Write a statement about how much the average score is increased if each individual score is increased x points. Develop an argument to convince another student that the statement is true. Some students might need more than three instances to form a conjecture. This exercise focuses on a student's ability to generalize from specific cases. Students who can find the answer for each specific problem but who are unable to state the general case are less able to use inductive reasoning than those who can state the general case after three or four instances.
Students can work in small groups.
A computer can be used to investigate situations other than the three posed or to consider the scores of an entire class. The argument is plausible if it makes common sense and is mathematically correct. Students would need to collect data and set up and solve a proportion to answer this question. Other topics can be investigated in a similar way. Grades 9-12 1.