# Complete the Pattern Worksheets

Having students determine missing sequences is a great way to engage them in the learning process. They, for the most part, will enjoy the detective-like nature of these problems. It often encourages them to have a heightened sense of dedication to these problems. These worksheets and lessons will help students learn how to spot missing sections of math patterns and have them complete them.

### Aligned Standard: 5.OA.B.3

- Filling In Patterns Step By Step Lesson- What is missing in these patterns?
- Filling in Patterns Guided Lesson - You will find single and double step applied math patterns in here.
- Filling in Patterns Guided Lesson Explanation - This one does take quite a bit of explaining.
- Filling Patterns Worksheet 1 - Starting here is a really good idea.
- Function Machine Practice 1 - The first one is completed for you as a guide.

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

### Two Rule Pattern Sheets

The first two involve double patterns. The last one focuses on identifying fixed patterns.

- Homework 1 - Find the difference or operations between successive boxes.
- Homework 2 - Since it follows a pattern, whatever operation was applied to the first number, must be applied to the second number too.
- Homework 3 - Identify the number pattern and fill in the missing numbers.

### Practice Worksheets

Complete the incomplete is the basic theme we have going here.

- Practice 2 - The best way to attack these types of problem is to look at what operation(s) is/are going on between successive integers.
- Practice 3 - We do have a lot to work off of here, because the first four integers are in succession.

### Math Skill Quizzes

The first two are basically a primer for the third quiz.

- Quiz 1 - If the values were to decrease, we would have thought subtraction and division.
- Quiz 2 - We can identify two sets of successive boxes.
- Quiz 3 - Fill in the missing number(s) in each function machine.

### How to Look for Patterns in Number Sequences

Have you ever played, "hangman?" The game where you have to fill the missing letters in the blanks until you guess the word completely? It is really fun to play, right? Well, similar to the game, math has a number series that goes on and on. The secret to filling the number in the sequence is to find the pattern that is being followed. Before we move on to find the pattern, it is important that you first know what sequence itself means. In math, the word sequence refers to a set of things, usually numbers that are presented in order. Every number in the sequence series is known as term, member, or element. The next step is to find what the pattern is, or what rule is being used in the given sequence.

For example; 3, 5, 7, 9, 11, 13, …

The dots at the end of the sequence indicate that the sequence is infinite. In the example, the pattern used is odd numbers. To find out the pattern, it is important that you thoroughly look at it. Just like this sequence, there are other sequences with patterns. You can solve them by paying attention; they are quite easy! Here is a basic approach that you use when trying to determine a mathematical pattern that may exist is a series of numbers or objects:

**Take a Step Back** - Start by looking at the pattern as a whole. What do you notice? Does the sequence increase or decrease in value? If so, this could indicate what type of math operators are at work here. Compare the starting values to the ending values in both directions left to right and right to left. Look at the difference between the values as they progress and fall.

**Look for Uniformity** - Patterns are built upon rules, use this to your advantage. There must be some form of unity in the pattern such as something that repeats or value increasing by a fixed value. Again, you will need to compare each of the data points to determine this.

**Think Exponentially** When you see a pattern that amplifies, or decays rapidly consider that there may be the use of squares or roots at work. Students often see patterns as being driven by counting or operators, but often sequences that have a great deal of scale often involve some form of exponential factor.