# Lesson 10

Using Long Division

### Lesson Narrative

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. In the partial quotients method, all numbers and their meaning are fully and explicitly written out. For example, to find $$657 \div 3$$ 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.

In addition to making sense of long division and using it to calculate quotients, students also analyze some place-value errors commonly made in long division (MP3).

### Learning Goals

Teacher Facing

• Interpret the long division method, and compare and contrast it (orally) with other methods for computing the quotient of whole numbers.
• Recognize and explain (orally) that long division is an efficient strategy for dividing numbers, especially with multi-digit dividends.
• Use long division to divide whole numbers that result in a whole-number quotient, and multiply the quotient by the divisor to check the answer.

### Student Facing

Let’s use long division.

### Required Preparation

Some students might find it helpful to use graph paper to help them align the digits as they divide using long division and the partial quotients method. Consider having graph paper accessible throughout the lesson.

### Student Facing

• I can use long division to find a quotient of two whole numbers when the quotient is a whole number.

Building On

Building Towards

### Glossary Entries

• long division

Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right.

For example, here is the long division for $$57 \div 4$$.

$$\displaystyle \require{enclose} \begin{array}{r} 14.25 \\[-3pt] 4 \enclose{longdiv}{57.00}\kern-.2ex \\[-3pt] \underline{-4\phantom {0}}\phantom{.00} \\[-3pt] 17\phantom {.00} \\[-3pt]\underline{-16}\phantom {.00}\\[-3pt]{10\phantom{.0}} \\[-3pt]\underline{-8}\phantom{.0}\\ \phantom{0}20 \\[-3pt] \underline{-20} \\[-3pt] \phantom{00}0 \end{array}$$