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.