Since my colleague Ms. Demailly fully covered discrete and continuous graphs with her classes and wanted it as the last part of our graphing situation skill question on the test, I had student volunteers read the Math Notes box. I then asked them to paraphrase the definition of discrete. It's basically a fancy way to say the points on the graph are not connected because the values in between do not make sense. Conversely, a continuous graph has points connected because there's growth in between the points. For example, you can find out how tall John's Giant Redwood Tree is at 2.5 years by looking at 2.5 years on the x axis and then going straight up and seeing where the line lines up with the y-axis.
Then students reminded me how to get the perimeter of the dented square from Friday. They reminded me of the two ways. Then I asked what values x could and could not be. They said it couldn't be negative and it couldn't be zero. They also said it couldn't be 1 because the unit tile's side length is 1 so it can't be the same as the x value. So, we made a table of x values 1 through 4 and they told me the outputs or y values. Then I asked how to scale the graph, and graphed the points. About 4 or 5 kids in each class remembered how to graph the inequality x>1. I asked them how we could show this on our coordinate graph. A few kids came up with an open dot. Then I asked if this was a continuous graph from there? They said yes, because x could be decimal numbers.
Then students worked on Goofy Graphing. They looked at a table, extracted the (x,y) coordinates, and then analyzed the mistakes students made in setting up the graphs. The end result was 3 huge mistakes to avoid when setting up a graph:
- Figure out how many quadrants you need to you can be efficient. If it's all positive numbers, only use a 1st quadrant graph.
- When graphing your coordinates, make sure you graph x first then y in an (x,y) coordinate.
- Always include the origin, (0,0).
- Even intervals so the graph is efficient and spaced out properly.
In accelerated I had volunteers review the absolute value equations. Then they started changing an equation from standard from into y=mx+b form. They showed me two different ways to do that. Then I had volunteers solve for force in the work formula: Work = Force * distance or W=Fd. This was difficult for some students. Then Alex David showed us how to solve for Celcius in the formula F=9/5C + 32. Some students still didn't understand so I showed the intermediate steps that he did mentally.
Then a student tried and got close to solving the hardest problem that involved an exponent:
Davin ended up doing it on the board and Nicholas confirmed it was correct. What I loved was that the first student was outside my room kneeling down on the ground and fixing the problem. Talk about perseverance! I was very proud of him, especially after when we gave him a 3 second clap for his effort in class and as he walked back to his desk he said "I bet everyone is happy to see I got it wrong."