As is typical each Wednesday, Warm Up problems today are replaced with another Continuous Improvement Quiz, #10, that focuses on number sense topics with which 8th graders often struggle. Fractions, decimals, percents, exponents, and integers 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" 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 Continuous Improvement quiz with the students, I distribute envelopes that contain 10 mixed sets of functions represented as tables, equations, and graphs for a total of 30 cards. Working with partners, the students must sort these into matching function sets.
I created these cards (which I will use again in a future activity) to expose my students to a variety of functional representations. Working in the pairs, students can make sense of the features of each representation and how it relates to the others. For example, students may use the data listed in the table to match to the graph. They might then match the rule to either the graph or the table by looking at rate of change or intercept.
As students look for function sets, I circulate through the room. When I see that a pair has found a set, I interview them with questions like: "Tell me how you knew these three cards made a set?" or "How can you prove to me that this equation matches this graph?" I am looking to improve my students' abilities to express themselves mathematically using appropriate terminology like 'rate of change', 'slope', and 'y-intercept'.
For closure, I give each student a "Ticket Out the Door" that contains a table, graph and equation. I ask them to explain, in writing, whether the three represent the same function. I am looking not only to see if students recognize the differences, but also I want to see how they articulate those differences in writing.