Easy guide to filling in input output tables in 4th grade math.

📚 Understanding Input-Output Tables

Input-output tables, also known as function machines or 'what's my rule' tables, are a way to show how a mathematical rule changes a number. Think of it like a vending machine: you put something in (input), the machine does something (rule), and you get something out (output)!

📜 A Little History

While the specific term 'input-output table' might be relatively recent, the concept of functions has been around for centuries. Mathematicians have always been interested in how one quantity relates to another. These tables provide a simple and visual way to explore those relationships, especially for young learners.

🔑 Key Principles

• ➡️ Input: The number that goes into the function. Think of it as the starting number.
• ⚙️ Rule: The mathematical operation (addition, subtraction, multiplication, or division) that is applied to the input.
• ⬅️ Output: The number that comes out of the function after the rule has been applied. It's the result!

➕ Addition Examples

Let's say our rule is '$+ 3$'.

➖ Subtraction Examples

What if our rule is '$- 2$'?

✖️ Multiplication Examples

Let's use the rule '$\times 4$'

➗ Division Examples

Now, let's try the rule '$\div 2$'

🌍 Real-World Examples

• 🍪 Baking Cookies: Input: Number of eggs. Rule: Multiply by 12. Output: Number of cookies.
• 🍕 Pizza Slices: Input: Number of pizzas. Rule: Multiply by 8. Output: Number of slices.
• 🚌 School Buses: Input: Number of buses. Rule: Multiply by 30. Output: Number of students.

💡 Tips and Tricks

• 🧩 Start Simple: Begin with addition and subtraction before moving to multiplication and division.
• 🔍 Look for Patterns: Sometimes, you can figure out the rule by looking at how the input changes to the output.
• ✍️ Use Scratch Paper: Don't be afraid to write down your calculations!

📝 Practice Quiz

Complete the following input-output tables:

1. Rule: $+ 5$

   Input	Output
   2
   4
   6

2. Rule: $- 3$

   Input	Output
   8
   10
   12

3. Rule: $\times 3$

   Input	Output
   2
   3
   4

4. Rule: $\div 3$

   Input	Output
   9
   12
   15

5. Rule: $+ 10$

   Input	Output
   5
   10
   15

6. Rule: $- 5$

   Input	Output
   15
   20
   25

7. Rule: $\times 5$

   Input	Output
   2
   4
   6

✅ Conclusion

Input-output tables are a fantastic way to understand how mathematical rules work! With a little practice, you'll be solving them like a pro. Keep exploring and have fun with math!