Product Per Digits

Overview

In this second lesson of the 8-lesson unit, students will multiply a 1-digit number by a 2-digit number using place value reasoning, an area model, and (when ready) the standard algorithm. This builds directly from prior work multiplying and understanding place value.

Learning intentions

Students will be able to:

• Represent 1-digit by 2-digit multiplication using an area model.
• Use place value to break a 2-digit factor into tens and ones to find partial products.
• Explain the multiplication using equations that match their model.
• Complete 1-digit by 2-digit multiplication using a standard algorithm accurately.

Learning outcomes (lesson 2 of 8)

• Students correctly perform 1-digit by 2-digit multiplications and show reasoning with models or equations.

Success criteria

• I can complete at least 5 multiplication problems (1-digit × 2-digit) correctly during classwork.
• I can show partial products (tens and ones) and write an equation that matches my model or strategy.

Curriculum links

• Number and Operations in Base Ten — understand place value relationships in multi-digit numbers (for tens/ones reasoning).
• Number and Operations in Base Ten — fluently multiply multi-digit whole numbers using the standard algorithm.
• Operations and Algebraic Thinking — write and interpret equations that record multiplication reasoning.

Lesson structure (30 minutes)

1. 0–5 min · Bell work + quick correction. Teacher displays 3–4 mixed multiplication items from yesterday; students correct in pairs using answer keys and then volunteer one “fix” explanation (what place value went wrong). Students update a single error-log for what they will remember today.

2. 5–10 min · Mini-lesson: area model and place value. Teacher models 4 × 23 using a rectangle split into 2 tens columns and 3 ones blocks (tens area and ones area), labeling partial products: 4×20 and 4×3, then totaling. Teacher emphasizes: tens part first, ones part second, then sum, and writes the matching equation. Students repeat with a second example on dry-erase boards: 6 × 14, completing the area model and equation.

3. 10–18 min · Guided practice: partial products to algorithm. Teacher works through 2 problems step-by-step where students choose a strategy (area model or partial products chart) and then connect it to the standard algorithm for recording.

• Example 1: 3 × 42
• Example 2: 7 × 18 Teacher checks each step: digit in the ones place, digit in the tens place, regrouping when needed, and final total. Students complete both in their notebooks, showing either (a) area model or (b) tens/ones partial products, then an equation; they also write the standard algorithm steps when they are ready.

4. 18–26 min · Independent classwork (target accuracy). Students complete a short set of 10 problems (1-digit × 2-digit), choosing one way to show work (area model or partial products). Teacher circulates, using a quick checklist for: correct tens/ones decomposition, accurate partial product computation, correct sum, and correctly written final equation. Students stop after 5 correct answers to meet success criteria, then continue for mastery.

5. 26–30 min · Exit ticket + wrap-up. Teacher gives one exit ticket item: “5 × 36. Show how you know using tens/ones or an area model, then write the equation.” Students solve independently and turn in.

Resources

• Copies of area model grids (10×10 or rectangle templates) or graph paper
• Dry-erase boards and markers (or scratch paper)
• Multiplication fact/partial product recording chart (Tens / Ones / Total)
• Student notebook or worksheet packet for classwork
• Exit ticket slips
• Answer key for bell work correction
• Teacher problem cards (4×23, 6×14, 3×42, 7×18)

Assessment

• During bell work correction: listen for the reason behind the corrected error (place value or regrouping).
• During guided practice: quick teacher checks for correct partial products and matching equations.
• Exit ticket: verify both the correct final product and a clear tens/ones explanation or model.

Differentiation

• Support: Provide a partially drawn area model for the first guided problem; include a sentence starter: “I multiplied ___ tens and ___ ones, then I added.”
• Support for struggling students: Use a tens/ones partial products chart and require only partial products + total (algorithm optional at first).
• Extension: For students finishing early, give an extra challenge: “Create your own 1-digit × 2-digit problem where regrouping is required, and show tens/ones partial products.”
• EAL/SEN: Allow visual explanation (area model) instead of lengthy writing; offer a word bank for steps (“tens,” “ones,” “partial product,” “total,” “equation”).

Lesson outcomes (students)

• Students can correctly multiply a 1-digit factor by a 2-digit factor, reaching at least 5 accurate classwork problems and demonstrating reasoning using tens/ones or an area model.