I have a logical reasoning question here.I want to know how best to explain my answer to a grade 7 class.Any ideas?
At a local furniture shop twelve chairs cost as much as 2 wardrobes, 4 tables cost as much as 6 chairs, and 8 bookcases cost as much as two tables. How many wardrobes could I exchange for 128 bookcases?
My answer was 8 wardrobes can be exchanged for 128 bookcases
(because 16 bookcases = 4 tables = I wardrobe)
I think this is a fine way of explaining things. The transitive property is key here, and it's important to show each reduction as they come in a chain so that the class can see how you get from the beginning to the end. In particular, perhaps do this in two steps, first reduce bookcases to tables (i.e. first divide by 4 in the 16/4 conversion to arrive at 32) then from there reduce from tables to wardrobes (i.e. then divide by 4 in the 4/1 conversion to arrive at
. First time students can grasp things much more easily from composing actual calculations rather than the later, more advanced, composing of conversion rates to do it all at once (which is what you did with the 16/1).