Using Input-Output Tables
Using Input-Output Tables is a Grade 4 math skill in enVision Mathematics, Chapter 14: Algebra: Generate and Analyze Patterns. Students analyze input-output tables to identify the rule relating inputs to outputs and use that rule to find missing values and extend patterns.
Key Concepts
An input output table organizes pairs of numbers that are related by a rule. The 'input' is the number you start with, and the 'output' is the result after applying the rule. We often use variables like $x$ for the input and $y$ for the output.
$$ \begin{array}{|c|c|} \hline \textbf{Input (x)} & \textbf{Output (y)} \\ \hline \text{value 1} & \text{value 1} \\ \hline \text{value 2} & \text{value 2} \\ \hline \end{array} $$.
Common Questions
What is an input-output table?
An input-output table shows pairs of values where each output is determined by applying the same rule to each input. You can use known pairs to discover the rule and find missing values.
How do you find the rule in an input-output table?
Look for what operation is applied to each input to produce the output. Check that the same operation works for all given pairs. The rule may be adding, subtracting, multiplying, or dividing a fixed number.
How do you use a rule to complete an input-output table?
Once you identify the rule, apply it to each missing input to find the corresponding output, or reverse the rule to find a missing input given its output.
What is an example of an input-output table?
Input: 3, 5, 7. Output: 12, 20, 28. The rule is multiply by 4. For input 9, output equals 9 times 4 equals 36.
What chapter covers input-output tables in enVision Grade 4?
Using input-output tables is covered in Chapter 14: Algebra: Generate and Analyze Patterns in enVision Mathematics Grade 4.