In this Grade 5 Illustrative Mathematics lesson, students interpret partial products diagrams to multiply three-digit numbers by two-digit numbers, building on the place value strategies introduced in Grade 4. Using rectangular diagrams, students decompose factors and calculate individual partial products before combining them to find the full product, as in 222 × 14 broken into 2,800 + 280 + 28. This lesson from Chapter 4 lays the groundwork for understanding the standard multiplication algorithm covered later in the chapter.
Section 1
Decomposing Three-Digit Numbers by Place Value
A three-digit number can be decomposed into its place values: .
This is represented on a place value chart by placing disks in the hundreds column, disks in the tens column, and disks in the ones column.
Section 2
Representing Multiplication with an Array
To multiply two two-digit numbers, we can decompose each number into tens and ones and use the distributive property.
This can be visualized with an array, where the total area is the sum of four smaller areas, known as partial products.
For factors and :
Section 3
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 4
Area Models for 3-Digit by 2-Digit Multiplication
To multiply a three-digit number by a two-digit number, we can decompose them by place value and apply the distributive property. This creates six partial products, which are the areas of the smaller rectangles in the model.
Expand to review the lesson summary and core properties.
Section 1
Decomposing Three-Digit Numbers by Place Value
A three-digit number can be decomposed into its place values: .
This is represented on a place value chart by placing disks in the hundreds column, disks in the tens column, and disks in the ones column.
Section 2
Representing Multiplication with an Array
To multiply two two-digit numbers, we can decompose each number into tens and ones and use the distributive property.
This can be visualized with an array, where the total area is the sum of four smaller areas, known as partial products.
For factors and :
Section 3
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 4
Area Models for 3-Digit by 2-Digit Multiplication
To multiply a three-digit number by a two-digit number, we can decompose them by place value and apply the distributive property. This creates six partial products, which are the areas of the smaller rectangles in the model.