Distributive Practice

Overview

In this final lesson of the unit, students apply the distributive property to solve multiplication problems, focusing on multi-digit numbers. Students connect base-ten place value thinking to build efficient strategies and explain their work with equations and models.

Learning intentions

Students will be able to:

• WALT use the distributive property to break apart multi-digit factors into expanded forms.
• WALT compute products by multiplying each part and combining partial products.
• WALT illustrate their thinking using area models or rectangular arrays.
• WALT solve and verify multiplication problems accurately using distributive property steps.

Success criteria

Students can:

• I can rewrite a multiplication problem as an equivalent expression using addition of place-value parts.
• I can show partial products for each part and add them correctly.
• I can use an equation to explain how the distributive property makes the multiplication easier.
• I can solve 4 distributive-property problems accurately (with correct answers and clear work).

Curriculum links

• Number and Operations in Base Ten — understand place value as related to powers of 10 and use place-value reasoning in computation.
• Number and Operations in Base Ten — find whole-number quotients using place value and related multiplication/division relationships (as background reasoning for inverse operations).
• Operations and Algebraic Thinking — write and interpret numerical expressions that record calculations (including expressions that represent “multiply by a sum”).
• Number and Operations in Base Ten — fluently use strategies that build toward efficient multi-digit multiplication.

Lesson structure (30 minutes)

1. 0–5 min · Bell work + homework corrections. Teacher returns the homework from Lesson 7, briefly reviews common distributive-property steps, and posts 1 quick “spot the error” example. Students correct their work in pairs, then check against a model equation written on the board.

2. 5–10 min · Mini review + goal setting. Teacher shows one problem: 23 × 14, and demonstrates breaking 23 into 20 + 3 and 14 into 10 + 4, then computing partial products. Students do a “thumbs-check” discussion: which parts multiply together, and how partial products combine; they state the goal for today in one sentence.

3. 10–18 min · Direct teach: area model + equations. Teacher introduces the consistent strategy:

• Step A: Write each factor as a sum of place-value parts (e.g., 37 = 30 + 7).
• Step B: Multiply part-by-part.
• Step C: Add partial products.
• Step D: Record the distributive equation (e.g., 37 × 20 = (30 × 20) + (7 × 20)). Students follow along using a blank area model: they label rows/columns with place-value parts, then fill in each section’s product and add totals. Teacher circulates and prompts students to connect the model to the equation.

4. 18–26 min · Guided practice: solve 4 problems (distributive set). Teacher distributes a “Solve 4” sheet with four problems of increasing complexity (aim for multi-digit × two-digit or two-digit × two-digit). Students solve independently first, then do a quick partner check focusing on correctness of partial products and the final sum. Teacher calls on 2–3 students to share one equation and one explanation using the distributive property.

5. 26–30 min · Exit ticket + wrap-up. Teacher gives an exit ticket with one short problem (or a one-step verification item like: “Show how 26 × 12 becomes (20×12) + (6×12) and compute”). Students complete quietly, then turn in. Teacher ends by reminding students today’s unit outcome: using distributive property to simplify multi-step multiplication.

Resources

• Distributive-property “Solve 4” worksheet (4 problems with space for area model and equations)
• Blank rectangle/area model templates (or graph paper)
• Base-ten place value cards (20, 3, 10, 4 style) or drawn number-part cards
• Board/markers or projector
• Exit ticket slips (one per student)
• Sample completed example from the mini review (23 × 14 or similar)
• Timer for keeping activities on pace

Assessment

• During bell work corrections: teacher checks for common errors (mis-partitioning numbers, incorrect addition of partial products).
• During guided practice: teacher uses quick conferencing to verify that students correctly form equivalent expressions using the distributive property.
• Exit ticket: one distributive rewrite plus a computed product (or rewrite-only plus verification), graded quickly for accuracy and clarity.

Differentiation

• Support: provide a partially completed area model and a sentence frame: “I broke ____ into ____ and ____ so I could multiply ____ and ____, then add the products.”
• Support: allow students to use a “place-value first” chart showing expanded forms (e.g., 34 = 30 + 4; 12 = 10 + 2).
• Extension: for students who finish early, include one problem that requires breaking both factors into two parts and adding four partial products (or a word problem version with multiplication).
• EAL/SEN: emphasize consistent labeling (rows = one factor’s parts, columns = the other factor’s parts) and provide a checklist: rewrite → partial products → add → equation.

Learning outcomes for this lesson

• Students will successfully use the distributive property to solve multi-digit multiplication problems by rewriting factors as sums of place-value parts, computing partial products, and combining them accurately.
• Students will demonstrate understanding by solving 4 distributive-property problems accurately with clear equations and/or area models.