Fibonacci Sequences Worksheet – Examples

The Fibonacci sequence is one of the most famous number patterns in math, and it turns up everywhere from pinecones and pineapples to the petals on a daisy. This Fibonacci Sequences Worksheet – Examples helps 4th grade students discover the rule hiding inside that pattern: every number is the sum of the two numbers just before it. Once children can say the rule in their own words, they can carry the sequence as far as they like, and they can recognize the same kind of pattern in a list of numbers that starts somewhere else entirely.

This 4th grade numbers worksheet moves from guided practice to independent thinking across four short parts. Students begin by completing a twelve-space Fibonacci strip, filling in the terms that have been left out. Next they extend four Fibonacci-style patterns that each begin with different starting numbers, so the rule has to be applied rather than remembered. Then they work backward to recover a number missing from the middle of a pattern, which takes subtraction as well as addition. The final part is a short word problem about the spirals on a pinecone: students write the next two Fibonacci numbers and explain their reasoning on the lines provided. Use it as a math-center activity, an early-finisher challenge, morning work, or a quick homework page.

What’s Included

• 1 print-ready PDF worksheet
• Answer key
• A 12-space Fibonacci sequence strip with 5 missing terms
• 4 extend-the-pattern problems
• 3 find-the-missing-number problems
• 1 word problem with a written explanation

There are three good reasons this Fibonacci Sequences Worksheet – Examples helps children learn. First, it builds addition fluency with a real purpose, because every answer depends on adding two numbers correctly and a single slip changes every term that follows. Second, it teaches students to generalize a rule instead of memorizing a list; the patterns that start with other numbers cannot be answered from memory of 1, 1, 2, 3, 5. Third, the missing-middle problems ask for inverse thinking, so students subtract to undo the rule and strengthen the link between addition and subtraction.

Teachers and parents can stretch the lesson in simple ways. Bring in real pinecones, sunflower heads, or a pineapple and let children count the spirals, because the counts really are Fibonacci numbers and the discovery sticks. Build the sequence with connecting cubes or squares on graph paper so students can watch it grow, or invite each child to start a Fibonacci-style pattern from the numbers in their own birthday and compare results with a partner. For a fast warm-up, write the first four terms on the board and ask students to race to the tenth term, then talk together about the strategies they used.

Related Resources

• Finding Number Patterns Worksheet
• Fibonacci Sequence Patterns Worksheet
• Multiples Worksheet
• Prime Numbers Song (Have Fun Teaching on YouTube)