By the third and fourth grades, students should have grasped the basics of simple addition, subtraction, multiplication, and division, and as these young learners become more comfortable with multiplication tables and regrouping, two-digit multiplication is the next step in their mathematics educations.

Although some might question having students learn how to multiply these large numbers by hand instead of by using a calculator, the concepts behind long-form multiplication must be fully and clearly understood first so that the students are able to apply these basic principles to more advanced mathematics courses later in their education.

## Teaching the Concepts of Two-Digit Multiplication

Remember to guide your students through this process step by step, making sure to remind them that by isolating the decimal value places and adding the results of those multiplications may simplify the process, using the equation 21 X 23.

In this instance, the result of the one's decimal value of the second number multiplied by the full first number equals 63, which is added to the result of the tens decimal value of the second number multiplied by the full first number (420), which results in 483.

## Using Worksheets to Help Students Practice

Students should already be comfortable with the multiplication factors of number up to 10 prior to attempting two-digit multiplication problems, which are concepts typically taught in kindergarten through second grades, and it's equally important for third and fourth-grade students to be able to prove they fully grasp the concepts of two-digit multiplication.

For this reason, teachers should use printable worksheets like these (#1, #2, #3, #4, #5, and #6) and the one pictured to the left in order to gauge their students' understanding of two-digit multiplication. By completing these worksheets using only pen and paper, students will be able to practically apply the core concepts of long-form multiplication.

Teachers should also encourage students to work out the problems like in the above equation so that they may regroup and "carry the one" between these one's value and ten's value solutions, as each question on these worksheets requires students to regroup as part of two-digit multiplication.

## The Importance of Combining Core Math Concepts

As students progress through the study of mathematics, they will begin to realize that most of the core concepts introduced in elementary school are used in tandem in advanced mathematics, meaning that students will be expected to not only be able to compute simple addition but also make advanced calculations on things like exponents and multi-step equations.

Even in two-digit multiplication, students are expected to combine their understanding of simple multiplication tables with their ability to add two-digit numbers and regroup "carries" that occur in the computation of the equation.

This reliance on previously understood concepts in mathematics is why it's crucial that young mathematicians master each area of study before moving on to the next; they will need a complete understanding of each of the core concepts of math in order to eventually be able to solve the complex equations presented in Algebra, Geometry, and eventually Calculus.