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.
Which of the following word problems best corresponds to the model shown?

A. Max had $24. He gave $18 to Olivia and the rest to Sarah. How much money did Max give to Sarah?
B. Max had $24. He gave 1/3 of his money to Sarah and the rest to Olivia. How much money did Max give to Olivia?
C. Max gave $24 to his friend Sarah and $18 to his friend Olivia. What is the total amount of money Max gave to his two friends?
D. Max has $24 in his piggy bank, which is 23
of the amount of money that Max has altogether. How much money does Max have altogether?

Answer 1

Option A is the correct word problem corresponding to the model. It involves a total sum of money ($24) with a known part given to Olivia ($18) and an unknown part given to Sarah, fitting the structure of bar models.

Step-by-step explanation:

The word problem that best corresponds to the model shown by Ms. Howe would be one where a total amount is given, and part of it is allocated to one person while the remainder is allocated to another person, with the second allocation being an unknown quantity. The provided options suggest different scenarios involving allocation of money among people. Considering the structure of bar models, where one bar usually represents a quantity and it is divided into parts to represent the distribution of that quantity among different entities, we can discern which option aligns with this representation.

Option A is the most fitting because it provides an initial total amount of $24, of which $18 is given to Olivia, and the rest (unknown quantity) is given to Sarah. This matches the concept of bar models, as there is a defined total and a part given away, leaving an unknown remainder. The use of bar models here would result in one bar representing the total $24, with $18 marked for Olivia, and the remaining portion marked with a question mark for Sarah.

Bar graph

,

unknown quantity

, and

allocation

are important components in understanding how the model works with the word problem.