Multiplication Properties

Overview

Students explore and apply multiplication properties (associative, commutative, distributive) to rewrite expressions and solve problems without needing to compute every intermediate value. This builds on prior learning in the unit by using properties as tools to reason about calculations.

Learning intentions

Students will be able to:

• WALT identify which multiplication property matches a given situation or equation.
• WALT write equivalent numerical expressions using parentheses and factors.
• WALT interpret numerical expressions (read them as “calculations”) without immediately evaluating them.
• WALT use at least one multiplication property to solve a problem and justify the step.

Success criteria

Students can:

• I can explain whether a change in an equation uses commutative, associative, or distributive property.
• I can rewrite an expression using equivalent factors and correct parentheses.
• I can interpret what an expression represents (what operation sequence it means) without calculating everything.
• I can complete practice problems showing the property used and an equivalent result.

Curriculum links

• Operations and Algebraic Thinking: write simple expressions that record calculations with numbers and interpret expressions without evaluating.
• Operations and Algebraic Thinking: use parentheses to record calculations in numerical expressions.
• Number and Operations in Base Ten: use place-value reasoning when working with factors of 10 or patterns with zeros.
• Number and Operations in Base Ten: relate multiplication to division reasoning when interpreting fact families (as a support check).

Lesson structure (30 minutes)

1. 0–5 min · Bell work & homework corrections. Teacher displays 3 “property match” items from the homework and 1 quick rewrite prompt; students correct in pairs, then teacher checks answers. Students explain which property is used and update one solution step using the correct property language.

2. 5–10 min · Mini lesson: what properties really do. Teacher models how properties create equivalent expressions, showing commutative (factor order), associative (grouping), and distributive (splitting one factor). Students copy one “before/after” equation per property and underline the part that changes.

• Example commutative: 6 × 7 = 7 × 6
• Example associative: (2 × 3) × 4 = 2 × (3 × 4)
• Example distributive: 4 × (10 + 3) = (4 × 10) + (4 × 3)

3. 10–17 min · Guided practice: recognize properties from expressions. Teacher gives 6 short cards (on the board or projector). Each card shows an original expression and an equivalent expression; students label the property and rewrite correctly with parentheses when needed. Students work at desks in pairs, writing “C” (commutative), “A” (associative), or “D” (distributive), then one sentence: “Because I changed ___.”

4. 17–23 min · Small-group strategy: interpret first, calculate second. Teacher provides 3 word problems that translate to expressions with parentheses, then asks students to interpret what the expression means before solving. Students turn and talk: “What does this expression represent?” then solve, using at least one property in their work.

• Problem set (examples):
• “Three times the quantity of 8 plus 5” → 3 × (8 + 5)
• “A factor of 6 multiplied by a sum of 9 and 2” → 6 × (9 + 2)
• “How can you regroup to make it easier?” with expressions like (7 × 4) × 2 and 7 × (4 × 2)

5. 23–28 min · Independent practice (property check). Teacher circulates with a quick checklist: correct property label, correct parentheses/rewriting, and equivalent result. Students complete a short worksheet of 6 problems:

• 2 commutative rewrites
• 2 associative rewrites
• 2 distributive problems where the student must split the sum and show equivalent expressions.

6. 28–30 min · Exit ticket & wrap. Teacher collects a one-question exit ticket on the board and reads it aloud. Students answer and show one justification: “Write an equivalent expression using a multiplication property and name the property.”

Resources

• Property match cards (commutative/associative/distributive)
• Guided practice worksheet (expressions with parentheses)
• Independent practice sheet (6 problems)
• Exit ticket slips
• Whiteboards or scrap paper for quick rewrites
• Colored pencils or highlighters for underlining changed parts
• Teacher checklist for circulation

Assessment

• Formative checks during bell-work corrections: students can explain the property used for each corrected item.
• Guided practice observation: students label property correctly and use parentheses correctly when rewriting.
• Independent practice: accuracy of equivalent expressions and correct property language.
• Exit ticket: student names a property and writes an equivalent expression with justification.

Differentiation

• Support:
• Provide sentence frames: “I used the ___ property because I changed the ___.”
• Offer a model “before/after” example card at student tables.
• Allow students to highlight what changed (order vs grouping vs splitting).
• Targeted scaffolds:
• If distributive is difficult, give a partially completed example: 4 × (10 + 3) → (4 × 10) + (4 × 3) and students fill in the numbers.
• Extension:
• For students who finish early: ask them to create their own equivalent expression using two different properties and explain both.
• EAL/SEN considerations:
• Keep problems visually consistent (same layout for “original” and “equivalent”).
• Emphasize oral rehearsal: students state the meaning of the expression before computing.