The first three lessons of this unit help students make sense of division situations. In this opening lesson, students begin thinking about the relationships between the numbers in a division equation. They see that they can estimate the size of the quotient by reasoning about the relative sizes of the divisor and the dividend.
Students begin exploring these relationships in concrete situations. For example, they estimate how many thinner and thicker objects are needed to make a stack of a given height, and how many segments of a certain size make a particular length.
Later, they generalize their observations to division expressions (MP7). Students become aware that dividing by a number that is much smaller than the dividend results in a quotient that is larger than 1, that dividing by a number that is much larger than the dividend gives a quotient that is close to 0, and that dividing by a number that is close to the dividend results in a quotient that is close to 1.
- Comprehend the terms “dividend” and “divisor” (in spoken language) to refer to the numbers in a division problem.
- Explain (orally) how to estimate quotients, by comparing the size of the dividend and divisor.
- Generalize about the size of a quotient, i.e., predicting whether it is a very large number, a very small number, or close to 1.
Let’s explore quotients of different sizes.
Print and cut up slips containing expressions from the blackline master. Consider copying Set 1 and Set 2 on paper of different colors. Prepare 1 copy (8 slips of Set 1 and 8 slips of Set 2) for every 3 students.
- When dividing, I know how the size of a divisor affects the quotient.