In earlier lessons, students have learned systematic strategies for solving application problems based on a single operation of addition or subtraction with whole numbers. These strategies were taught in the context of and applied to three general types of scenarios: 1) combination situations in which two numbers representing separate groups or measures were either combined or separated, 2) comparison situations in which two numbers representing separate groups or measures were compared to find either the larger or the smaller number, and 3) increase/decrease situations (also referred to as “change” situations). Within each category, the strategies allow students to determine which operation is needed to solve the problem - addition or subtraction.
In this lesson, students extend the use of the same strategies for the same types of problems to those in which the number representing the groups or measures are fractions instead of whole numbers. The fractions used in these problems are both proper and improper fractions.
In earlier lessons, students have learned systematic strategies for solving application problems based on a single operation of multiplication or division with whole numbers. These strategies were taught in the context of and applied to two general types of scenarios: 1) “equal groups” situations in which the values on one measurement dimension are parts of a whole that are segregated on the basis of the values on the second measurement dimension, and 2) multiplicative “comparison” situations, also referred to as “times as many” situations, in which the values on the two measurement dimension are not parts of a whole, but are independent of each other. The value on one dimension is compared to the value on a second dimension.
Within each category, the strategies allow students to determine which operation is needed to solve the problem - multiplication or division.
In this lesson, students extend the use of the same strategy described above for the second type of situation, equal group situations. The only difference is that the problems are based on situations involving a fraction and a whole number instead of just whole numbers. When these problems involve fractions as well as whole numbers, they are referred to as “fraction of” problems rather than “equal group” problems.
In this lesson, students extend the use of the same strategy for the first situation, equal group situations, for the same types of problems in which the number representing the groups or measures are fractions instead of whole numbers.
When these problems involve fractions instead of whole numbers, they are still referred to as “times as many” problems.
The fractions used in these problems are both proper and improper fractions.