Multiply by 3 Patterns

Overview

In this lesson, students discover number patterns in the 3-times table and use properties of operations to solve multiplication and related division facts. This builds toward fluent multiplication/division within 100 and using patterns to explain “why” answers make sense.

Learning intentions

• Students will identify patterns when multiplying by 3.
• Students will use properties of operations to multiply by 3 mentally and explain reasoning.
• Students will connect multiplication and division facts (the relationship between them).
• Students will determine unknowns in simple multiplication/division equations.

Success criteria

• I can describe a pattern in a 3-times table (for example, counting by 3).
• I can use a property of operations (commutative, associative, distributive) to help me multiply by 3.
• I can write and solve a multiplication or division equation involving 3 that has an unknown.
• I can explain how a division fact matches a multiplication fact.

Curriculum links

• Operations and Algebraic Thinking — apply properties of operations as strategies to multiply and divide.
• Operations and Algebraic Thinking — identify arithmetic patterns in a multiplication table and explain them using properties of operations.
• Operations and Algebraic Thinking — determine the unknown whole number in a multiplication or division equation.
• Operations and Algebraic Thinking — fluently multiply and divide within 100 using strategies; know products of two one-digit numbers from memory.

Lesson structure (60 minutes)

1. 0–6 min · Warm-up: “3-Count Sprint.” Teacher writes “3, 6, 9, 12…” on the board and asks students to continue for three more numbers. Students count forward by 3 aloud and silently, then answer where the sequence goes next.

2. 6–15 min · Direct teach: Patterns in the 3s. Teacher models a short “3 × n” table (n = 1 to 10) using repeated addition as groundwork (3 = 3×1, 6 = 3×2, etc.). Students complete missing entries and explain the pattern in one sentence using “each time we add 3.”

3. 15–25 min · Properties of operations trick: make 3×(bigger) easier. Teacher gives two examples and thinks aloud:

• 3 × 4 = (3 × 2) + (3 × 2) and then add results
• 3 × 7 = 3 × (5 + 2) = (3×5) + (3×2) Students practice with two teacher prompts, using drawings, counters, or number lines to support the “break it apart” strategy.

4. 25–35 min · Fluency practice: Flashcards with explanation. Teacher runs a quick cycle:

• Show a card “3 × 6” (and a matching division card “18 ÷ 3”).
• Ask: “What multiplication fact matches this division?”
• Ask: “What pattern helps you?” Students answer both the product and the matching division fact, then share one explanation (pattern or property).

5. 35–45 min · Guided practice: Unknown whole number. Teacher displays 4 equations on the board one at a time and models the first:

• 3 ×? = 21 -? = 24 ÷ 3
• 3 × 6 =?
• 27 ÷ 3 =? Students solve each equation and show reasoning using either the pattern (count by 3) or a fact they know from memory.

6. 45–55 min · Application game: “True or Not True.” Teacher reads statements and students decide if each is true, then correct it if false:

• “3 × 8 = 24” (true)
• “24 ÷ 3 = 9” (false; fix it)
• “3 × 5 = 15 and 15 ÷ 3 = 5” (true) Students respond with a reason that references multiplication/division relationship and/or a pattern.

7. 55–60 min · Exit ticket. Teacher collects a short written set:

• Complete: 3 × 9 = __
• Complete: 30 ÷ 3 = __
• Explain: “How do you know the division matches the multiplication?” (1–2 sentences)

Resources

• Index cards or printed flashcards for “3 × n” and matching division facts
• Counters or base-ten blocks
• Blank 3-times table template (n = 1 to 10)
• Whiteboard/markers or chart paper
• Small dry-erase boards (optional if available)
• Exit ticket slips
• Number line 0–30 (printed) and/or fraction of it taped to board
• Visual equation cards for “3 ×?” and “? ÷ 3”

Assessment

• Observe accuracy and reasoning during the pattern discussion and property-of-operations examples.
• Listen for whether students can connect a division fact to the matching multiplication fact during flashcards and the “True or Not True” game.
• Review the exit ticket for correct products/division and for a brief explanation about the match between multiplication and division.

Differentiation

• Support: Provide a partially completed 3-times table and a sentence starter like “I know because I count by 3” or “3 × 6 means 6 groups of 3.”
• Support: For unknown equations, offer a choice of tools (counters, number line, or multiplication table) and allow drawing one simple representation.
• Extension: If students finish early, ask them to create one “unknown” equation for the class using 3 (for example, “3 ×? = 30”) and explain the method to solve it.
• EAL/SEN: Use consistent language prompts (“What is the matching fact?” “How does the pattern help?”) and keep card sets small so attention stays on key relationships.