What is a Fact Family for 13?

S0-SA1-1312

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A fact family for a number like 13 is a group of four related math facts (two addition and two subtraction) that use the same three numbers. These three numbers show how they are connected through addition and subtraction operations.

Simple Example

Quick Example

Imagine you have 5 cricket balls and your friend gives you 8 more. You now have 13 balls. This gives us 5 + 8 = 13. From this, we can also say 8 + 5 = 13. If you started with 13 balls and gave 5 away, you'd have 8 left (13 - 5 = 8). If you gave 8 away, you'd have 5 left (13 - 8 = 5). The numbers 5, 8, and 13 form a fact family!

Worked Example

Step-by-Step

Let's find the fact family for 13 using the numbers 6 and 7.

1. Identify the three numbers: Our target number is 13, and the two parts that add up to it are 6 and 7.
---2. Write the first addition fact: Add the two smaller numbers to get the largest number. So, 6 + 7 = 13.
---3. Write the second addition fact: Reverse the order of the two smaller numbers. So, 7 + 6 = 13.
---4. Write the first subtraction fact: Start with the largest number and subtract one of the smaller numbers. So, 13 - 6 = 7.
---5. Write the second subtraction fact: Start with the largest number and subtract the other smaller number. So, 13 - 7 = 6.

Answer: The fact family for 13 using 6 and 7 is: 6 + 7 = 13, 7 + 6 = 13, 13 - 6 = 7, and 13 - 7 = 6.

Why It Matters

Understanding fact families helps you see the relationship between addition and subtraction, which is super useful for quick mental math and solving problems. This skill is key in fields like finance for balancing accounts, engineering for calculating forces, and even in daily budgeting to manage your pocket money.

Common Mistakes

MISTAKE: Using only two numbers instead of three to form the family. For example, writing 5 + 8 = 13 and 8 + 5 = 13, but then forgetting the subtraction facts. | CORRECTION: Remember that a fact family always has three numbers and includes both addition and subtraction.

MISTAKE: Not starting subtraction facts with the largest number. For example, writing 6 - 13 = 7. | CORRECTION: In subtraction for fact families, always start with the largest number (the sum) and subtract one of the smaller numbers.

MISTAKE: Mixing up the numbers in the subtraction facts. For example, for 5, 8, 13, writing 13 - 5 = 5. | CORRECTION: After subtracting one number from the total, the answer should be the *other* number from the family. So, 13 - 5 = 8.

Practice Questions

Try It Yourself

QUESTION: Write the fact family for 13 using the numbers 4 and 9. | ANSWER: 4 + 9 = 13, 9 + 4 = 13, 13 - 4 = 9, 13 - 9 = 4

QUESTION: If a shopkeeper sold 13 samosas in total, and 10 were potato samosas, how many were paneer samosas? Write the complete fact family for this situation. | ANSWER: The numbers are 10, 3, and 13. Fact family: 10 + 3 = 13, 3 + 10 = 13, 13 - 10 = 3, 13 - 3 = 10. (So, 3 paneer samosas)

QUESTION: A bus has 13 seats. If 5 seats are empty, how many passengers are there? Form the fact family for this. What if 8 seats were empty instead? | ANSWER: For 5 empty seats: Numbers are 5, 8, 13. Fact family: 5 + 8 = 13, 8 + 5 = 13, 13 - 5 = 8, 13 - 8 = 5. So, 8 passengers. | For 8 empty seats: Numbers are 8, 5, 13. Fact family: 8 + 5 = 13, 5 + 8 = 13, 13 - 8 = 5, 13 - 5 = 8. So, 5 passengers.

MCQ

Quick Quiz

Which set of facts is NOT part of the fact family for 13, using the numbers 3, 10, and 13?

3 + 10 = 13

10 + 3 = 13

13 - 3 = 10

13 + 3 = 16

The Correct Answer Is:

Options A, B, and C are correct facts within the family of 3, 10, and 13. Option D (13 + 3 = 16) is an addition fact but it does not use only the numbers 3, 10, and 13.

Real World Connection

In the Real World

Fact families are like understanding how money works. If you have 13 rupees and spend 5 rupees on a chai, you know you have 8 rupees left. You also know that 5 rupees (chai) + 8 rupees (leftover) equals your original 13 rupees. This simple concept helps you manage your daily expenses and savings, just like how shopkeepers calculate change.

Key Vocabulary

Key Terms

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

What's Next

What to Learn Next

Once you're comfortable with fact families for smaller numbers, you can move on to larger numbers and even multiplication and division fact families. This will strengthen your number sense and make solving more complex math problems much easier!