Fibonacci Sequence Patterns Worksheet

The Fibonacci Sequence is one of the friendliest number patterns in all of mathematics, and it is a perfect way to show fourth graders that a pattern is really just a rule you can repeat. The sequence starts with 0 and 1, and every number after that is the sum of the two numbers before it, which is how 0, 1, 1, 2, 3, 5, 8 keeps marching forward. This fibonacci sequence patterns worksheet gives students a clear rule, a worked example, and plenty of room to practice generating the terms themselves. Working with a growing pattern like this builds exactly the kind of thinking fourth grade standards ask for: generate a number pattern that follows a given rule, then notice features of the pattern that were not stated in the rule itself.

This printable 4th grade patterns worksheet moves from guided practice to independent problem solving in three short parts. Part A puts the rule in a highlighted box with four worked examples, then asks students to finish the Fibonacci Sequence itself by filling in the last four cells. Part B stretches the same rule across four brand-new patterns that start from different pairs of numbers, and several of the missing cells sit in the middle of a row, so students have to run the rule backwards and subtract instead of simply adding forward. Part C closes with a garden word problem and a written explanation, so students have to put their reasoning into words. Use it as morning work, as a small-group station, as homework, or as a quick check before a unit test on number patterns.

What’s Included

• 1 print-ready PDF worksheet
• Answer key
• 3 activities: an 11-cell Fibonacci Sequence to complete, 4 missing-number pattern rows, and 1 word problem with a written explanation

There are three big reasons this resource helps students learn the skill. First, the rule is stated once and then reused everywhere, so students practice applying a single rule to new situations rather than memorizing one special list of numbers. Second, the missing cells in the middle of a row turn addition practice into real reasoning, because a student has to ask what number added to 5 gives 13 instead of just adding the two numbers in front of them. Third, this fibonacci sequence patterns worksheet ends with a word problem that asks students to explain their thinking, which is the constructed-response habit that shows up on almost every state assessment in fourth and fifth grade.

Teachers and parents can keep the pattern work going long after the page is finished. Hand students a stack of index cards and have them build a Fibonacci chain across a table, one term per card, checking each new card against the two cards before it. Try starting the rule from a different pair of numbers, such as 4 and 7, and compare how quickly that chain grows next to the classic one. Take the pattern outside and count the petals on daisies or the spirals on a pinecone, since so many of those counts land on Fibonacci numbers. For a fast warm-up, write the first four terms of a mystery chain on the board and let students race to name the fifth, then have them invent a chain for a partner to solve.

Related Resources

• Finding Number Patterns Worksheet
• Complete the Patterns Worksheet
• Patterns in Multiplication and Division Worksheet
• Counting By Eights Song (Have Fun Teaching)