In this Grade 4 enVision Mathematics lesson, students learn how to use area models and the Distributive Property to multiply two 2-digit numbers by breaking apart factors into tens and ones and finding partial products. The lesson guides students through multiple strategies for problems like 25 × 15, showing how splitting factors such as 25 into 20 + 5 and 15 into 10 + 5 generates up to four simpler multiplication problems whose products are then added together. This foundational skill in Chapter 4 builds fluency with 2-digit multiplication and connects visual area models to the algebraic structure of the Distributive Property.
Section 1
Area Model with Four Partial Products
When you multiply two 2-digit numbers, the four partial products you calculate correspond to the areas of the four smaller rectangles in an area model.
For factors decomposed as and , the four partial products are , , , and .
Section 2
Area Model with Two Partial Products
To multiply a two-digit number by another two-digit number, you can decompose one factor into its tens and ones. The total product is the sum of the two resulting partial products. This can be represented by an area model split into two sections. For a problem , where is composed of (tens) and (ones), the property is:
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Section 1
Area Model with Four Partial Products
When you multiply two 2-digit numbers, the four partial products you calculate correspond to the areas of the four smaller rectangles in an area model.
For factors decomposed as and , the four partial products are , , , and .
Section 2
Area Model with Two Partial Products
To multiply a two-digit number by another two-digit number, you can decompose one factor into its tens and ones. The total product is the sum of the two resulting partial products. This can be represented by an area model split into two sections. For a problem , where is composed of (tens) and (ones), the property is:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter