The worksheet titled "Completing Patterns and Writing the Rule: Letters, Numbers, Fractions, and Decimals" challenges students to complete patterns and discover the rules for each pattern in a wide range of situations.

The worksheet starts simple with letter and single-digit number patterns, including addition patterns. Later, patterns display a series of numbers in boxes, and students fill in the blank boxes. Eventually, students complete the pattern for fractions, large numbers, and even decimals.

In some cases, students must complete multiple patterns using the same rule. Sometimes, they get a hint, like looking at the movement of digits in a series of large numbers. Every set of patterns has space underneath where students must describe the rule they have discovered.

Learning patterns help students develop logical thinking skills and improve prediction and problem-solving abilities. It can also form the foundation for algebraic thinking, which is important at higher grade levels.

To support pattern learning, students should be exposed to patterns of increasing difficulty at the appropriate grade level. For example, very young students can decipher simple patterns with pictures or letters. As they get good at that, they can discover the missing numbers in an addition pattern. Older students can solve patterns in unique configurations, like filling in a grid of boxes. Upper elementary students can be challenged by finding the missing fractions or decimals in a series.

No matter how old, students should always be encouraged to write the rule for each pattern. They could even be asked to draw a pattern of their own that follows the same rule, which helps cement the concept that many different types of patterns can follow the same rule.