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Patterns and Sequence Worksheets

What is the Difference Between a Pattern and a Sequence? Two terms that we come across very frequently in our lives is pattern and sequence. Whether its bioscience, computer science, mathematics, or daily life, we very commonly use these terms, mostly interchangeably. However, the question that arises is whether these two terms are the same or not. Well, these terms are not the same and cannot be used interchangeably. When one event repeats itself in a particular manner, we refer to this phenomenon as a pattern. It comprises of elements that predictably repeat themselves. It is not well defined but can be used to establish a sequence. Sequence, unlike a pattern, is well defined using mathematical formula. It is a string of organized elements, an increasing/decreasing order and is established on a pattern. There are two categories of sequences including finite and infinite. There are different types of mathematical number sequences that you will come across including arithmetic, geometric, and harmonic. You will find a huge mix of skill levels here. If you can think up any sub-topics that we are missing here, just let us know.


  • Arithmetic Patterns and Systems - We would classify these as having a moderate level of difficulty. This skill helps us to transition to working with functions and creating our own.
  • Consecutive Numbers - These are two or more numbers that are in proper sequential order. It is important to understand their role in numeracy.
  • Counting Patterns - They can be straight counts or skip counts. This is a fundamental skill that helps us learn to analyze more complex systems of numbers.
  • Creating and Breaking Down Math Patterns - This gives you a strategy to start using and applying to problems. These are steps that are fundamental to cracking any coded message or transmission.
  • Explicit Expressions and Recursive Processes - These are helpful for students that are begging to work with abstract and system-based math forms. One transmits a clear and concise series of directions for you. The other is much more round about.
  • Function and Chart Patterns - Students see how to find patterns in input-output functions as well as spotting similarities in data patterns. This will help you not only learn how to analyze them, but how to manipulate them for your own applications.
  • Generating Math Patterns From Rules - You are basically asked to act like a computer program. Given a rule, generate data. You will learn how to compose these yourself and influence those that have already been created for you.
  • Halfway - This is usually a good jump off point. It also helps you display trends that you may have noticed along the way.
  • Identifying and Complete Math Patterns - These are mostly unfinished. You are tasked with completing them.
  • Math Patterns on Number Lines - This makes it a little easier to clearly spot them.
  • Math Rules and Patterns - These are slightly complex and start out simple and advance to moderate problems.
  • Mixed Skip Counting - This is great practice for this topic. While it does not directly relate, the skills involved with indirectly effect your ability to understand most of these topics.
  • Patterns of Association (Using Data Tables) - We are tasked with asking our self how this value affects the next value and the value before it. It is all about being able to understand data and rearranging it to help us understand trends. We then can use this data to make smart decisions.
  • Pre-Algebraic Number Sequences and Patterns - We are almost on to full blown equations. This may confuse students who do not have a pre algebra background. Just do a quick review.
  • Relating Counting to Addition and Subtraction - If you think about it, these skills apply to all non-algebraic types of sequences we come across. This is usually the first pattern that most cryptographers attempt to spot.
  • Skip Counting By 2s - Make for good practice prior to working on the more advanced sheets.
  • Skip Counting By 3s - Just one more than the last series.
  • Skip Counting By 5s - Two more than the last series of sheets, but three more than the other set.
  • Skip Counting to 1000 (5s, 10s, 100s) - This cranks up the counting and we go to a pretty large end value.
  • Sudoku Math Patterns - The name of this puzzle game comes from the Japanese words for "single number". Once you get a hang of these, you will see how it is all about the sequence.
  • Understanding Numeric Patterns - This is a basic introduction to the skills we will be learning in this topic. We show you how to make sense of these types of problems.
  • Variable Expressions and Sequences - Expressions give students a little bit of trouble at first and then they can move forward on sequences. The expressions help us model a situation with math.
  • Visual Math Pattern - This is a great way to model this skill for students. This skill has a ton of applications in your daily life.
  • Writing Expressions for Geometric Sequences - These are sequences that involve normally multiplying by a consonant. The scientific and financial communities uses geometric sequences to model many different phenomena.