Lesson 11
Dividing Numbers that Result in Decimals
Lesson Narrative
So far, students have divided whole numbers that result in wholenumber quotients. In the next three lessons, they work toward performing division in which the divisor, dividend, and quotient are decimals. In this lesson, they perform division of two whole numbers that result in a terminating decimal. Students divide using all three techniques introduced in this unit: baseten diagrams, partial quotients, and long division. They apply this skill to calculate the (terminating) decimal expansion of some fractions.
Students analyze, explain, and critique various ways of reasoning about division (MP3).
Learning Goals
Teacher Facing
 Interpret different methods for computing a quotient that is not a whole number, and express it (orally and in writing) in terms of “unbundling.”
 Use long division to divide whole numbers that result in a quotient with a decimal, and explain (orally) the solution method.
Student Facing
Let’s find quotients that are not whole numbers.
Required Preparation
Students may choose to draw baseten diagrams in this lesson. If drawing them is a challenge, consider giving students access to:
 Commercially produced baseten blocks, if available.
 Paper copies of squares and rectangles (to represent baseten units), cut up from copies of the blackline master of the second lesson in the unit.
 Digital applet of baseten representations https://www.geogebra.org/m/FXEZD466
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.
Learning Targets
Student Facing
 I can use long division to find the quotient of two whole numbers when the quotient is not a whole number.
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 \(57 \div 4\).
\(\displaystyle \require{enclose} \begin{array}{r} 14.25 \\[3pt] 4 \enclose{longdiv}{57.00}\kern.2ex \\[3pt] \underline{4\phantom {0}}\phantom{.00} \\[3pt] 17\phantom {.00} \\[3pt]\underline{16}\phantom {.00}\\[3pt]{10\phantom{.0}} \\[3pt]\underline{8}\phantom{.0}\\ \phantom{0}20 \\[3pt] \underline{20} \\[3pt] \phantom{00}0 \end{array} \)