As is typical each Wednesday, Warm Up problems today are replaced with another Continuous Improvement Quiz, #9, that focuses on number sense topics with which 8th graders often struggle related to number sense. Rational and irrational numbers, fractions, decimals, percents, and exponents all appear on this week's quiz. Students have 15 minutes to complete the quiz and then I take up the answer sheets and go over the answers with the class. I check the answer sheets and return them to the students without putting them in the grade book. They keep track of their weekly progress in the data folders. I also maintain a class run chart, where we celebrate when our class earns an "All Time Best" average score.
This ungraded assessment provides me excellent data, especially when students miss problems based on topics we have already learned. This is an indication that I need to revisit these troublesome topics in subsequent Warm Ups.
See my Strategies Folder for a full explanation of the CI Process and all the related tools needed to effectively implement this system!
After going over the CI Quiz answers for the week, I ask students to get out their penny bridge activity from the day before so we can debrief. I have already scanned one student's graph and put it on the smartboard to focus our class discussion.
I begin by asking students to raise their hands if their scatter plot looked like the example. I then asked what caused the data points to be in lines parallel to the y-axis. A student explained that each dot stood for one of the trials they did for each bridge length.
I then lead a discussion about the correlation of the data. I tell students to take 30 seconds discuss with their table mates how they would complete the following statement: According to our data, the longer the bridge length, the _______________ number of pennies it will hold. be sure you can justify your answer with your data.
When the timer sounds, I ask a for a volunteer to give their groups answer and explanation. The student explains that they finished the statement with the word 'less' because when they looked at their data, the longer the table was, the fewer pennies it held.
I wanted to judge student understanding of the correlation so I said, "Now I want you to think about the correlation of this data. In just a moment, I am going to ask you to vote whether you believe the data show a positive correlation, a negative correlation, or no correlation.
I then began the poll, asking students to raise their hand. All the students voted for negative correlation, so I pulled a stick (from a cup full of sticks with student's names on them) and asked that student to describe why it would be considered a negative correlation. She explained that when you made a line of best fit for the data it was going down. I asked if anyone had another idea that could be used to explain why the data was considered a negative correlation. Another student volunteered her idea: "As the bridge gets longer, it holds less pennies, so that makes it a negative correlation."
I then showed the example scatter plot again and asked if we could write the equation of the line for the line of best fit (I wanted students to have some guided practice on this skill.) I asked, "Can we tell what the slope of the line is? The person who made this graph has really helped us out by drawing in these triangles. What do they show?" One student responded, "The slope is down six over two." but was immediately corrected, "Down six, over 1. Two boxes equal one on the x-axis."
I continued,"So we know the slope is -6. Do we know the y-intercept?" Several students called out 50. I then wrote the full equation of the line and asked students if that equation made sense based on the data. In closing, I explained that we would have several other opportunities to practice writing the equations of given situations in the coming days.