As the school year winds down and the kids get more and more antsy, and I feel the pressures to FINISH everything, the challenge is ever-more present to find ways to engage and motivate students to meet objectives. One of the grade level content expectations I have always struggled with getting across to students is inverse relationships. While I will acknowledge we do not have a firm understanding of the ins and outs of what these are, my kids really "GET" the idea at a basic level.
First we looked at side lengths of a rectangle with a fixed area. This was interesting since we had already looked at fixed perimeters and considering the difference in how fixed area and perimeter affect side lengths forced them to think in ways they usually don't. Our first task was a 48 square foot garden which I had purchased mulch for. We generated a table of possible whole number side lengths and graphed them. Very cool! Students then did the same exercise with a 60 square foot area. That laid the ground work.
Then today, I gave each partner group a card with a service on it and a total amount of money to be earned. (ex. Earn $250 mowing lawns) They then generated a table of possible combinations. (ex. Mow 250 lawns @ $1 a piece, or mow 1 lawn @ $250, or 10 @ $25, etc..) They graphed their combinations on a HUGE piece of graph paper, and then added an arrow at what they thought was their best, most reasonable choice. These were then hung on the board and each partnership explained their graph and choice to class. We finished up by talking about how an inverse relationship would look if negative numbers were included.
I am impressed they were able to write their equations, complete their tables and graph their points. It was overall, a cool activity!
Tomorrow, is GLAD(grade level assessement device) day. YUCK! This is only a 30 question online assessment from our ISD but it really seems like a waste of a day of class. I am curious to compare their pre and post test scores though.
The days are winding down and I am going to be sad to see most of them move on to 8th grade!