Lesson 11

Dividing Numbers that Result in Decimals

Lesson Narrative

So far, students have divided whole numbers that result in whole-number 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: base-ten 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 base-ten diagrams in this lesson. If drawing them is a challenge, consider giving students access to:

• Commercially produced base-ten blocks, if available.
• Paper copies of squares and rectangles (to represent base-ten units), cut up from copies of the blackline master of the second lesson in the unit.
• Digital applet of base-ten 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.

Student Facing

• I can use long division to find the quotient of two whole numbers when the quotient is not 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 $$57 \div 4$$.

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

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