In this Grade 5 Illustrative Mathematics lesson, students build fluency with the standard algorithm for multiplying two-digit and three-digit whole numbers, including problems that require composing multiple new units. Students explore different ways to apply the algorithm and practice placing digits strategically to maximize products, deepening their understanding of place value. The lesson addresses standard 5.NBT.B.5 within Chapter 4 on multi-digit multiplication and division.
Section 1
Calculate Partial Products
The partial products algorithm uses the distributive property to solve multiplication.
A multi-digit number is broken into the sum of its place values (expanded form), and each part is multiplied separately before adding the results.
Each partial product can be represented as a section of an array, showing how the total product is composed of smaller, manageable parts.
Section 2
The Standard Algorithm for Multiplication
The standard algorithm for multiplication is a procedure for multiplying numbers by breaking the problem into partial products.
You multiply the top factor by each digit of the bottom factor, one at a time from right to left, and then add the resulting partial products together.
Section 3
Multiplying 2-Digit Numbers Using the Standard Algorithm
To multiply two-digit numbers, calculate two partial products.
The first is the top number multiplied by the ones digit of the bottom number.
The second is the top number multiplied by the tens digit of the bottom number, with a zero placed in the ones place to account for place value.
The final product is the sum of these two partial products.
Expand to review the lesson summary and core properties.
Section 1
Calculate Partial Products
The partial products algorithm uses the distributive property to solve multiplication.
A multi-digit number is broken into the sum of its place values (expanded form), and each part is multiplied separately before adding the results.
Each partial product can be represented as a section of an array, showing how the total product is composed of smaller, manageable parts.
Section 2
The Standard Algorithm for Multiplication
The standard algorithm for multiplication is a procedure for multiplying numbers by breaking the problem into partial products.
You multiply the top factor by each digit of the bottom factor, one at a time from right to left, and then add the resulting partial products together.
Section 3
Multiplying 2-Digit Numbers Using the Standard Algorithm
To multiply two-digit numbers, calculate two partial products.
The first is the top number multiplied by the ones digit of the bottom number.
The second is the top number multiplied by the tens digit of the bottom number, with a zero placed in the ones place to account for place value.
The final product is the sum of these two partial products.