Student Approach and Difficulties
Approaches:
1.Students can either start with the graphing or algebra. Some may want to see how many marbles it takes to get to 100 ml and then figure out their rate, others may feel more comfortable proceeding step by step and then plotting their points.
2.Students may show their graph as linear or show the small discrepancies between points ( this would be a good place to talk about real life and modeling with linear equations, which is basically what they are doing).
3.Students may keep adding marbles until the glass overflows or they may end up with the marbles overtaking the water!
Difficulties:
Students will need to understand the difference between and independent and dependent variable and they may get this mixed up.
Students may have difficulty understanding a fractional slope and think they have done something wrong.
Students may plot their water as the abcissa and their marbles as the ordinate value, which may confuse them.
Also students could start at different water levels and have different y intercepts, which may be confusing, because they will get a different equation from their neighbor.
Student
1.Students can either start with the graphing or algebra. Some may want to see how many marbles it takes to get to 100 ml and then figure out their rate, others may feel more comfortable proceeding step by step and then plotting their points.
2.Students may show their graph as linear or show the small discrepancies between points ( this would be a good place to talk about real life and modeling with linear equations, which is basically what they are doing).
3.Students may keep adding marbles until the glass overflows or they may end up with the marbles overtaking the water!
Difficulties:
Students will need to understand the difference between and independent and dependent variable and they may get this mixed up.
Students may have difficulty understanding a fractional slope and think they have done something wrong.
Students may plot their water as the abcissa and their marbles as the ordinate value, which may confuse them.
Also students could start at different water levels and have different y intercepts, which may be confusing, because they will get a different equation from their neighbor.
Student