Students should begin dividing with base ten materials. At this grade level, it is important for students to understand that division has two distinct meanings: "number of groups" or "how many groups." For example, if students are dividing a pizza by three, they can either share with three friends or give three slices to as many friends as possible. An interesting initial activity is to give students base ten materials representing 165 and ask them to demonstrate division by four. With no further instruction, some students will begin making four equal groups and others will make as many groups of four as possible. Encouraging students to share their strategies will help your class see there are different acceptable answers.
At first, any algorithm should be connected to students' previous work with base ten materials. Traditional long division can be matched step by step to division with base ten blocks and is useful for this reason. Simpler to use is short division, in which only the quotient and remainder are recorded at each step. Finally, students can also find success using a repeat subtraction model. For example, to divide a number by four, keep track of how many times four can be subtracted from the dividend. A quicker version of repeat subtraction is to subtract multiples of the divisor. For example, take away 100 groups of four at a time, or subtract 400 from the dividend.
Using real-life contexts, students should explore the appropriate treatment of remainders. If they are finding out how 91 students will fit on three buses, the answer 30R1 is not practical. Through various problem-solving activities, students should recognize that remainders can be ignored, the answer can be rounded up to include the remainder, the remainder can be split into a fraction or a special situation can be applied. The bus problem is an example of a special situation: it would be unrealistic to hire an entire extra bus for one student, leave the student behind or split the student into three equal pieces.
Typically, fourth-grade students encounter "rate" questions, such as "Kevin earned $45 in nine hours. What is his hourly wage?" Students should also explore "comparison" problems ("Andrea saved $52 and David has half as much") and "combination" problems ("The sandwich shop has 12 different menu items and two types of bread. How many fillings are there?") Students can also begin to solve division problems by estimating quotients.