# Arithmetic Patterns Worksheets

This is often the first experience students have with making sense of data sets. I like to present it in a puzzle form. This often motivates students and if you make them true to their own lives you with engage them and they will work hard to solve these types of exercises. At first, students will just see a list of numbers. As they progress, they will see that data is fluid and can be used to understand many different situations. I find that as students get confidence with this skill, they apply it to all types of math problems. Start with the very simplest of data sets, build a repour at this level. Start focusing on two consecutive integers and then build up to three and four. Once they can work with streams of four data points with success, then it is time to introduce the concept of patterns across a larger data set. Students learn how to find patterns in data through the help of these worksheets.

### Aligned Standard: Grade 3 Operations - 3.OA.9

- 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.

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

### 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 that are presented. You will also build your own tables.
- 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. This is a great skill to have.

### 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- You will need to breakdown a data set and understand what is happening at each stage.

### Math Skill Quizzes

The quizzes will look for you to determine the patterned rule among other things.

- Quiz 1- Complete the input/output charts based on the rules that are given to you.
- Quiz 2- Fill in the missing numbers and name the rule for each pattern.

### How to Identify Arithmetic Patterns or Systems in Data Sets

A number pattern is a sequence or series of numbers where two or more consecutive numbers are linked through a mathematical relationship. In basic number sets and sequences, the arithmetic patterns and systems are the simplest forms. It is a pattern that is formed using simple addition and subtraction operations. There is a common difference, "d" between two consecutive numbers in an arithmetic pattern which is satisfied by one or both of these operations.

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 is comprised of 10 rows and 10 columns. The value is a count from 1 to 100. The chart helps you identify common differences between consecutive terms of a pattern. You can use the chart vertically, horizontally, and even diagonally to identify patterns. The is a handy tool for the most basic of 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:

- 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 Lines**- The number line is a super useful tool in identifying number patterns. It uses "termsâ€ť and not common differences to identify a pattern in a data set. You will often need to draw these up yourself. I do find it helpful to write out and laminate a 0 to 30 number line. I also find that skip counts such as by 2s, 5s, and 10s to be invaluable when spotting patterns.