So far, students have divided whole numbers that result in whole-number quotients. In this lesson, they start performing division in which the quotient or dividend are decimals. First, they perform division of two whole numbers that result in a terminating decimal. Then, they look at division of a decimal by a whole number. In both cases, students begin reasoning about the problems by using base-ten diagrams. They see that, just like the units representing powers of 10, those for powers of 0.1 can also be divided into groups. They then divide using long division and notice that the principle of placing base-ten units into equal-size groups is likewise applicable.
Students analyze, explain, and critique various ways of reasoning about division (MP3).
- Divide decimals by whole numbers, and explain the reasoning (orally and using other representations).
- 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.
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://ggbm.at/NJPVks38.
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.
- I can divide a decimal by a whole number.
- I can use long division to find the quotient of two whole numbers when the quotient is not a whole number.
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