When first learning to multiply two two-digit numbers your child will use the area model.
To start, your child will use her knowledge of place value to decompose into tens and ones. To decompose means to break apart. Let’s decompose these numbers by the value of each digit.
The value of two tens is twenty. The value of three ones is three. Three tens is thirty. And five ones is five. Decomposing numbers allows your child to use the multiplication fluency she developed in third grade to multiply large numbers with mental math.
So, what is twenty-three times thirty-five?
Three tens times two tens equals sixty tens or six-hundred. Thirty tens times three equals nine tens or ninty. Twenty tens times five equals ten tens or one-hundred. And three times five equals fifteen.
Your child will then add these products together. Six-hundred plus ninety equals six-hundred ninety. One-hundred plus fifteen equal one-hundred fifteen. By fourth grade, your child will fluently add three-digit numbers, like this, using the standard algorithm.
Your child can clearly see why twenty-three times thirty-five equals eight-hundred-five. The area model gives your child a visual representation that decomposes the numbers she is multiplying. At this point in fourth grade, your child is developing a pictorial level of understanding, which will give her a strong foundation for using partial products and, later, using the standard algorithm to multiply.