Whole-Number Multiplication

Overview

Today students practice multiplying and dividing multi-digit numbers using strategies and models, then connect those ideas to the standard algorithms. The lesson also includes fraction division word problems to strengthen understanding that division means “how many groups” or “how much per group.”

Learning intentions

Students will be able to:

• fluently multiply multi-digit numbers using a clear standard algorithm.
• fluently divide multi-digit numbers using the standard algorithm.
• interpret remainders in context when appropriate.
• interpret and compute quotients of fractions and solve related word problems.

Success criteria

• I can multiply multi-digit numbers correctly using the standard algorithm.
• I can divide multi-digit numbers correctly using the standard algorithm.
• I can explain what the quotient means in a word problem.
• I can compute a fraction division quotient using models or equations.

Curriculum links

• The Number System: fluently divide multi-digit numbers using the standard algorithm (6.NS.B.2).
• The Number System: fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm (6.NS.B.3).
• The Number System: interpret and compute quotients of fractions; solve word problems involving division of fractions by fractions (6.NS.A.1).

Lesson structure (60 minutes)

1. 0–5 min · Warm-up quick check. Teacher displays two quick items: one multi-digit multiplication and one division with small numbers; students solve silently, then hold up answers. Students compute and show work enough to explain one method.

2. 5–12 min · Mini-lesson: meaning of division (groups and per group). Teacher briefly reviews that division can represent “how many in each group” and “how many groups” and that quotient answers depend on what is being shared. Students write a one-sentence explanation for each meaning using a simple example from the board.

3. 12–24 min · Direct teach: multiplication standard algorithm (practice first). Teacher models multiplying 428 × 37 (show place-value partial products, then compact into the standard algorithm), emphasizing alignment of place value. Students complete a similar problem: 356 × 28, using the algorithm and checking reasonableness.

4. 24–36 min · Direct teach: division standard algorithm (fluency target). Teacher models dividing 6,492 ÷ 36 step-by-step (estimate the first quotient digit, multiply back, subtract, bring down, repeat). Students work a parallel problem: 7,560 ÷ 45; they must record each subtraction step and include a quick estimate to check.

5. 36–44 min · Guided connection: multiplication/division relationship. Teacher asks: “If quotient q is correct, what should q × divisor equal (plus any remainder)?” and demonstrates a check using the division model. Students perform a check for their division problem by multiplying quotient × divisor and comparing to the dividend context.

6. 44–56 min · Fraction division word problems (visual model + equation). Teacher presents: “How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?” Students interpret division as equal sharing, draw a simple model (rectangles/strips), then write an equation to compute the quotient; teacher circulates and prompts for reasoning.

7. 56–60 min · Exit ticket (1 item, mixed focus). Teacher gives one short task: compute (2/3) ÷ (3/4) and briefly explain what the quotient means using a sentence or diagram. Students submit work showing either a visual model or an equation explanation.

Resources

• Board/markers or slides with example problems
• Grid paper and pencils
• Fraction strips or rectangle models (paper cutouts)
• Decimal/place-value chart (optional)
• Exit ticket sheet (1 question per student)
• Stopwatch or timer for pacing
• Calculator (optional for checks only; not for primary computation unless teacher allows)

Assessment

• Warm-up: check for correct answers and quick identification of common errors (place-value misalignment, estimate issues).
• During guided division: listen for correct estimation and use of “multiply back” checks.
• Exit ticket: confirm students can compute a fraction division quotient using a model or equation and explain meaning.

Differentiation

• Support: provide sentence starters such as “The quotient tells me ____,” and provide a partially completed standard algorithm template for one example problem.
• Support for division: allow a “check step” card showing: estimate → multiply back → subtract → bring down.
• Extension: challenge students to create their own word problem that matches (a/b) ÷ (c/d) and solve it with a visual model.
• EAL/SEN considerations: use consistent vocabulary (“divisor,” “dividend,” “quotient,” “remainder,” “equal groups”), and offer an alternate representation (drawings of models) for students who struggle with explanation writing.