## Arithmetic Patterns and Systems

#### Aligned To Common Core Standard:

**Grade 3 Operations** - 3.OA.9

How to Identify Arithmetic Patterns or Systems In Data Sets?
Number pattern is a sequence or series of numbers where two consecutive numbers are linked through a mathematical relationship. In numbers and sequencing, the arithmetic patterns and systems are the simplest forms. It is a pattern that is formed using simple addition and subtraction. There is a common difference, "d" between two consecutive numbers in an arithmetic pattern.
Identifying an arithmetic pattern within a data set can get tricky, but these simple tools can make it very simple and easy.
**Hundreds Chart** - The hundreds chart comprises of 10 rows and 10 columns and counts from 1 to 100. The chart helps in finding out the common difference between two consecutive terms of a pattern. You can use the chart vertically, horizontally, and even diagonally to identify patterns.
**Addition Chart**- The addition chart is another very helpful tool to identify arithmetic patterns in a data set. There are three principles of addition that we can clearly see in an addition chart are;
- The sum of two even numbers is always even
- The sum of two odd numbers is always even
- The sum of an odd and an even number is always odd
**Number Line**- The number line is the last and a very useful tool in identifying number patterns. It uses "terms" and not common differences to identify a pattern in a data set.
Students learn how to find patterns in data through the help of these worksheets.

### Printable Worksheets And Lessons

- Input, Output Step-by-step
Lesson- We give you an add 15 rule and ask you to complete the
chart.

- Guided Lesson
- 3 rules that include differences, products, and quotients.

- Guided Lesson Explanation
- Every step is plotted out for you on this one.

- Practice Worksheet
- 10 input, output charts with a varied mix of operations and rules.

- Matching Worksheet
- Find 3 and you can solve the whole thing.

#### Homework Sheets

The first set requires you to explain the pattern and the second is looking for the outcomes.

- Homework 1- Explain the rule to the patterns below.
- Homework 2- Debby practices her free throws. Every day she takes 20 shots from the foul line. The table below shows how many shots she made.
- Homework 3- Complete missing segments of the input/output charts.

#### Practice Worksheets

We mix in the input/output charts. We get a lot of requests for those.

- Practice 1- Based on the rule that is provided; write the next 4 numbers in the pattern.
- Practice 2- Write the next 3 numbers of the pattern and state the rule.
- Practice 3- For each pattern below describe the rule in place.