# Math Rules and Patterns Worksheets

Math patterns are created or explained based on formula or rule that is applied to all the data in a string of numbers. There are generally two different types of numerical patterns. Ascending patterns increase in value as they go from left to right. Ascending patterns often involve addition and/or multiplication operations. Descending patterns go in the other direction, decrease from left to right. As you would guess, these rules generally involve either subtraction, division, or both of these. These worksheets will help students develop skills to help them sniff out patterns and rules with in equation, operations, or data sets. We start out with most basic forms of these, but they begin to get more complex as you move on to homework sheets and quizzes.

### Aligned Standard: Grade 4 Operations - 4.OA.5

- Pattern Fill Step-by-Step Lesson- Complete the patterns.
- Guided Lesson - Fill in the missing arrow, number, letter what ever. Then break into using math table rules.
- Guided Lesson Explanation - I know I'm a little weak on the directions for the first one. I'll get it right on the rebound.
- Practice Worksheet - 10 math patterns all with missing pieces that you need to fill.
- Matching Worksheet - Match the pattern to the next piece of the pattern.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Each is drastically different in premise. Fill in the missing numbers to the pattern. Fill in the missing shapes. You will finish off with operations based patterns.

- Missing #s Homework - Write the numbers that are missing from the pattern.
- Shapes Homework 2 - Fill in the missing parts of pattern.
- Operations Homework 3 - That means that we multiply the number by 3 and then add 2 to that number.

### Practice Worksheets

We give you set functions and ask you to complete them. Use the equation based rules to solve the patterns.

- Functions Practice 1 - Complete the table by using the function.
- Equations Practice 2 - Write the next number by following the rule. Rule: - multiply by 2 then add 8.
- Complete Practice 3 - Find the final value of the following problem.

### Math Skill Quizzes

We cover each skill in each quiz. Missing or incomplete patterns, using functions, and missing shapes patterns.

- Incomplete Quiz 1- Write the missing numbers for the patterns.
- Functions Quiz 2 - Complete the table by using the function.
- Shapes Quiz 3 - Fill in the missing parts of pattern.

### What Are Math Rules and Patterns?

To have a strong understanding of a rule, there needs to be a sequence. A sequence is a set of numbers in a particular order, and in math, a rule tells us what operation or set of operations are needed to be performed on a sequence to get the indicated outcomes. For instance, adding to, dividing by 6, these are commonly used rules in math that are used for particular patterns. Let's try learning this with an example.

**Example** What is the rule that applies in this string of data? - 103, 140, 177, 214.

We need to identify a pattern in each and then use the pattern to make a rule. If we look at the numbers in the example, we can immediately identify that the numbers are increasing, which means they are either being added, multiplied, or a combination of both. You first instinct should be always be to look at the data set as a whole and see if there is an increase or decrease in the value as you move from left to right.

Let's try doing some addition, i.e., trying to add a number in the first number that can bring the number next to it.

103 + 37 = 140

140 + 37 = 177

177 + 37 = 214

As we are adding the same number, this means we have an additional pattern. So, let's make a rule for this pattern. Rule: Add 37 to get to the next number.