This lesson introduces students to long division. Students see that in long division the meaning of each digit is intimately tied to its place value, and that it is an efficient way to find quotients.

When using partial quotients to calculate quotients, all numbers and their meaning are fully and explicitly written out. For example, to find we write that there are at least 3 groups of 200, record a subtraction of 600, and show a difference of 57. In long division, instead of writing out all the digits, we rely on the position of any digit—of the quotient, of the number being subtracted, or of a difference—to convey its meaning, which simplifies the calculation.

Students begin by analyzing a long division for . Having seen the same division calculated using partial quotients, students can better interpret what each digit represents and can focus on making sense of the structure of the algorithm. Next, students use the algorithm to perform division with whole-number dividends, divisors, and quotients.

An optional activity allows students to further practice using long division and to analyze a place-value error commonly made in long division.