What is a Fact Family for 8?

S0-SA1-1309

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A fact family for a number like 8 is a group of related addition and subtraction sentences that use the same three numbers. These numbers show how addition and subtraction are opposite operations. For example, if you have 3, 5, and 8, they form a fact family.

Simple Example

Quick Example

Imagine you have 8 ladoos. You eat 3 ladoos, so 5 are left. This shows 8 - 3 = 5. You also know that if you had 3 ladoos and someone gave you 5 more, you would have 3 + 5 = 8 ladoos. All these are part of the fact family for 8.

Worked Example

Step-by-Step

Let's find the fact family for 8 using the numbers 2, 6, and 8.

1. First, write the addition sentences. We know 2 + 6 = 8.
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2. Next, reverse the order of the first two numbers: 6 + 2 = 8.
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3. Now, write the subtraction sentences. Start with the largest number, 8. If we take away one of the smaller numbers, we get the other. So, 8 - 2 = 6.
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4. Finally, subtract the other smaller number: 8 - 6 = 2.
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So, the fact family for 8 using 2, 6, and 8 is: 2 + 6 = 8, 6 + 2 = 8, 8 - 2 = 6, and 8 - 6 = 2.

Why It Matters

Understanding fact families helps you learn addition and subtraction facts much faster, like knowing your multiplication tables. This skill is crucial for solving daily math problems, from calculating change at a shop to managing your pocket money. It's used by shopkeepers, accountants, and even software engineers who work with numbers.

Common Mistakes

MISTAKE: Using four different numbers in the family, like 2, 3, 5, and 8. | CORRECTION: A fact family always uses only THREE numbers. Two smaller numbers and their sum (the largest number).

MISTAKE: Writing only addition sentences or only subtraction sentences. | CORRECTION: A complete fact family for a given set of three numbers will always have two addition sentences and two subtraction sentences (unless the two smaller numbers are the same, like 4, 4, 8).

MISTAKE: Forgetting to start subtraction sentences with the largest number. For example, writing 2 - 8 = 6. | CORRECTION: In subtraction, always start with the largest number (the sum) and subtract one of the smaller numbers to get the other.

Practice Questions

Try It Yourself

QUESTION: What are the two addition sentences for the fact family using numbers 1, 7, and 8? | ANSWER: 1 + 7 = 8 and 7 + 1 = 8

QUESTION: Complete the fact family for 8 using the numbers 3, 5, and 8. You have: 3 + 5 = 8, 5 + 3 = 8. What are the two subtraction sentences? | ANSWER: 8 - 3 = 5 and 8 - 5 = 3

QUESTION: If a fact family for 8 uses the numbers 4, 4, and 8, how many unique sentences will there be? List them. | ANSWER: There will be 2 unique sentences. They are: 4 + 4 = 8 and 8 - 4 = 4.

MCQ

Quick Quiz

Which set of sentences is a complete fact family for 8 using the numbers 2, 6, and 8?

2 + 6 = 8, 8 - 2 = 6

2 + 6 = 8, 6 + 2 = 8, 8 - 2 = 6, 8 - 6 = 2

2 + 6 = 8, 6 - 2 = 4, 8 - 6 = 2

8 + 2 = 10, 8 - 6 = 2

The Correct Answer Is:

Option B correctly lists all four sentences (two addition and two subtraction) that use only the numbers 2, 6, and 8. Options A, C, and D are incomplete or use incorrect operations/numbers.

Real World Connection

In the Real World

When you are sharing a packet of 8 biscuits with your friend, and you take 3, your friend gets 5. This is 8 - 3 = 5. If you combine your 3 biscuits and your friend's 5, you get 8 again (3 + 5 = 8). This simple everyday sharing and combining is a real-world example of a fact family.

Key Vocabulary

Key Terms

FACT FAMILY: A group of related addition and subtraction sentences using the same three numbers. | ADDITION: Combining two or more numbers to find their total sum. | SUBTRACTION: Taking one number away from another to find the difference. | SUM: The result of adding two or more numbers. | DIFFERENCE: The result of subtracting one number from another.

What's Next

What to Learn Next

Great job understanding fact families! Now that you know how addition and subtraction are linked, you can explore fact families for multiplication and division. This will help you see how those operations are also related and make learning times tables much easier.