The purpose of this lesson is to engage students in the practice of argumentation. The warm up illustrates the use of a number line as evidence to support the solution. The sorting activity provides opportunities for students to dissagree and argue about the solutions. Students must use explanations and/or mathematical models to support their reasoning. (mp 3)Their evidence and explanations may include reference to the hot & cold cube context learned in earlier lessons (Mathmaster Chef series), number line, or plus (+) and minus (-) symbols. (mp 4) I remind students that their modeling and explanations are useful not only in convincing their peers, but also are helpful in convincing themselves during a test. Evidence can be used to help them decide how to solve or figure something out just as it can be used to convince someone else of the solution. (mp1)
The Warm up asks students to solve the following problems and asks what they would look like on a number line:
As we go over the Warm up notes I draw the open number line for each problem to emphasize that subtracting negatives moves in the positive direction on the number line in order to reinforce the idea of adding the opposite. Not only does this help them visualize the math, but it also helps familiarize them with a tool they can use to help them explain and support their results. This helps them later use the appropriate tools as evidence during argumentation (mp3 & 5)
Students work collaboratively in pairs or trios to sort the integer operation sort cards.docx into two categories. They need to group the problems according to whether the solution will be positive or negative. This is a good way to engage students in argumentation and to encourage the use of mathematical modeling and explanation to support their reasoning. (mp3)
As students are sorting I circulate to check progress. Asking questions like "how do you know this solution will be negative?" helps students practice explaining their reasoning. It also promotes the expectation that students need to provide evidence. Asking questions like "are there any that you are unsure of?" helps surface any disagreement or uncertainty. Many times the quieter or more timid student may not speak up and this question encourages them. If I see one that is in the wrong category I may even point it out and ask "does any one have any doubts about this one?" Asking questions like "what could you try that would help you decide?" and "what could your partner show you that might convince you?" promotes the idea that evidence can be used to both figure something out as well as to prove a solution already solved.
As some groups will finish up at different times I also have some questions three factors.docx for partners to work on when they finish sorting the cards. I only give them one at a time and they may work on one or several by the end of class. These questions provide a product of three factors and ask what the three factors could be. There are several possible solutions to each question. As I continue to circulate I may ask these groups questions like "how do you know all the factors can't be negative?" or "would it be possible for all the factos to be negative?" to help them generalize the patterns of multiplication.
I want to provide some time at the end of class for homework integer operations.docx because when I ask students to "explain" in their homework they are less likely to do it unless I give them time to start in class where they have access to support. This assignment does not ask for a single solution to a numeric problem, but for explanations and conclusions. I want them to use contextual verbal explanations and mathematical models (number lines & symbols). As I circulate I will suggest that they "draw a number line" or "write an explanation using hot and cold cubes", etc.