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Private: Learning Math: Geometry

Professional Development > Private: Learning Math: Geometry > 10. Classroom Case Studies, K-2 > 10.4 Homework

Mathematics

K-2, 3-5, 6-8

Classroom Case Studies, K-2 Homework

Session 10: K-2, Homework

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences.

 

Problem H1

Interview a teacher in the grade level above you. Show the teacher the Cutting Corners activity in this session, and ask him or her the following questions:

  1. How does the content of this activity prepare students for geometric thinking in your grade?
  2. Why do you think this content is important?
  3. How could this activity be extended for students in your grade?

 

 

Problem H2

Look at a lesson or activity in your own mathematics program for your grade level that you think has potential for developing students’ geometric reasoning. If you were to use this lesson or activity now, after taking this course, how might you modify or extend it to bring out more of the important ideas about geometry?

Series Directory

Private: Learning Math: Geometry

Sections

10.1 Part A: Geometry as a Problem Solving Process (25 minutes)

Session 10: K-2, Part A

10.2 Part B: Developing Geometric Reasoning (40 minutes)

Session 10: K-2

10.3 Part C: Activities That Illustrate Geometric Reasoning (55 minutes)

Session 10: K-2, Part C

10.4 Homework

Session 10: K-2, Homework

Sessions

Session 2 Triangles and Quadrilaterals

Learn about the classifications of triangles, their different properties, and relationships between them. Examine concepts such as triangle inequality, triangle rigidity, and side–side–side congruence, and look at the conditions that cause them. Compare how these concepts apply to quadrilaterals. Explore properties of triangles and quadrilaterals through practical applications such as building structures.

Session 3 Polygons

Explore the properties of polygons through puzzles and games, then proceed into a more formal classification of polygons. Look at mathematical definitions more formally, and explore how terms can have different but equivalent definitions.

Session 4 Parallel Lines and Circles

Use dynamic geometry software to construct figures with given characteristics, such as segments that are perpendicular, parallel, or of equal length, and to examine the properties of parallel lines and circles. Look past formal definitions and discover the properties and relationships among geometric figures for yourself.

Session 5 Dissections and Proof

Review and explore transformations such as translation, reflection, and rotation. Apply these ideas to solve more complex geometric problems. Use your knowledge of properties of figures to reason through, solve, and justify your solutions to problems. Analyze and prove the midline theorem.

Session 6 The Pythagorean Theorem

Continue to examine the idea of mathematical proof. Look at several geometric or algebraic proofs of one of the most famous theorems in mathematics: the Pythagorean theorem. Explore different applications of the Pythagorean theorem, such as the distance formula.

Session 7 Symmetry

Investigate symmetry, one of the most important ideas in mathematics. Explore geometric notions of symmetry by creating designs and examining their properties. Investigate line symmetry and rotation symmetry; then learn about frieze patterns.

Session 8 Similarity

Examine your intuitive notions of what makes a "good copy" and then progress toward a more formal definition of similarity. Explore similar triangles and look into some applications of similar triangles, including trigonometry.

Session 9 Solids

Explore various aspects of solid geometry. Examine platonic solids and why there are a finite number of them. Investigate nets and cross-sections for solids as a way of establishing the relationships between two–dimensional and three–dimensional geometry.

Session 10 Classroom Case Studies, K-2

This is the final session of the Geometry course! In this session, we will examine how geometry as a problem-solving process might look when applied to situations in your own classroom. This session is customized for three grade levels.

Session 11 Classroom Case Studies, 3-5

This is the final session of the Geometry course! In this session, we will examine how geometry as a problem-solving process might look when applied to situations in your own classroom. This session is customized for three grade levels.

Session 12 Classroom Case Studies, 6-8

This is the final session of the Geometry course! In this session, we will examine how geometry as a problem-solving process might look when applied to situations in your own classroom. This session is customized for three grade levels.

Watch Videos 11 and 12 in the 10th session for grade 6–8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6–8 teachers (former course participants) who have adapted their new knowledge to their classrooms.

Join us for conversations that inspire, recognize, and encourage innovation and best practices in the education profession.

Available on Apple Podcasts, Spotify, Google Podcasts, and more.

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