Lesson 23

The purpose of this lesson is for students to divide a whole number by a decimal less than 1 by reasoning about the number of groups of one tenth or one hundredth in one whole.

In the previous lesson, students divided whole numbers by one tenth and one hundredth and made generalizations about how to divide any whole number by those units. The purpose of this lesson is for students to extend that work to divide whole numbers by any number of tenths or hundredths (with total value less than 1). Consistent divisors are used in repetition to highlight relationships between the dividends and the quotients (MP8). Students evaluate expressions with larger divisors such as \(12 \div 0.2\) in order to encourage them to use the relationship between multiplication and division. Rather than drawing 12 unit squares and dividing all of them into groups of 2 tenths, students may draw a single whole divided into 2 tenths and then use multiplication.

What aspects of today’s lesson allowed each of your students to see themselves as productive mathematical reasoners?