missing numbers for different fact families.
- Create flashcards with fact families on them. Have students match the addition and subtraction or multiplication and division sentences that belong to the same family.
- Write a word problem that involves a fact family and have students solve it. For example: “John had 4 apples. He gave 2 to his friend. How many apples does John have now?” This problem involves the fact family 2, 4, and 6.
- Have students create their own fact families by choosing three numbers and writing the addition, subtraction, multiplication, and division sentences that belong to that family.
- Play a game of Fact Family Bingo. Create bingo cards with different fact families on them. Call out the numbers, and students mark the corresponding fact family on their card.

Overall, fact families are a crucial concept in mathematics, and they help children develop a solid foundation for understanding arithmetic. By understanding the relationships between numbers and operations, children can build their math skills and confidence, and apply their knowledge to solve real-world problems.

Watch the video to learn more about fact families and build a strong foundation in arithmetic to solve more complex problems.

## Related Video Resources

- Addition and subtraction of squares and cubes
- Notation of squares
- Notation of cubes
- How to find factors of a number

To watch more math video resources, click here.

Video Created by: Maddy Taylor

**FAQs**

**What is a fact family 3 numbers?**

A fact family with 3 numbers consists of three related mathematical facts that involve addition and subtraction, such as 2+3=5, 3+2=5, and 5-3=2.

**What are fact families called?**

Fact families are also known as number families or addition and subtraction families. They are a set of related addition and subtraction facts that use the same numbers.

**What are the 4 fact families?**

There are four fact families: addition, subtraction, multiplication, and division. For example, the fact families for addition and subtraction involving the numbers 3, 4, and 7 are as follows 3 + 4 = 7, 4 + 3 = 7, 7 – 4 = 3, and 7 – 3 = 4. Similarly, the fact families for multiplication and division involving the numbers 3, 4, and 12 are as follows: 3 x 4 = 12, 4 x 3 = 12, 12 ÷ 3 = 4, and 12 ÷ 4 = 3.

**Why teach fact families?**

Fact families are essential in teaching arithmetic because they help children understand how numbers are related and how different operations are related. Fact families provide a visual representation of the relationships between numbers and operations, making it easier for children to learn and remember math facts. By seeing how different operations are related, children can develop a deeper understanding of arithmetic and apply their knowledge to solve more complex problems.

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