This warm-up is basically asking the same question in several ways, but students can come to that realization themselves. If students are struggling to figure out any one problem, ask them to try to turn that problem into one of the other problems. When circulating, if a student seems unable to get started on any section, I ask the students to figure out how the data tables relate to the bunny problems. Usually this remainder is enough to help them understand what they are looking for. Once they realize that they are basically looking for the multiplier in all the situations, they start to look for shortcuts and this search for shortcuts will frame the entire lesson.
This lesson is another one that differentiates itself in the sense that students will develop their own methods to find these rules. The fractions will be challenging for some students, so there is a method described in the middle of the lesson that you can show these students if they have trouble getting started. If students are using the guess and check method, they can be encouraged to develop a more efficient method, two of which are described in the middle section of the lesson.
Today’s lesson is very much about MPS1 and MPS2. In terms of MPS1, the goal is for students to figure out their own way to understand or make sense of the problems and for them to be able to explain why their methods make sense to them. In terms of MPS2, student should be using both numerical and algebraic methods to solve these problems and to verify their solutions, and they should be encouraged to reflect on which methods they prefer and why.