One of the goals in my modeling dream unit is, "I can interpret the graph of a function in terms of a given context" based off of the Common Core Standard "CCSS.MATH.CONTENT.HSF.LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context". This goal involves students being given a model of a situation in graphical or tabular form and being asked to interpret what they see in terms of the context. This might include explaining what the x and y intercepts represent, comparing different rates of change across the graph, describing what local maximums and minimums represent, and other key features of the model. This is a fun goal for me because I can tie the model to the students interests. Many of my students this semester are interested in football and soccer, so I could give them models that show football or soccer statistics. Another big interest in the classroom is anime. I'm not sure what mathematical model I could find that ties into anime, but I'm sure with some creativity I could find one. So this goal is fun because it is easy to connect to student interest and modify for each group of students.
I would assess this goal through individual student work. I would have students select a model from a range of available models, and then have prompts for students to answer. Some prompts would be, "What is happening during the decreasing intervals of the graph?", "What does the y intercept represent for this model?", and "Write a short story about what is happening in this model." By having multiple prompts students would be able to start with the mathematical ideas they feel most comfortable with and build up to more difficult prompts, and I can see where the class struggles the most for future lesson planning. Interpreting a graph in terms of the graph's context is a difficult task. Students have to identify the key features, then understand what the key features represent mathematically and then tie that mathematical knowledge to the real world context of the model. This would be a cognitive demand of Level 4 Evaluate from the Hess Cognitive Matrix.
The language demands for this goal would initially include reading and writing, and then listening and speaking. Students will have to read the graph to understand the model, and then write their responses to the prompts. After individually working on the models and prompts I could have group/whole class discussions to practice the speaking and listening language demands and for the students to get a deeper understanding of the mathematical ideas by hearing the thinking of other students, and defending their own ideas about the model with their groups.