# Solutions to a Math Problem Reaction Paper

**Pages:** 4 (1249 words) ·
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1 · **File:** .docx · **Level:** College Senior · **Topic:** Education - Mathematics

Problem Solving Report

The task that was proposed to the students was as follows: Conrad's Taxi Service charges $1.50 for the first mile and $.90 for each additional mile. How far could Mr. Kulp go for $20 if he gives the driver a $2 tip? (taken from Holtz and Malen). The students were 7th grade students, and a group of 5 students was formed. According to the instructions, the students worked separately to solve the problem, then jointly. It is interesting to note (and this will be further expanded when describing the choice and interaction between the students) that some of the students were able to solve the problem individually on their own and that, for them, the interaction phase implied convincing the other students of the viability of their solutions.

The standard used here was CCSS.MATH.CONTENT.7.EE.B.4, which states the "use of variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities" (Common Core). Particularly CCSS.MATH.CONTENT.7.EE.B.4.A was useful in this case, namely the solving word problems by conceiving equations of the form px + q = r and p (x + q) = r, where p, q, and r are specific rational numbers.

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for only $8.97. The group was formed relying on the principle of differentiation. To the degree to which this was possible, the aim was for a mixed group boys/girls. At the same time, there was a preference for an uniform representation knowledge-wise: the student were selected to have average math scores and no obvious aptitude or extraordinary performance in this field. In order to further study the interaction of particular individuals with the rest of the group, an ESL student was included in the group.

## Reaction Paper on

In terms of the learning trait, two of the students included in the group were known for their extracurricular activities in art-related areas, including drama, art and music. The reason they were selected was so as to compare their solution to the problem to the others'. One would want to understand whether particular hobbies or higher creativity provide different approaches and solutions to a math problem.

There were five students, three boys and two girls. They were also taking the same math class and this is how they were selected for the test. They were also among the best math students, so their proficiency was an additional argument in their selection. There was a meeting with their math teacher (and without the students) so as to understand more of their individual characteristics and personalities. With that in mind, this is how I have come to know so much about them.

This was important to understand whether someone who worked out the problem on his own would also be willing to share it with the others in the group or whether he preferred to wait for a group solution to be successfully worked out. It would also be interesting to understand whether some of the group participants would try to impose their own solution in the group.

The first thing to note from the interaction of the students was that two large categories of math thinking can be differentiated: algebraic and graphic. The first category noted with X the number of miles and, to similar degrees, came up with the formula:

1.50 X + 0.90X + 2 = 20. In this formula, 20 is the total amount of money that Mr. Kulp has, 0.90 the sum paid for each additional mile, 1.50 the sum for the first mile (note that this is the same X, representing the number of miles). Working X from this algebraic equation, they came up with the result that Mr. Kulp could go 7.50 miles with the amount of money he has,… [END OF PREVIEW] . . . READ MORE

The task that was proposed to the students was as follows: Conrad's Taxi Service charges $1.50 for the first mile and $.90 for each additional mile. How far could Mr. Kulp go for $20 if he gives the driver a $2 tip? (taken from Holtz and Malen). The students were 7th grade students, and a group of 5 students was formed. According to the instructions, the students worked separately to solve the problem, then jointly. It is interesting to note (and this will be further expanded when describing the choice and interaction between the students) that some of the students were able to solve the problem individually on their own and that, for them, the interaction phase implied convincing the other students of the viability of their solutions.

The standard used here was CCSS.MATH.CONTENT.7.EE.B.4, which states the "use of variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities" (Common Core). Particularly CCSS.MATH.CONTENT.7.EE.B.4.A was useful in this case, namely the solving word problems by conceiving equations of the form px + q = r and p (x + q) = r, where p, q, and r are specific rational numbers.

Get full access

for only $8.97. The group was formed relying on the principle of differentiation. To the degree to which this was possible, the aim was for a mixed group boys/girls. At the same time, there was a preference for an uniform representation knowledge-wise: the student were selected to have average math scores and no obvious aptitude or extraordinary performance in this field. In order to further study the interaction of particular individuals with the rest of the group, an ESL student was included in the group.

## Reaction Paper on *Solutions to a Math Problem* Assignment

In terms of the learning trait, two of the students included in the group were known for their extracurricular activities in art-related areas, including drama, art and music. The reason they were selected was so as to compare their solution to the problem to the others'. One would want to understand whether particular hobbies or higher creativity provide different approaches and solutions to a math problem.There were five students, three boys and two girls. They were also taking the same math class and this is how they were selected for the test. They were also among the best math students, so their proficiency was an additional argument in their selection. There was a meeting with their math teacher (and without the students) so as to understand more of their individual characteristics and personalities. With that in mind, this is how I have come to know so much about them.

This was important to understand whether someone who worked out the problem on his own would also be willing to share it with the others in the group or whether he preferred to wait for a group solution to be successfully worked out. It would also be interesting to understand whether some of the group participants would try to impose their own solution in the group.

The first thing to note from the interaction of the students was that two large categories of math thinking can be differentiated: algebraic and graphic. The first category noted with X the number of miles and, to similar degrees, came up with the formula:

1.50 X + 0.90X + 2 = 20. In this formula, 20 is the total amount of money that Mr. Kulp has, 0.90 the sum paid for each additional mile, 1.50 the sum for the first mile (note that this is the same X, representing the number of miles). Working X from this algebraic equation, they came up with the result that Mr. Kulp could go 7.50 miles with the amount of money he has,… [END OF PREVIEW] . . . READ MORE

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