Once you have tried out the activity, what are some concepts students could discuss?
- Name of graph
- Parent graph & transformations
- Table, rule, context, verbal description
- Domain and range
- Where increasing/decreasing
- Linear: constant rate of change, std form of eqn, point-slope, etc.
What is valuable about such a prompt?
- Everyone has access (lo floor/hi ceiling).
- Both of the graphs represents lines, one slants to the left, one to the right….
- Lines represent rates of change of parabolas y = …
- Opportunity to recognize, identify, discuss important characteristics
- Opportunity to make math connections
- The teacher can learn the distinctions students can make, their mix-ups, their depth of knowledge.
Consider how you will fit this into your teaching
If you want to be able to guide students, you must first do the problem yourself and establish goals and expectations. Don’t expect much the first time you use an open-ended prompt. Repeat the prompt type regularly (say every week or two). Look for growth over time. Make sure to respond to student thinking perhaps peer review, gallery walk, swap meet, group/partner and whole class discussions, individual teacher comments. Importantly, give students time to reflect, revise, revisit
Here is an example of two students’ work:
What math do they know? What feedback could we give to move their learning forward? Next steps?
As you work on these problems over the year, encourage students to use multiple representations in their comparisons.
Follow up ideas
Make up some that use non-linear comparisons as well.
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