Notes & FAQs

For students to understand the division, area and other representations these are key. For example, students often come with the misconception that division always makes a number smaller. Using base ten tiles or pictures with the problem 2.1 / .2 could help challenge this misconception. The problem becomes how many two-tenths are in two wholes and one tenth or how many two-tenths are in twenty-one tenths. The answer of 10.5 makes sense as a bigger number as it is the number of groups that can be made. This could also be represented linearly on a number line as an alternate representation. By the way, part of the misconception might be related to not understanding that there are two ways to divide: partitive division and measurement division.

Before using base ten tiles for division, it would help for students to have familiarity with them when adding, subtracting, and multiplying; therefore 6.NS.3 has been placed in this unit next. After utilizing concreteness-fading to move toward the standard algorithm, 6.NS.2 can be accomplished while continuing to work on the division portion of 6.NS.3.  By the way, 6th grade should be the FIRST TIME students learn the traditional algorithm for division if prior grade levels have been following the CCCS standards.

Solving real-world problems such as finding the area, surface area or volume of a figure sets the stage contextually for expressions, equations & even inequalities later by dealing with numerical expressions in simple equations.