Fourth-graders might use a visual drawing to depict factor multiplication. The drawing method uses something like graph boxes in sets related to the numbers. For example, if the factors are 21 and 12, the student might draw a box of 20 squares across and 10 squares down to represent 20 x 10. The student then draws 2 x 20 with two boxes of 20 squares across. The student then draws a box of 10 squares in row 1 to represent 10 x 1. The final part is drawing two small squares, separated, to show 2 x 1. The student then adds all of the numbers together, such as 200 + 40 + 10 + 2, to get a total of 252.
Writing out the factors is the common method of multiplying factors that have more than one-digit numbers. For example, if the problem is 23 x 13, the student writes out all of the parts below the problem. First the student takes 3 x 3, or the one's place, to get 9. The 9 goes to one side under the problem. The student then multiplies the 3 from the bottom one's place by 20 to get 60. She then writes the 60 below the 9 on the bottom. From there, she multiplies 10 x 3 to get 30. The 30 is placed below the 60. Finally, she multiplies 10 x 20 to get 200. After adding the numbers together, she would arrive at 299.
In the fourth grade, beyond adding double-digit numbers to multiplication, students learn how to multiply more than two numbers. Three-number factors are usually written with a bracket, such as 2 x (3 x 4). Fourth-graders solve the problem by first multiplying the numbers in the bracket, or the 3 x 4, then multiplying the first number by the parenthetical answer. For example, the order of 2 x (3 x 4) ends up with 2 x (12) for an answer of 24.
Multiplying, or factoring, can vary by student. When students first learn factoring skills, they might require visuals, such as drawn boxes, tally marks or even counting on fingers to better understand the problems. From there, students learn other factoring methods. Drawing boxes, tally marks and other visuals to represent numbers for factoring requires the most time to figure out the problem because of the time needed to draw the boxes.