The sixth grade assessment often has a question in which the students must identify which of four choices is an example of the (distributive property, associative property, commutative property, identity property, inverse property, foreclosed property). While I find such a question to be of some importance, I would prefer a question that tests the students' ability to apply the property, or to create examples that would explain their ability to use the property in context.
Consider the following use of the distributive property:
Luke is asked to determine the solutions to the equations 6 x 81 = M and 6 x 79 = N. How can Luke apply the distributive property and the expression "6 x 80" to determine the values of M and N?
In this case, the student must use the equations:
6 x 81 = 6 x (80 + 1) 6 x (80 + 1) = (6 x 80) + (6 x 1) = 480 + 6 = 486
6 x 79 = 6 x (80 - 1) 6 x (80 - 1) = (6 x 80) - (6 x 1) = 480 - 6 = 474
I would like feedback on this problem. I wish to hear positive and negative responses regarding the complexity of the assignment, the relative worth of the assignment compared to the current line of questioning, the use of this problem to instruct students and/or teachers on the use of mathematical properties, etc.
Thank you for any information or opinion you can give me.