Lesson 19

The purpose of this lesson is for students to recognize that the two interpretations of division still apply when dividing larger numbers and to use base-ten diagrams to interpret and represent division within 100.

Prior to this lesson, students have interpreted and represented division in terms of making equal-size groups. In this lesson, they revisit the two interpretations of division and recall that the divisor can be seen as either the number of groups or the size of each group.

Students use base-ten blocks and diagrams to analyze and represent division expressions such as \(55 \div 5\) and \(84 \div 7\). They see that, depending on the numbers involved, one interpretation of division may be more useful or productive than the other.

Students also recognize that it is helpful to use tens and ones to make equal groups (for example, to think of 84 as 8 tens and 4 ones, rather than 84 ones), and to decompose tens into ones as needed.

How is students’ knowledge of place value and the properties of operations helping them make sense of division strategies?