Attached is a learning progression for CCSSM Critical Area #1 as it relates to Chapter 4 (Triangle Congruence) in the Holt Textbook. Also attached are sample benchmark assessments and classroom assessments. The learning progression and two assessments can be used to communicate with colleagues some key areas to focus on in this unit and ideas to present important concepts. If teachers collaborate using these things, especially throughout the entire curriculum, there will be more consistency in the mathematics program. This can be greatly beneficial for both students and teachers. Teachers will have a better idea of a student’s background knowledge since all classes are consistent in content. Also, students will be receiving the same high quality instruction regardless of which teacher they have.
Triangle Congruence Learning Progression– This learning progression would fit into the Holt Curriculum in Chapter 4 – Triangle Congruence. In Chapter 1, we talk about the transformations, so students should have a good understanding of reflections, translations, and rotations. Dilations aren’t typically covered until later in the textbook, so there will need to be some time for a discussion on dilations and non-rigid motions. This learning progression fits together in the big picture because the CCSS is very focused on transformations. Since this learning progression involves talking about triangle congruence through transformations, it fits in with both the standards and the curriculum very well.
Triangle Congruence Benchmark Assessment– I would use this benchmark assessment as a quick summative assessment at the end of the unit. Since it is so short, you could always include another couple problems to make this more like a test.
Triangle Congruence Classroom Assessment– I would use this classroom assessment as a quiz to check for student understanding and help the teacher determine what areas need to be re-covered. This would not be a big summative assessment, more of a formative assessment to make sure the students “get it”.
I really like your learning progression and how you used many visual representations of the main ideas. My only suggestion is to expand on your progression of math tasks to teach the interconnectedness and completeness of the congruency theorems.
In the benchmark assessments you did a nice job of creating the scoring criteria. My only suggestion is that I think some of the assessment item 1(a) is missing.
The classroom assessment is nicely done. I especially like questions 12 and 13. My suggestion is to explain how you will use the the classroom assessment items in your instruction/learning progression in your blog post.
I updated my learning progression to include more discourse about the Congruence Theorems, focusing on why the Congruence Theorems work and how they are related. I also included a discussion of AAA and SSA, including a way to explain how they do not guarantee unique triangles.
I edited my benchmark assessments, changing the rubric for 1a.
You made good adjustments. Since your benchmark assessment is limited to a single problem per standard, most of your guide instruction assessment information will have to come from your classroom assessments.
As always you learning progression looks very complete. I noticed the changes you made since last time I read it. I was curious about your classes, how long are the periods and if you have quarters or semesters. My question is because of the classroom assessment, was that for the end of the unit or a quiz for the week? I like how your questions are multiple choice but makes the student really think before they chose their answer. Makes it easy to grade and you know generally if they understood the concept.