Factor Trees

Overview

In this lesson (6 of 8), students use factor trees to find prime factors and to reinforce prime/composite number ideas from earlier multiplication concepts. They will create factor trees for several numbers and explain how each branch leads to prime factors.

Learning intentions

Students will be able to:

• break whole numbers into prime factors using factor trees
• represent factor relationships using multiplication equations that match the factor tree
• recognize when numbers are prime or composite based on whether the tree ends in primes
• accurately build factor trees for at least five numbers during practice

Success criteria

Students can:

• produce correct factor trees for at least five given numbers
• show all prime factors with no composite numbers left at the leaves
• write matching multiplication equations for the prime factors shown in the tree
• check their work by confirming the product of prime factors equals the original number

Curriculum links

• Number and Operations in Base Ten: fluently use place value and relationships between multiplication and division to support factor reasoning
• Number and Operations in Base Ten: use multiplication and division relationships and explain calculations using equations and models
• Number and Operations - Fractions: interpret multiplication as repeated partitioning (used later in the unit; practiced here by careful meaning of multiplication equations)

Lesson structure (30 minutes)

1. 0–5 min · Bell work (prime/composite quick check). Teacher displays 4 numbers (e.g., 12, 15, 17, 21) and asks students to write “prime” or “composite,” plus one reason (in one sentence). Students work independently, then do a 1-minute partner share to compare reasons.

2. 5–9 min · Homework correction + connection. Teacher quickly reviews the most common error pattern from the homework (e.g., stopping early, treating 1 as a prime, or mixing composite leaves with primes). Students correct one problem in their notes using a “Fix it” template: What was wrong? What should the factor tree show?

3. 9–13 min · Mini-lesson: What a factor tree guarantees. Teacher models a factor tree for one number (choose 60 or 84) by showing branching into two factors, then continuing until the leaves are all prime. Students watch and answer two teacher prompts: “What should we do next when the factor is still composite?” and “How do we know the leaves are prime?”

4. 13–18 min · Direct guided practice (one tree together). Teacher guides the class through a second example (e.g., 36), using think-alouds: choose factors, split, and stop only when prime. Students build the tree on paper and also write a matching multiplication equation using the leaf primes (for example, 2 × 2 × 3 × 3 = 36).

5. 18–26 min · Independent practice: build factor trees for five numbers. Teacher hands out a “Factor Tree Sprint” sheet with five target numbers (e.g., 18, 24, 28, 45, 72). Students create factor trees for all five numbers, write one multiplication equation for each, and circle the primes at the leaves.

6. 26–29 min · Partner check + targeted teacher feedback. Teacher pairs students and gives a checklist: “Leaves are prime,” “No missing prime factors,” “Product matches original number.” Students swap papers, check using the checklist, and write one improvement comment.

7. 29–30 min · Exit ticket (1 question). Teacher collects quickly with one final number (e.g., 32 or 33): students draw a mini factor tree and write the multiplication equation. Students submit their exit ticket to show readiness for the next lesson.

Resources

• Factor Tree Sprint worksheet (5 numbers per student)
• Graph paper or blank paper for clear branching
• Pencil, eraser, colored pencils (optional for highlighting primes)
• “Fix it” correction template (for homework review)
• Teacher example chart paper or document camera for the modeled trees

Assessment

• Bell work: prime/composite classification with a short reason (formative)
• Guided practice: correctness of one shared factor tree and its multiplication equation (formative)
• Independent practice: accuracy across five numbers using the leaf-prime checklist (summative-in-class)
• Exit ticket: mini factor tree and multiplication equation for a new number (quick check)

Differentiation

• Support: Provide a factor bank (pairs like 2×?, 3×?, 4×?, etc.) and sentence starters: “I can branch because __ is composite.” and “I stop when __ is prime.”
• Support: For students who struggle, allow use of divisibility tests (2, 3, 5, 10) to choose the first factor pair before drawing the tree.
• Extension: Challenge students to write prime factorization using exponents after completing the tree (e.g., 12 = 2^2 × 3) and explain why the exponent counts repeated branches.
• EAL/SEN: Reduce writing load by requiring either (a) correct factor tree plus one equation, or (b) tree plus a completed leaf prime list, then build to full equations for all five numbers.