Math activity
Factor Forest
Plant number trees! Draw a tree for different numbers and hang 'fruit' on the branches — each fruit shows a group that makes that number. A tree for 6 has branches of 2 and 3.
Materials and setup
- paper
- pencil
- crayons
- small counters for grouping
How this changes by age
Pre-K (ages 3–4)
Plant number trees! Draw a tree for different numbers and hang 'fruit' on the branches — each fruit shows a group that makes that number. A tree for 6 has branches of 2 and 3.
Steps
- Draw a tree trunk and write the number 4 on it.
- Can you share 4 objects into 2 equal groups? Yes, 2 and 2! Draw two branches with 2 fruit each.
- Draw a tree for the number 6. Try splitting into 2 groups of 3 and 3 groups of 2.
- Draw trees for numbers 2, 3, 4, 5, and 6.
- Ask: 'Which numbers could only be split into 1 and themselves?' Those are special numbers (primes)!
- Tell a grown-up one thing that surprised you.
Learning objectives
- Split small numbers into equal groups
- Visualize numbers as collections of equal parts
- Begin to notice that some numbers split more ways than others
Kindergarten (ages 5–6)
Build factor trees by finding pairs of numbers that multiply to make a target number. Draw trees with branches showing factor pairs.
Steps
- Explain: 'Factors are numbers that multiply together to make another number. 2 and 3 are factors of 6.'
- Find all factor pairs for 12: (1,12), (2,6), (3,4). Use objects to prove each pair works.
- Draw a tree: put 12 at the top, draw branches down to 3 and 4, then branches from 4 down to 2 and 2.
- Make factor trees for 8, 10, 15, and 20.
- Which numbers only have 1 and themselves as factors? Circle those trees — they are 'prime' numbers.
- Tell a grown-up one thing that surprised you.
Learning objectives
- Find factor pairs for numbers up to 20
- Draw factor trees showing how numbers break into parts
- Identify numbers that cannot be broken into smaller equal groups (primes)
Early elementary (ages 6–8)
Build complete factor trees to find prime factorizations. Identify factors, multiples, prime and composite numbers. Use factor knowledge for simplifying fractions.
Steps
- List ALL factors of these numbers: 12, 18, 24, 30, 36. A factor divides evenly with no remainder.
- Build prime factor trees for each number: 36 -> 6 x 6 -> (2 x 3) x (2 x 3). So 36 = 2 x 2 x 3 x 3.
- Identify all prime numbers between 1 and 30. Use factor trees to prove each one is prime.
- Find the Greatest Common Factor (GCF) of 3 pairs of numbers using factor lists.
- Use the GCF to simplify fractions: 12/18 -> GCF is 6 -> 12/6 = 2, 18/6 = 3 -> simplified: 2/3.
- Create a poster showing the 'Factor Forest' for numbers 1 through 20.
- In one sentence, tell a parent or sibling what surprised you today.
Learning objectives
- Find all factors and prime factorizations of numbers
- Distinguish between prime and composite numbers
- Use greatest common factor to simplify fractions
Upper elementary (ages 8–10)
Master prime factorization, GCF, and LCM. Use factor trees to solve advanced problems with fractions, explore divisibility rules, and investigate number theory concepts.
Steps
- Find the prime factorization of 10 numbers between 50 and 200 using factor trees.
- Use prime factorizations to find the GCF and LCM of 5 pairs of numbers.
- Apply GCF to simplify 5 complex fractions. Apply LCM to find common denominators for adding 5 fraction pairs.
- Investigate: is 1 prime? Why or why not? Research and write your explanation.
- Explore the Fundamental Theorem of Arithmetic: every number has exactly one prime factorization. Test with 5 numbers, building the tree different ways.
- Challenge: what is the smallest number with exactly 3 factors? 4 factors? 5 factors? 6 factors? Explain the pattern.
- In one sentence, tell a parent or sibling what surprised you today.
Learning objectives
- Find prime factorizations of large numbers efficiently
- Use GCF and LCM in fraction operations
- Explore number theory concepts including the Fundamental Theorem of Arithmetic
Safety and evidence note
Read the full activity before beginning. An adult should supervise tools, heat, food, outdoor work, movement, and experiments as appropriate. Completion records that the activity was done; the child’s explanation, work sample, photo, or demonstration is stronger evidence of learning than a completion check alone.
Related math activities
Addition and Subtraction Stories
Use toy animals to tell math stories. '3 ducks are swimming. 2 more come. How many now?' Act it out and count together.
Algebra Adventures: Patterns and Variables
Build a pattern with red and blue blocks — red, blue, red, blue! What comes next? Find patterns on shirts, tiles, and bricks too.
Angle Explorers
Explore turns and corners! Open a book wide or just a little bit. Discover that doors, scissors, and your arms all make angles when they open and close.
Animal Counting Corral
Round up toy animals into corrals (bowls or boxes) and count how many are in each group. Practice counting up to 10 with one-to-one correspondence.