What is a Number Family (of 4)?

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Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A Number Family (of 4) shows how three numbers are related through addition and subtraction. It means these three numbers can be used to create two addition facts and two subtraction facts. Think of it like a small family where everyone is connected!

Simple Example

Quick Example

Imagine you have 5 cricket balls, and your friend gives you 3 more. Now you have 8 balls. This creates a number family: 5, 3, and 8. You can add 5 + 3 = 8, or subtract 8 - 3 = 5, or even 8 - 5 = 3.

Worked Example

Step-by-Step

Let's find the number family for the numbers 4, 6, and 10.

Step 1: Identify the three numbers in the family. Here, they are 4, 6, and 10.

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Step 2: Find the two addition facts. Remember, the two smaller numbers add up to the largest number.
4 + 6 = 10
6 + 4 = 10

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Step 3: Find the two subtraction facts. The largest number is always at the beginning of a subtraction fact in this family.
10 - 6 = 4
10 - 4 = 6

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So, the number family for 4, 6, and 10 is: 4 + 6 = 10, 6 + 4 = 10, 10 - 6 = 4, and 10 - 4 = 6.

Why It Matters

Understanding number families helps you solve math problems faster and makes mental calculations easier. It's a foundational skill for algebra and problem-solving. Engineers use these relationships to balance equations, and data analysts use them to understand how different numbers connect.

Common Mistakes

MISTAKE: Using numbers that don't belong in the family, e.g., for 2, 3, 5, writing 2 + 4 = 6 | CORRECTION: Always use only the three specific numbers given for the family. In this case, 2, 3, and 5.

MISTAKE: Mixing up addition and subtraction, e.g., for 7, 2, 9, writing 7 - 2 = 9 | CORRECTION: Remember that the two smaller numbers add up to the largest, and subtraction always starts with the largest number.

MISTAKE: Forgetting one of the four facts, e.g., only writing 3 + 5 = 8 and 8 - 5 = 3 for the family 3, 5, 8 | CORRECTION: Always ensure you write down two addition facts and two subtraction facts for a complete number family.

Practice Questions

Try It Yourself

QUESTION: Write the complete number family for the numbers 5, 2, and 7. | ANSWER: 5 + 2 = 7, 2 + 5 = 7, 7 - 2 = 5, 7 - 5 = 2

QUESTION: If a number family includes 8 and 15, what is the third number, and what are all the facts? | ANSWER: The third number is 7. The facts are: 8 + 7 = 15, 7 + 8 = 15, 15 - 7 = 8, 15 - 8 = 7.

QUESTION: A chaiwala sells 12 cups of chai in the morning and some more in the afternoon. By evening, he sold a total of 20 cups. What is the number family for this situation, and how many cups did he sell in the afternoon? | ANSWER: The numbers are 12, 8, and 20. The family is: 12 + 8 = 20, 8 + 12 = 20, 20 - 8 = 12, 20 - 12 = 8. He sold 8 cups in the afternoon.

MCQ

Quick Quiz

Which set of facts forms a complete number family for the numbers 6, 3, and 9?

6 + 3 = 9, 9 - 3 = 6

6 + 3 = 9, 3 + 6 = 9, 9 - 6 = 3, 9 - 3 = 6

6 + 3 = 9, 9 - 6 = 3, 3 - 6 = 9

6 + 9 = 3, 9 - 3 = 6, 3 + 6 = 9

The Correct Answer Is:

Option B correctly shows two addition facts (6+3=9, 3+6=9) and two subtraction facts (9-6=3, 9-3=6) using only the numbers 6, 3, and 9. Other options are incomplete or incorrect.

Real World Connection

In the Real World

When you manage your pocket money, if you have 50 rupees, spend 20 rupees on a snack, and are left with 30 rupees, that's a number family (50, 20, 30) in action. It helps you quickly calculate how much you spent or how much you started with.

Key Vocabulary

Key Terms

ADDITION: Combining two or more numbers to find a total | SUBTRACTION: Taking one number away from another to find the difference | NUMBER FACT: A basic arithmetic equation (like 2+3=5) | RELATIONSHIP: How different numbers or things are connected

What's Next

What to Learn Next

Great job learning about number families! Next, you can explore 'Fact Families with Multiplication and Division.' This will show you how numbers are related through multiplying and dividing, building on what you've learned here.