Grades 9-12: Geometry - Circles and Triangles
Common Core Standards
HSG.SRT.A – Understand similarity in terms of similarity transformations
HSG.SRT.C – Define trigonometric ratios and solve problems using right triangles
HSG.C.A – Understand and apply theorems about circles
Standards for Mathematical Practice
MP.1. Make sense of problems and persevere in solving them
MP.2. Reason abstractly and quantitatively.
MP.3. Construct viable arguments and critique the reasoning of others.
MP.6. Attend to precision.
MP.7. Look for and make use of structure.
Description of Unit
This unit titled "Circles and Triangles" from map.mathshell.org is a high quality curriculum resource because it allows students to work with areas of triangles, relationships with circles, and similarity. The unit focuses on right triangles and their connection to similarity and area. Students are given an image and asked to find the ratio of the two areas. Students then engage in small group work to find a collective solution to the given problem. Sample responses have also been provided, to allow for students to compare and contrast different solution strategies. The unit also includes possible solutions provided by students, different ways to solve the problem, prompting questions to help focus students’ attention, and a scoring rubric to use for scoring student responses.
Some of the cautions for this unit are that there is a lack of incorporation of technology into the lessons, as well as a lack of manipulatives to use for solving the problem. There are not explicit accommodations made for struggling learners or advanced learners. There is also a lack of information about accommodating for English language learners. There is an emphasis on conceptual understanding, having a limited focus on a balanced approach to include procedural fluency and promoting transfer.
Rationale for Selection
The unit is a valuable resource due to its emphasis on the Common Core standards and the Mathematical Practices. Students actively engage in critiquing the reasoning of others as they examine different student work samples of imaginary students. There are different instructional techniques included in the unit, also including a variety of grouping strategies. The unit provides areas for pre-assessment, post-assessment, and formative assessment. The unit also includes a rubric for scoring student responses. The sequencing of tasks and sections is conducive to student learning. The prompting questions help for teachers to provide feedback to students and help all students achieve.