Geometry

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Course Summary

In high school Geometry at Match students further their understanding of geometric relationships and learn to make formal mathematical arguments about geometric situations. This course, which follows the Common Core standards for Geometry and the Massachusetts Curriculum Frameworks, takes a somewhat different approach from more traditional Geometry classes in its heavy emphasis on transformation. Transformations are used to help students understand and prove congruence and other geometric relationships. There is also a strong emphasis on proofs: students learn to prove concepts and ideas they have been learning about for years. Class time focuses on six main topics 1) establishing criteria for congruence of triangles based on rigid motions; (2) establishing criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally developing explanations of circumference, area, and volume formulas; (4) applying the Pythagorean Theorem to the coordinate plan; (5) proving basic geometric theorems; and (6) extending student work with probability. (See Massachusetts Curriculum Frameworks.) Because Match seeks to offer students a pathway to study Calculus in their senior year, this Geometry course also covers advanced standards that are sometimes covered in advanced math and pre-calculus courses.

Foundations for Success:

High school geometry builds on geometry instruction that has occurred throughout elementary and middle school but with the key difference that students must prove and explain concepts they learned about in prior years. In elementary school, students learned about the attributes of shapes, compared and categorized these attributes, and learned to compose and decompose shapes. In middle school, students developed conceptual understanding of angle relationships in parallel line diagrams and angle relationships within and outside of triangles. They have also learned to describe geometric features, measure circumference and area of circles, and make observations and conjectures about geometric shapes using sound reasoning and evidence. Students have learned to “construct” a triangle using different side lengths and that the properties of a triangle are based on the relationship between the side lengths and the interior angle measures. These foundational understandings will be essential to students’ success in this course as they build chains of reasoning to explain, model and prove geometric relationships and situations.

How to Use This Course

 

Mathematics at Match

The goals of Match Education’s math program are intrinsically tied to our school’s mission of providing our students with the skills and knowledge they will need to succeed in college and beyond. At Match, we seek to inspire our scholars to pursue advanced math courses, and we provide them with the foundations they will need to be successful in these courses.

Our math curriculum is designed around several core beliefs about how to best achieve our ambitious goals. These beliefs drive the decisions we make about what to teach and how to teach it.

  1. Content-rich Tasks: We believe that students learn best when asked to solve problems that spark their curiosity, require them to make novel connections between concepts, and may offer more than one avenue to the solution.
  2. Practice and Feedback: We believe that practice and feedback are essential to developing students’ conceptual understanding and fluency.
  3. Productive Struggle: We believe that students develop essential strategies for tackling complex problems, and build non-cognitive skills such as grit and resilience, through productive struggle.
  4. Procedural Fluency Combined with Conceptual Understanding: We believe that knowing “how” to solve a problem is not enough; students must also know “why” mathematical procedures and concepts exist.
  5. Communicating Mathematical Understanding: We believe that the process of communicating their mathematical thinking helps students solidify their learning and helps teachers assess student understanding.

For more information, view our full Mathematics Program Overview.