One of the objectives for my upcoming capstone lessons is “I can determine the slope of a line from a graph or table.” One way I could connect the lesson to students’ interests and create a cognitively demanding task or assessment for class time would be to have students analyze a football scenario. The students in my class are very interested in football, especially since the season recently started, so for the last task or as a formative assessment/exit ticket of the day I could have a graph (time vs. distance) with multiple lines representing football players running at different speeds and have a few questions comparing the speeds (slopes) of the players (cognitive demands: Understand Level 2, Apply Level 1), and at the end for a more challenging question asking, “If player B was chasing player A, would player B be able to catch up and tackle Player A? Explain your answer using slope. If Player B catches up to Player A, at what time do the two players meet? If Player B does not catch up to Player A, what is the distance between the two players at 12 seconds?” (Cognitive demand: Understand Level 3, Analyze Level 2). This task would cover the language demands of reading and writing. Students would have to be able to read the description of the football scenario, understand the graph, and then describe in writing and through calculation work how they got their answers and what those answers mean in context. I could make parts of this task, maybe the final question, a collaborative piece that would allow for the language demands of speaking and listening as well, since students would have to listen to other students' ideas and also express their own ideas to other students. The final question and the ones before it where students compare different slopes would show me how well students can determine slope from a graph (the objective), while introducing the connection between slope to rate of change in context, and also challenge them to create lines using slope which will be introduced in later lessons. I could use the rate of change information and the line creation question as a way to help modify my future lessons based on where students seem to be based off of their answers, and I would get good data for the determining slope lesson objective. This also gives the students an opportunity to explore the math further and discover on their own how we can use slope in a real world context.
Some useful resources I have used for planning are: Desmos, textbooks (I've used textbooks as a guide for unit planning, because the books do a great job showing how knowledge builds through a section), and asking veteran teachers for ideas