NumberWonders Fibonacci and Pattern Puzzle Pack v1
Pilot release - direct download edition
This pack helps grades 4-8 learners build sequence fluency, pattern reasoning, and rule-explanation skills through Fibonacci-focused puzzles and visual tasks.
Fibonacci Sequences Visual patterns Reasoning Answer key included
Teacher Quick Start
- Use one worksheet as warmup and one as challenge each session.
- Ask students to state the pattern rule in words before calculating.
- Compare two different valid methods after each puzzle.
- Use the challenge board tasks for stations or homework.
Worksheet Index
| # | Topic | Target Skill |
|---|---|---|
| 1 | Fibonacci Basics | Generate terms from rule |
| 2 | Is It Fibonacci? | Membership checks |
| 3 | Recursive and Explicit Clues | Rule interpretation |
| 4 | Pattern Machines | Input/output reasoning |
| 5 | Visual Dot Patterns | Figure growth analysis |
| 6 | Golden Ratio Approximations | Ratio behavior |
| 7 | Number Pattern Puzzles | Mixed sequence logic |
| 8 | Word Problems with Sequences | Modeling contexts |
| 9 | Pattern Proof Starters | Explain and justify |
| 10 | Fibonacci Challenge Board | Extended puzzles |
Worksheet 1: Fibonacci Basics
Complete each sequence using F(n)=F(n-1)+F(n-2).
1) 0, 1, 1, 2, 3, __, __, __
2) 1, 1, 2, 3, 5, __, __
3) 2, 3, 5, 8, 13, __, __
4) 5, 8, 13, 21, __, __
5) 13, 21, 34, __, __, __
6) 34, 55, 89, __, __
7) 3, 5, 8, 13, __, __
8) 8, 13, 21, 34, __, __
Worksheet 2: Is It Fibonacci?
Mark Yes/No and justify your answer for four numbers.
1) 21: Yes / No
2) 22: Yes / No
3) 34: Yes / No
4) 35: Yes / No
5) 55: Yes / No
6) 56: Yes / No
7) 89: Yes / No
8) 90: Yes / No
Worksheet 3: Recursive and Explicit Clues
Find the next terms and identify the rule style.
1) 4, 7, 11, 18, 29, __, __
2) 2, 6, 12, 20, 30, __, __
3) 1, 4, 9, 16, 25, __, __
4) 3, 6, 12, 24, 48, __, __
5) 5, 9, 14, 23, 37, __, __
6) 10, 7, 11, 8, 12, 9, __, __
Worksheet 4: Pattern Machines
Use each rule machine to fill outputs.
| Input n | Rule | Output |
|---|---|---|
| 1 | 2n + 1 | __ |
| 2 | 2n + 1 | __ |
| 3 | 2n + 1 | __ |
| 4 | n^2 + 1 | __ |
| 5 | n^2 + 1 | __ |
| 6 | n^2 + 1 | __ |
| 7 | Fibonacci index n | __ |
| 8 | Fibonacci index n | __ |
Worksheet 5: Visual Dot Patterns
Count dots by pattern, then predict figure 6.
Pattern A counts by +3 each step starting at 2: figure 1..5 = __________
Pattern B is square numbers: figure 1..5 = __________
Pattern C follows Fibonacci: figure 1..7 = __________
For Pattern A, figure 6 = ____ ; Pattern B figure 6 = ____ ; Pattern C figure 8 = ____
Extension: Draw a dot sketch for one of the sequences and explain the growth.
Worksheet 6: Golden Ratio Approximations
Compute each ratio F(n+1)/F(n) and observe the trend.
1) 2/1 = __________
2) 3/2 = __________
3) 5/3 = __________
4) 8/5 = __________
5) 13/8 = __________
6) 21/13 = __________
7) 34/21 = __________
8) 55/34 = __________
What value do these seem to approach? ____________________
Worksheet 7: Number Pattern Puzzles
Find the missing number or expression.
1) 7, 10, 13, 16, __
2) 3, 6, 12, 24, __
3) 1, 1, 2, 3, 5, 8, __
4) 2, 5, 10, 17, 26, __
5) 81, 27, 9, 3, __
6) 4, 9, 16, 25, 36, __
7) 2, 4, 7, 11, 16, __
8) 5, 9, 14, 20, 27, __
Worksheet 8: Word Problems with Sequences
Build an equation and solve.
- A rabbit model follows Fibonacci births: 1,1,2,3,5,... How many in month 8?
- A staircase pattern adds 2 tiles each step starting with 3. How many at step 12?
- A club doubles members every week starting at 4. How many after 6 weeks?
- A square garden grows by one ring each season. If side lengths are 1,3,5,7,... what is side at season 10?
Worksheet 9: Pattern Proof Starters
Complete each explanation sentence.
1) This sequence is arithmetic because ___________________________
2) This sequence is geometric because ___________________________
3) Fibonacci differs from arithmetic because ______________________
4) To verify a term belongs to a sequence, I should ________________
5) A visual model helps because __________________________________
6) If two rules fit early terms, we can decide by _____________________
Worksheet 10: Fibonacci Challenge Board
Solve any 8 tasks.
1) Write Fibonacci terms from F1 to F12.
2) Find two consecutive Fibonacci numbers whose ratio is closest to 1.62.
3) Build a sequence with rule a(n)=a(n-1)+3 starting from 2.
4) Build a sequence with rule a(n)=2a(n-1) starting from 3.
5) Which grows faster after 10 terms: Fibonacci or powers of 2?
6) Write an explicit formula for sequence 5,9,13,17,...
7) Give one real-world pattern that is approximately Fibonacci-like.
8) Create a 6-term puzzle sequence for a partner to solve.
9) Decide whether 144 is Fibonacci and justify.
10) Explain one common mistake when extending sequences.
Answer Key
Worksheet 1
1) 5,8,13 2) 8,13 3) 21,34 4) 34,55 5) 55,89,144 6) 144,233 7) 21,34 8) 55,89
Worksheet 2
1 Yes 2 No 3 Yes 4 No 5 Yes 6 No 7 Yes 8 No
Worksheet 3
1) 47,76 2) 42,56 3) 36,49 4) 96,192 5) 60,97 6) 13,10
Worksheet 4
2n+1 outputs: 3,5,7 ; n^2+1 outputs for 4,5,6: 17,26,37 ; Fibonacci index 7 and 8: 13,21
Worksheet 5
Pattern A: 2,5,8,11,14 ; Pattern B: 1,4,9,16,25 ; Pattern C: 1,1,2,3,5,8,13 ; next values A6=17, B6=36, C8=21
Worksheet 6
1) 2.00 2) 1.50 3) 1.67 4) 1.60 5) 1.625 6) 1.615 7) 1.619 8) 1.618 ; approaches about 1.618
Worksheet 7
1) 19 2) 48 3) 13 4) 37 5) 1 6) 49 7) 22 8) 35
Worksheet 8
1) 21 2) 25 3) 256 4) 19
Worksheet 9
Open responses. Key points: arithmetic has constant difference, geometric has constant ratio, Fibonacci uses two previous terms.
Worksheet 10
Sample outcomes: F1..F12 = 1,1,2,3,5,8,13,21,34,55,89,144 ; ratio close to 1.62 from 55/34, 89/55, etc.; 144 is Fibonacci (F12).