Geometry: My Own Personal Flatland

Lesson: My Own Personal Flatland

Essential Understandings:

Looking at the shapes and vocabulary words, according to what criteria would you sort the shapes into ranks (classes)?
How would placing figures on a coordinate plane organize flatland?
How would you value similarity and congruence?
Extend your flatland designs (requirements) from the previous questions into Spaceland.

Essential Questions for Flatland (pdf)
Assessment Flatland (pdf)
Notemaker Flatland (pdf)
Coordinate Geometry Problem (pdf)
Geometric manipulatives or dynamic software such as Geometer's Sketchpad©
Idea Development Rubric, Voice or Organization Rubric

Writing Traits:

  • Idea Development:
    • Writing with a clear, central idea or theme in mind
    • Putting researched ideas into one's own words
  • Organization:
    • Beginning the writing with a strong introduction
    • Ending the writing with a satisfying conclusion by linking the conclusion back to the introduction
  • Voice:
    • Conveying passion towards the message of the writing or the topic
    • Thinking about and making decisions to acknowledge the intended audience

Prior Knowledge/ Possible Warm-up Activities:

Students had the opportunity to explore writing content area recipes and personification poems, using the lessons outlined on Also, I gave students a list of vocabulary words consisting of line, angle, point, ray, segment, polygon, vertex, adjacent, bisect, obtuse, acute, and right. We worked on definitions and drawings for each vocabulary word. I then gave them three different theories of Geometry and asked them which definition they agreed with and why.
1) Einstein said that Geometry happened by discovery.
2) Plato's Republic said that geometric figures only exist in our minds.
3) The mirror argument says that Geometry reflects what we see in nature.

Time needed:
10 minutes to introduce, the rest of the time can be done outside of class.


1) I read the students the Essential Questions and asked them to use a highlighter when we are reading whenever they see important information that might help them answer any of the questions. In addition, I passed out the assessment_flatland sheet. Students would be asked to answer the essential questions with a choice of writing either a recipe poem or personification piece.

2) I handed each student an overhead pattern block (they are thinner than the actual pattern blocks), and then I read the students chapter 1 of Flatland. The pattern block is a great prop to use as the author is describing Flatland. After reading chapter 1, we worked on the definition of plane, which students then added to their vocabulary sheet.

3) I passed out the notemaker_flatland to the students (it is a 8 x 14) legal size paper. My intention was to use Geometer's Sketchpad to introduce the shapes and their qualities, once students made important discoveries, we would then fill in the notemaker. A finished notemaker (in two images) is here.

4) Once we read chapter one, we focused on angles in Geometer's Sketchpad. We discovered that vertical angles are congruent, and we played with bisecting angles and measuring complementary and supplementary angles.

5) Read chapter 2 of Flatland. Investigate and discover properties of triangles on Geometer's Sketchpad or with cutting paper. We worked on triangles' angles adding to 180o and types of triangles. Similarity and congruence were also a stressed topic here. I also had the students work collaboratively on a problem on a Cartesian graph (cartesian_graph_problem).

6) Read chapter 3 of Flatland. After reading this chapter, we explored quadrilaterals, pentagons, hexagons. We focused on characteristics of each shape, similarity and congruence, and connecting properties of the shapes with a Venn diagram and writing counter-examples to statements about them.

7) Read chapter 6 of Flatland. Go back to the shapes and explore interior and exterior angles of shapes.

8) Read chapter 7 of Flatland. Define regular and irregular figures and discuss their properties and how they relate to angle measures. I also spent time here exploring parallel and non-parallel lines cut by a transversal and what angle relationships ensue.

9) Read chapters 15 and 16. At this point, I did an activity on predicting what solids are formed by nets. We explored vocabulary of 3-D shapes and how congruence and similarity work in three dimensions.

10) I asked students to look at the assessment_flatland page again. I asked them to brainstorm ideas on how to write their paper while answering all the essential questions. They shared their ideas with a partner.

11) I had the students write a rough draft. Students writing a personification piece focused on ideas and voice, while students writing a recipe piece focused on ideas and organization. We reviewed the trait rubrics before students started writing, highlighting important qualities to include in their writing.

12) After completing a rough draft, students had a peer review their writing and give feedback using the appropriate rubrics. I asked students to revise their work and turn it in.

13) I provided feedback to the students, not only on the traits but how they scored on the trait rubric with respect to each of the four essential questions. Even if a student scored a five in all areas, I still provided feedback on how to improve the individual piece.

14) When I handed back the papers, I gave the students four different colored highlighters. I had each essential question color-coded to match an essential question. Yellow was ranking the shapes, pink was similarity and congruence, green was the coordinate plane, and orange was Spaceland. I asked the students to re-read their drafts and highlight where they had addressed each question in the appropriate color. This way, students could get a visual picture on how much time and details they provided to answer each question.

15) Next, I conferenced with 4-5 students at a time. I took recipe writers together and personification writers together. We discussed how they could better address answering the questions as a group. We provided suggestions for one another and celebrated the parts of our papers that were done well. Each student was then asked to revise their papers again.

Student Examples

See examples of work done by past students for this lesson: Flatland Student Examples 

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