Question

Ms. Howe's students are learning how to use models to help them answer word problems. The models use bars to represent the relationships between the given quantities and the unknown quantity. In each model, the unknown quantity is represented with a question mark. The quantities given in the word problem occupy the other boxes. Ms. Howe shows the following model to her students. The model shows a whole number that is missing, it is broken into 3 parts in an area model. Two thirds are represented as one part and the remaining 1/3 is separate. Which of the following word problems best corresponds to the model shown?

A. "Jill had 9 apples, and she gave away some. Now she has 3 apples left. How many apples did she give away?"
B. "A pizza is divided into 3 equal parts. Two of the parts have pepperoni, and the remaining part has mushrooms. What fraction of the pizza has mushrooms?"
C. "A rectangle is divided into three equal parts. Two of the parts are shaded, and the remaining part is not shaded. What fraction of the rectangle is not shaded?"
D. "John had a total of 15 marbles. He gave away some, and now only 5 marbles are left. How many marbles did he give away?"

Answer 1

The corresponding word problem to Ms. Howe's bar model is C, as it pertains to dividing a rectangle into three equal parts, with two-thirds shaded, and asks for the fraction of the part that is not shaded.

Step-by-step explanation:

The word problem that best corresponds to Ms. Howe's bar model is "C. A rectangle is divided into three equal parts. Two of the parts are shaded, and the remaining part is not shaded. What fraction of the rectangle is not shaded?" This problem directly relates to the model where the whole is represented as an area divided into three equal parts. The shaded portion represents two-thirds of the area (⅓ each), while the non-shaded portion represents the remaining one-third (⅓).

In this problem, the two shaded parts correspond to the two parts of the bar model that are filled, and the one non-shaded part corresponds to the empty part of the model with a question mark. Therefore, the fraction of the rectangle that is not shaded is indeed one-third, which aligns with the model presented by Ms. Howe.