Patterns and number sequences help Grade 3 students see that math is not just a collection of isolated facts but a system full of structure and predictability. Third graders learn to identify rules behind repeating and growing patterns, extend sequences, and work with input-output tables — skills that form the foundation of algebraic thinking in middle school.
The main challenge at this level is that students often describe a pattern by listing what they see rather than stating the rule that generates it. In second grade, students extended simple repeating patterns; by fourth grade, they will generate and analyze more complex numeric rules and use function tables. Naming the rule precisely — add 4, subtract 7, multiply by 3 — is the key habit to develop in Grade 3.
Our patterns and number sequences worksheets give third graders guided practice identifying rules, correcting sequence errors, extending both repeating and growing patterns, and completing input-output tables with operations including multiplication — covering everything needed to build algebraic readiness.
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Browse all 12 printable worksheets below — click any card to open the full page.
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
Patterns and Number Sequences
What's Included in This Download
What You'll Learn
These patterns and number sequences worksheets help grade 3 students develop essential math skills through engaging activities.
Learning Objectives
- Arithmetic Patterns: Add and multiply patterns
- Input-Output Tables: Use pattern rules
- Growing Patterns: Extend patterns
- Repeating Patterns: Identify and continue
- Pattern Rules: Describe in words
Skills Covered
How to Use These Worksheets
- Download & Print: Click the download button to get the PDF. Print on standard 8.5" x 11" paper.
- Start Simple: Begin with easier pages before moving to more challenging activities.
- Daily Practice: Dedicate 10-15 minutes each day for consistent learning.
- Use Manipulatives: Pair worksheets with physical objects like blocks or counters.
- Provide Encouragement: Celebrate progress and effort to build confidence.
- Check Progress: Use the included answer key to review work together.
Common Mistakes to Watch For
- Describing the pattern by listing terms rather than stating the rule — writing 'it goes 5, 10, 15' instead of 'the rule is add 5' means students cannot use the pattern to predict values much farther along in the sequence.
- Confusing growing patterns with repeating patterns — students sometimes apply a repeating-unit approach to a growing sequence and produce the wrong next term instead of applying the arithmetic rule consistently.
- Misidentifying subtraction rules as addition — when a sequence decreases (such as 80, 72, 64, 56), students sometimes write 'add 8' because they see a difference of 8, failing to note that the numbers are getting smaller.
Frequently Asked Questions
What is the difference between a repeating pattern and a growing pattern?
A repeating pattern uses the same unit or core that cycles over and over — like A, B, C, A, B, C — so you predict the next term by identifying where you are in the cycle. A growing pattern changes by a consistent rule at each step, such as adding 4 each time, so the terms get larger (or smaller) rather than cycling.
How do you find the rule for a number sequence?
Look at the difference between consecutive terms. If each term is 3 more than the one before, the rule is add 3. If each term is 5 less, the rule is subtract 5. For more advanced sequences, check whether each term is being multiplied by a constant — for example, 2, 6, 18, 54 triples each time, so the rule is multiply by 3.
What is an input-output table and how does it work?
An input-output table (also called a function table) shows pairs of numbers where a single rule connects each input to its output. For example, if the rule is multiply by 4 and the input is 5, the output is 20. Students use the table to find missing outputs, missing inputs, or to identify the hidden rule from a set of completed pairs.
Why do patterns matter for later math learning?
Recognizing and describing patterns is one of the earliest forms of algebraic thinking. The skills students build in Grade 3 — finding rules, completing tables, and predicting terms — directly become the concept of a function in middle school algebra. Students who can describe a pattern with a rule rather than just listing terms are already thinking algebraically.
What should students do when they are stuck on a hard pattern like 1, 3, 7, 15?
Look at more than one relationship. Check the differences between consecutive terms: 3-1=2, 7-3=4, 15-7=8 — the differences are doubling. That clue reveals the rule: each difference is twice the previous difference, so the next difference is 16, and the next term is 31. When a simple add or subtract rule does not fit, check whether differences or ratios follow their own pattern.
Are these worksheets really free?
Yes! All our worksheets are 100% free to download and print. There's no subscription, no hidden fees, and no registration required.
Can I use these in my classroom?
Absolutely! Teachers are welcome to print and use these worksheets in their classrooms. Make as many copies as needed for your students.