My 7th graders just hit the part with 3x - 7x and totally got lost. They were trying to picture how far 3 was from zero and how far -7 was from zero. So I had to pull out a couple of number lines and other manipulatives to show that you start and 3 and move seven places to the right. I know that we'll be doing number lines and such to help them understand that the 3 units is taken from the 7 going left.
Then in Algebra, I introduced Absolute Value. Students have learned that all answers come out positive but they don't know why so out came the explanations about distance. Absolute value is like distance in that it is always a positive number but the signs indicate direction. so the distance might be 5 miles away so going there might be -5 because you are going away from your starting point, and + 5 as you come back. It could be the other way round depending on the kids do.
When you put it as traveling to a near by village, they understand things much better why the answer to an absolute value problem is always positive and when you solve it, why you have to set it equal to two values. They relate so much better to this explanation than any other I've done.
Then in Geometry, my students are doing transformations, specifically translations. This meant they had to learn to express movement using signed numbers so that when someone read x +6, y-2, they knew the point moved right six spaces and down two. We have had multiple discussion over the past couple of days on the horizontal movement + is movement to the right, - signifies movement to the left. For vertical movement, + indicates moving up and - moving down. I think it is finally sinking in.
I try to talk about context and how the context helps students decide how to interpret what a sign means. Let me know what you think, I'd love to hear. Have a great day.
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