I think a goal I'd have for my students is to have them come up with a scenario where they can compare two similar functions to then make an informed prediction. This covers a lot of standards, including interpreting functions, graphing functions, and analyzing functions, all including different cognitive levels. Observing graphs is required for them to compare graphs that they create, and comparing and creating graphs demand higher levels of rigor, respectively Understand level 2 and Create level 4. They also would then make a prediction based on the graphs and what they notice, which is Understand level 3. The goal in essence, then, is to understand functions in order to make informed decisions.
I think this could relate to my students specifically because they could come up with the scenarios for the graphs they might create. Perhaps my students want to compare students who read books at different speeds and different sized lengths. Maybe they will want to compare different artists with how many songs they make annually and how much money they get from those songs on average. Maybe they'll choose to compare top athletes in sports, seeing how much some make in one sport versus another sport, and also seeing how many games are played per year. Maybe they'll compare salespeople for different businesses, comparing their starting pay versus their commission rates. They have the freedom to choose their scenarios, but I would just look for key features that are needed in functions. How are the variables relating with one another? What type of function might the scenarios be presenting? I would also look for labeled graphs, intercepts, points of intersection, and educated predictions for a certain output based off an input value not on the graph.
This would connect to language demands by focusing on the reading and writing domains, which in this case is creating scenarios to then draw graphs, and then reading those graphs to make an informed conclusion. This could be a group activity where students can discuss their thoughts and ideas of which scenarios they might like to implement, touching on the speaking and listening domains as well. Examples would also be given, and there would be visual aids for what graphs look like and the important features they contain.
When it comes to unit planning, the most important thing seems to be the big idea. I have to make sure all of the goals and tasks connect back to that big idea. This connects with lesson planning because the mini goals and tasks inside those plans also need to connect back to the big idea. Sometimes, it is difficult to make sure everything connects, so it is crucial to have a big idea that continues to shed light on everything that comes afterwards. My big idea is being able to predict information through the usage of functions, so knowing how to create scenarios, graph scenarios, compare and analyze functions, and predict information based on the functions all point back to the big idea.