In any event, they were very attentive and we had some pretty great discussions. In Math 7, we started the section on multiplication of integers and framing in terms of repeated addition. Standard of Mathematical Practice 2 asks students to think about numbers in many ways. So we did.
We came up with 10 ways to represent multiplication.
I spent the entire period on 2 examples because I wanted to emphasize the language that we will be using going forward.
Being able to think about multiplication as "3 groups of 2" makes the transition to division much easier, especially division of fractions, using phrases such as "How many groups of 1/2 are there in 3?"
In Pre-Algebra, we looked at specific examples from the quiz and talked about the common mistakes that I saw in assessing. The two major problems with long division were putting the decimal in the wrong place and having the vinculum (the repeater bar) cover either too much, or not enough.
|I know fancy words!|
When we discussed converting repeating decimals back into fractions, I showed the algebraic method, but we talked more about strategies that we could use to estimate and then find the answer.
It's a process, but I can feel that we're moving in the right direction. I had a parent contact our superintendent in a fury over what was happening in my class. After writing directly to the parent, she thanked me for my thoughts and expressed appreciation for my methods.
It was a good day.
I hope to put a vinculum over this feeling.
I helped out w/ our pre-Algebra course and we had a sub one day who usually taught higher math. He was lecturing them about doing these (obnoxious) complicated "order of operations" exercises where they had a mess on top of a fraction bar and a mess on the bottom. He referred to the fraction bar as a "vinculum." Yes, I had to look it up. (Yes, he made just a little face as he said it as if he knew that wasn't a term anybody else in the room would know.)