We are doing a garden design project as a follow up to our measurement unit. Using grid paper where 1 square equals 1 foot, a student needs to draw and cut out a square planter with side length 2' 4". He comes to me to ask how to do this. Fair enough. 4" can be tricky. It is a fraction of a foot.
The conversation below occurs more or less as follows (at several different times, with the same student and with other students):
Me: How much of a foot is 4 inches?
Me: No, just the 4 inches.
Student: Oh, 0.4.
Me (thinking): He's stuck in a base 10 metric system. Let's try something else.
Me: OK. How many inches are in half a foot?
Me (thinking): What?!?! Oh! He means 50%.
Me: How many inches are in half a foot?
Me: No. Inches. How many inches?
Student: Oh, 0.5.
Me: You are thinking about 50% right? I am asking you how many inches?
Me: OK. How many inches in a whole foot?
Student: What? Ummmm 12.
Me: Right! So how many inches in half a foot?
At this point, the student starts writing ratios to do a unit conversion, converting 4 inches to feet. Then he grabs his papers and says, "I'll work on it." But, he doesn't really work on it. Later when I drop by to see his progress, he has nothing. But he stills wants me to draw 2' 4" for him.
It is so much easier to just draw it for him and walk away. Miraculously, I resist this urge and proceed to have another conversation as before. This time, he gets it (at least he guessed the right answer) and he draws the square.
But now, there is a circle with radius 1' 3". Oh No!