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Multi-Digit Multiplication with Partial Products

  • Grade 4
  • Mathematics
  • 4.NBT.B.5
  • Operations & Algebraic Thinking
  • Free lesson

Aligned to 4.NBT.B.5 — Common Core State Standards for Mathematics.

What this lesson teaches

Break each number apart by place value, multiply the parts, then add them back together. The area model draws this as a rectangle split into pieces — it shows why multi-digit multiplication works instead of just memorizing steps.

Worked examples

Example 1

36 × 24 → split into (30+6) and (20+4). Partial products: 30×20=600, 30×4=120, 6×20=120, 6×4=24. Add: 600+120+120+24 = 864.

Example 2

7 × 58 → split 58 into (50+8). Partial products: 7×50=350 and 7×8=56. Add: 350+56 = 406.

Example 3

Every partial product is a piece of the area model's rectangle. Forget one piece and the answer comes up short — 36×24 needs all four, not just 30×20 and 6×4.

Practice questions

  1. Use partial products for 47 × 23.
  2. Draw an area model for 52 × 16.
  3. Explain why 25 × 100 is easy but 25 × 99 is one group of 25 less.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Multiplicación de números de varios dígitos con productos parciales

Separa cada número por valor posicional, multiplica las partes y luego súmalas. El modelo de área lo representa como un rectángulo dividido en secciones — muestra por qué funciona la multiplicación de varios dígitos en lugar de solo memorizar pasos.

Ejemplo 1: 36 × 24 → separa en (30+6) y (20+4). Productos parciales: 30×20=600, 30×4=120, 6×20=120, 6×4=24. Suma: 600+120+120+24 = 864.

Ejemplo 2: 7 × 58 → separa 58 en (50+8). Productos parciales: 7×50=350 y 7×8=56. Suma: 350+56 = 406.

Ejemplo 3: Cada producto parcial es un pedazo del rectángulo del modelo de área. Si olvidas uno, la respuesta sale corta — 36×24 necesita los cuatro, no solo 30×20 y 6×4.

More Operations & Algebraic Thinking lessons

Multi-Step Word Problems4.OA.A.3Factors, Multiples, and Patterns4.OA.B.4Times as Many: Multiplication as Comparison4.OA.A.1Word Problems with Times as Many4.OA.A.2Number and Shape Patterns4.OA.C.5

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