The Good and the Not So Good

The Good:

I was working with my students on Visual Patterns 102 as a warm up in class on Tuesday.  During my warm-up problems, there are generally a couple of students per class that can find the answer quickly, and others who either take longer or have a hard time understanding them at all.  While I was working this one, students kept giving me answers (129, 430, etc.) to which I usually respond “Why?” and that gets them thinking a little more.  One of my students who generally does not answer my problems raised her hand and said “I don’t know why, but they look like waffles with a bite taken out.”  The class laughed, and she thought it wasn’t particularly helpful, but I said “That’s actually a good observation.  What shape are waffles, generally?”  And as she was saying “square,” I could see others start to square 43, and one of them blurted out “1849” and I looked at the student who had described the waffle and said “Don’t forget to take a bite out” and she responded with 1848.  It  was a cool moment for that student to see an observation that she saw as a throw-away to be the right step to the solution.

The Not So Good:

Had a quiz in my 6th grade classes on Thursday that just did not go well.  I realized while I was reviewing some things with them that the differences between rational and non-rational numbers was just not something they were ready for.  But I was disappointed on their ability to identify the use of addition and multiplication properties and add and subtract negative fractions.  I think they will get the properties stuff, but does anyone have advice on adding and subtracting negative fractions?  I have a couple of ideas, but I have explained the use of improper fractions or dealing with whole numbers and fractions separately, but they seem to keep making the same mistakes (like getting a positive whole number and a negative fraction when dealing with them separately, but just putting those together and calling it their answer).

One other request for ideas: How do you get students to check for reasonableness in answers?  I ask them if their answer is reasonable when they offer it for the class, and I preach reasonableness of answers (this is actually how I teach decimal multiplication, not by counting decimal places, but by simply asking which whole number do you think this is closest to), but I get quizzes where 3.45+6.45 is 7.9.