Analyze patterns and relationships.

Standard: 5.OA.B.3

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Learning Outcomes

Recognize how one variable depends on another using rules or equations.
Use the rule (add 10 to x to find y) to generate values in a two-variable table.
Create ordered pairs from the x and y values in the table.
Plot points based on ordered pairs and observe the resulting pattern.
Describe the relationship between two variables and identify how changing one affects the other.
Gain a deeper understanding of relationships in data, preparing for more advanced concepts like functions and equations.
Recognize and describe the pattern formed by plotted points, understanding how the graph visually represents the relationship between x and y.
Use the established rule to predict new y values when given additional x values, reinforcing the concept of consistent relationships in variable pairs.

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Definition

A variable relationship is a connection between two variables (like x and y) where one variable depends on the other based on a specific rule or equation. This relationship helps us see how changing one value affects the other.

In this worksheet, the rule given is: To find y, add 10 to x.

Description

This rule tells us that each value of y is found by taking the value of x and adding 10 to it. This means that y depends on x and increases as x increases.

For example:

When x = 2, adding 10 gives y = 12.
When x = 3, adding 10 gives y = 13.
When x = 4, adding 10 gives y = 14.
When x = 5, adding 10 gives y = 15.

Using this table, we can form ordered pairs like (2, 12), (3, 13), etc. When we plot these points on a graph, they show a pattern, allowing us to visualize the relationship between x and y.

Why This Matters
Understanding variable relationships helps us work with patterns, make predictions, and understand how data behaves. It’s a fundamental concept in math that prepares us for working with functions and equations in more advanced math.

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