What is a Number Family?

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Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A Number Family is a group of three numbers that are related to each other through addition and subtraction. Think of it like a small family where two 'smaller' numbers add up to make one 'bigger' number, and then you can use these same three numbers to do subtraction too.

Simple Example

Quick Example

Imagine you have 3 cricket balls and your friend gives you 2 more. Now you have 5 cricket balls in total. Here, the numbers 3, 2, and 5 form a number family because 3 + 2 = 5. You can also say 5 - 3 = 2 and 5 - 2 = 3.

Worked Example

Step-by-Step

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

Step 1: Identify the two smaller numbers and the one larger number. Here, 4 and 6 are smaller, and 10 is larger.

Step 2: Write the addition facts. The two smaller numbers add up to the larger number. So, 4 + 6 = 10.

Step 3: Write the other addition fact by swapping the smaller numbers. So, 6 + 4 = 10.

Step 4: Write the first subtraction fact. Start with the larger number and subtract one of the smaller numbers to get the other smaller number. So, 10 - 4 = 6.

Step 5: Write the second subtraction fact. Again, start with the larger number and subtract the other smaller number. So, 10 - 6 = 4.

Answer: The number family for 4, 6, and 10 includes: 4 + 6 = 10, 6 + 4 = 10, 10 - 4 = 6, and 10 - 6 = 4.

Why It Matters

Understanding number families helps you solve addition and subtraction problems faster and check your answers easily. This basic idea is crucial for understanding more complex math later, like algebra and solving equations. It's used by shopkeepers calculating change, or even engineers designing bridges.

Common Mistakes

MISTAKE: Using numbers that are not related. For example, saying 2, 3, and 6 form a family because 2 + 3 = 5, which is not 6. | CORRECTION: Always ensure the two smaller numbers add up exactly to the larger number.

MISTAKE: Only writing addition facts and forgetting subtraction. For example, for 7, 3, 10, only writing 7 + 3 = 10. | CORRECTION: Remember that a number family includes two addition facts and two subtraction facts using the same three numbers.

MISTAKE: Subtracting a larger number from a smaller number within the family. For example, for 5, 2, 7, writing 2 - 5 = ? | CORRECTION: In subtraction facts for a number family, you always start with the largest number.

Practice Questions

Try It Yourself

QUESTION: What are the four facts in the number family for 5, 4, and 9? | ANSWER: 5 + 4 = 9, 4 + 5 = 9, 9 - 5 = 4, 9 - 4 = 5

QUESTION: If 8 + 7 = 15, what are the other three facts in this number family? | ANSWER: 7 + 8 = 15, 15 - 8 = 7, 15 - 7 = 8

QUESTION: My auto-rickshaw fare was Rs 12. My friend's fare was Rs 8. Together, we spent Rs 20. Write all four facts for this number family. | ANSWER: 12 + 8 = 20, 8 + 12 = 20, 20 - 12 = 8, 20 - 8 = 12

MCQ

Quick Quiz

Which set of numbers forms a number family?

2008-06-03T00:00:00.000Z

2010-05-05T00:00:00.000Z

2010-04-07T00:00:00.000Z

2012-02-09T00:00:00.000Z

The Correct Answer Is:

Option B (5, 5, 10) is correct because 5 + 5 = 10. For other options, the two smaller numbers do not add up to the largest number.

Real World Connection

In the Real World

When you're at a local kirana store and buy two items, say for Rs 25 and Rs 15, the shopkeeper quickly calculates the total as Rs 40. Then, if you pay with a Rs 50 note, they know to give you Rs 10 back (50 - 40 = 10). This quick mental math uses number family concepts every day!

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 | FACT FAMILY: Another name for a number family, showing related math facts | 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 learning about number families! Next, you can explore 'Fact Families with Multiplication and Division'. This builds on the same idea but uses multiplication and division instead of addition and subtraction, helping you see even more connections between numbers.