# Possible Values

## Worksheet Description

This worksheet is a set of problems centered on the application of divisibility rules for the numbers 3 and 9. Each problem presents a partially written number with a missing digit, represented by the letter ‘a’, and asks students to find all possible values of ‘a’ that make the number divisible by either 3 or 9. Students are required to not only determine the values of ‘a’ but also to write the complete number that results from each possible value of ‘a’. The worksheet combines the understanding of divisibility rules with basic algebraic substitution.

The worksheet is designed to teach students the more nuanced aspects of divisibility rules, specifically how to apply them in situations where a number is incomplete and a specific digit must be found to meet a divisibility condition. It encourages students to use critical thinking and problem-solving skills to explore the relationship between individual digits and the overall divisibility of a number. By working through these problems, students learn to manipulate and consider numbers in parts and wholes, an important skill in number theory. Additionally, this type of problem introduces foundational algebraic thinking by having students solve for an unknown in the context of arithmetic rules.