Math Problem Statement

what would be the unit rate for the following tables:

What would be the unit rate for the following tables?

Solution

To calculate the unit rate for the tables:

Table A

The unit rate is the change in grade per unit score. Using the data:

  • When the score increases from 00 to 11, the grade increases by 250=2525 - 0 = 25.
  • Similarly, from 11 to 22, 22 to 33, and 33 to 44, the increase in grade is consistently 2525.

Unit rate for Table A: 2525 (grade per score).

Table B

Similarly, calculate the unit rate:

  • When the score increases from 00 to 11, the grade increases by 4020=2040 - 20 = 20.
  • From 11 to 22, 22 to 33, and 33 to 44, the increase in grade is 2020.

Unit rate for Table B: 2020 (grade per score).


Would you like to know how this applies to other scenarios or additional insights?


Follow-up Questions:

  1. What does the unit rate represent in these tables?
  2. How can we compare the proportionality of Table A and Table B?
  3. Can we express the relationships in these tables using equations?
  4. What happens to the unit rate if the scores are multiplied by a constant factor?
  5. How could these tables be used to create graphs, and what would their slopes indicate?

Tip:

The unit rate corresponds to the slope of the line if the data is graphed, showing how one variable changes with respect to the other.

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Math Problem Analysis

Mathematical Concepts

Proportionality
Rates
Linear Relationships

Formulas

Unit rate = Change in Grade / Change in Score

Theorems

Linear Proportionality

Suitable Grade Level

Grades 6-8