NumberWonders Prime Activity Kit v1
Pilot release - direct download edition
This printable kit helps grades 5-9 learners master prime/composite logic, divisibility tests, factor trees, and reasoning through puzzle-style activities.
Primes Divisibility Factorization Reasoning Answer key included
Teacher Quick Start
- Warm up with worksheet mini-drills (10 minutes).
- Run one core worksheet in pairs or small groups (20-25 minutes).
- Discuss one strategy per team and compare methods (8-10 minutes).
- Use challenge board tasks as extension or homework.
Worksheet Index
| # | Topic | Target Skill |
|---|---|---|
| 1 | Prime or Composite Quick Check | Classification and reasoning |
| 2 | Divisibility Tests Lab | Rules for 2,3,5,9,10,11 |
| 3 | Sieve Sprint | Prime detection by elimination |
| 4 | Factor Tree Workshop | Prime factorization |
| 5 | Greatest Common Factor | GCF with factorizations |
| 6 | Least Common Multiple | LCM with prime powers |
| 7 | Prime Gap Explorer | Pattern spotting |
| 8 | Mersenne and Twin Primes | Special prime families |
| 9 | Cryptic Factor Puzzles | Reverse reasoning |
| 10 | Prime Detective Challenge Board | Mixed application |
Worksheet 1: Prime or Composite Quick Check
Mark each number as Prime (P) or Composite (C), then justify 3 choices.
1) 2 ___
2) 9 ___
3) 17 ___
4) 21 ___
5) 29 ___
6) 31 ___
7) 33 ___
8) 37 ___
9) 49 ___
10) 51 ___
Worksheet 2: Divisibility Tests Lab
For each number, list all tests that prove divisibility (2,3,5,9,10,11).
1) 120: _________________________
2) 231: _________________________
3) 495: _________________________
4) 693: _________________________
5) 1,210: _______________________
6) 1,001: _______________________
7) 2,970: _______________________
8) 4,356: _______________________
Worksheet 3: Sieve Sprint
Use a sieve to mark all primes from 2 to 100. Then answer:
1) How many primes are between 1 and 100? ______
2) List the primes between 50 and 80: ____________________________
3) Which composite numbers survived until the last elimination step? ______
4) Why can you stop checking divisors after sqrt(n)? __________________
Worksheet 4: Factor Tree Workshop
Find prime factorization and write in exponent form.
1) 84 = _________________________
2) 126 = ________________________
3) 180 = ________________________
4) 252 = ________________________
5) 432 = ________________________
6) 693 = ________________________
7) 945 = ________________________
8) 1,008 = ______________________
Worksheet 5: Greatest Common Factor
Compute GCF using prime factorization.
1) GCF(18, 24) = _________________
2) GCF(45, 75) = _________________
3) GCF(84, 126) = ________________
4) GCF(96, 144) = ________________
5) GCF(210, 315) = _______________
6) GCF(256, 640) = _______________
Worksheet 6: Least Common Multiple
Compute LCM using prime powers.
1) LCM(6, 8) = __________________
2) LCM(12, 18) = ________________
3) LCM(15, 20) = ________________
4) LCM(21, 28) = ________________
5) LCM(24, 36) = ________________
6) LCM(45, 60) = ________________
Worksheet 7: Prime Gap Explorer
Find prime gaps and describe patterns.
1) Gap between 11 and 13 = ______
2) Gap between 23 and 29 = ______
3) Gap between 47 and 53 = ______
4) Gap between 89 and 97 = ______
5) In the range 2..100, what is the largest prime gap? ______
6) Can prime gaps be odd? Explain. _____________________________
Worksheet 8: Mersenne and Twin Primes
Classify each statement as True/False.
1) If 2^p - 1 is prime, then p is prime. __________
2) (11, 13) is a twin prime pair. ________________
3) (23, 25) is a twin prime pair. ________________
4) 31 is a Mersenne prime. ______________________
5) 63 is a Mersenne number. _____________________
6) Every Mersenne number is prime. ______________
Worksheet 9: Cryptic Factor Puzzles
Use clues to find the hidden number.
- I am composite, less than 50, and my prime factors are 2, 3, and 5. Who am I?
- I am divisible by 9 and 11, between 80 and 120. Who am I?
- I have exactly three prime factors: 2^2, 3, and 7. Who am I?
- I am the smallest odd composite with two distinct prime factors. Who am I?
Worksheet 10: Prime Detective Challenge Board
Solve any 8 tasks. Circle your strategy for each: test, tree, or logic.
1) Is 221 prime? ___________________
2) Prime factors of 378 = ___________
3) GCF(168, 252) = _________________
4) LCM(42, 70) = ___________________
5) Next prime after 997 = ___________
6) Is 2,047 prime? _________________
7) Is 1,001 prime? _________________
8) Write one twin prime pair above 100.
9) Write one Mersenne number that is composite.
10) Create your own prime puzzle for a partner.
Answer Key
Worksheet 1
1 P, 2 C, 3 P, 4 C, 5 P, 6 P, 7 C, 8 P, 9 C, 10 C
Worksheet 2
1) 2,3,5,10 2) 3 3) 3,5,9 4) 3,9,11 5) 2,5,10,11 6) 7,11 (11 by alternating sum test) 7) 2,3,5,9,10,11 8) 2,3,11
Worksheet 3
1) 25 primes 2) 53,59,61,67,71,73,79 3) open response based on process 4) because any larger factor pairs with one below sqrt(n)
Worksheet 4
1) 2^2 x 3 x 7 2) 2 x 3^2 x 7 3) 2^2 x 3^2 x 5 4) 2^2 x 3^2 x 7 5) 2^4 x 3^3 6) 3^2 x 7 x 11 7) 3^3 x 5 x 7 8) 2^4 x 3^2 x 7
Worksheet 5
1) 6 2) 15 3) 42 4) 48 5) 105 6) 128
Worksheet 6
1) 24 2) 36 3) 60 4) 84 5) 72 6) 180
Worksheet 7
1) 2 2) 6 3) 6 4) 8 5) 8 (in 2..100) 6) gaps between odd primes are even (except involving 2)
Worksheet 8
1 True 2 True 3 False 4 True 5 True 6 False
Worksheet 9
1) 30 2) 99 3) 84 4) 15
Worksheet 10
1) 221 = 13 x 17 (composite) 2) 2 x 3^3 x 7 3) 84 4) 210 5) 1009 6) 2,047 = 23 x 89 (composite) 7) 1,001 = 7 x 11 x 13 8) example: 101 and 103 9) example: 2^11 - 1 = 2047 10) open response