Key Activities/Topics


Tips and Tools




Focus: Introduce the project and generate interest.

1. Introduce the challenge: Can we learn enough about Geometry to convince other students that it's important to life?

2. Describe the scenario and the task. Clarify, if necessary

3. Frame the task with the Driving Question: How can we, as a team of young Geometry specialists, create a presentation aimed at teens that combines geometric information and historical facts about Geometry to explain the significance of Geometry to their lives?

4.  Describe the concepts that students will learn as they complete the project. Include historical information and the ability to recognize and manipulate the key shapes in Geometry.

5. Discuss the 'why' behind the project: To gain a deeper appreciation of Geometry and set the tone for the remainder of the course.

6. Distribute Project Packets: Include project description, topics, timeline, and grading. Introduce Critical Areas, Standards, and Clusters for the unit. [link]

7. Anchor rubrics. [link] Students should understand project grading and rubric language.



Generate interest in the project by using an 'Entry Event to generate interest. Examples:


    - Have students watch a video on Euclid.

    - Have students watch the video: 'What's the point of Geometry?'

   - Have students individually or in teams spend 20 minutes finding online resources for Geometry, then discuss and generate questions or share observations.

Use Cloze notes to encourage retention and understanding of videos.

If your or students would like to change or refine the Driving Question, use this guide to Refining the Driving Question. [link]

If your students have no or little experience with Project Based Learning, you may have to begin the first day by explaining the process. They can also watch the video 'Project Based Learning: Explained or a video on PBL and Mathematics.


It's critical to a good start that students understand they will be assessed on (1) Geometry content; (2) Mathematical Practices; (3) teamwork; (4) presentations.





Focus: Form Teams.

1. Introduce the rationale for teamwork: This is a 21st century skill essential in the workplace.

2. Assign or create teams of 3 – 5 students.

3. Have teams review and discuss the teamwork rubric

4. Design an initial task for the teams: Have the teams brainstorm ideas on answering the Driving Question. Have them share their ideas with one other team.

5. Finish with discussion: What good ideas surfaced? How did we work together as a team?

6. Review the teamwork rubric again: Are teams off to a good start?



If necessary, use team building tools to establish effective working teams.[link]

Share initial brainstorm on the Driving Question using posts and gallery walk, or Curriki whiteboard,

Teams should review the project goals and timeline, and establish a task list using the Project Milestones form [link]. This document can be filled out by hand, but will be modified as the project proceeds.






Focus: Begin initial design work on presentations.

1. Teams review websites or other presentation methods.

2. Hand out story board or similar planning tools.[link].

3. Teams choose a presentation method and prepare preliminary sketch of ideas.

4. If time permits, teams share ideas using the ‘Does It Fit?’ Visible Thinking Routine. [link]




Have plenty of resources for students to look at, including website tips,, blog sites, Twitter,,,, and

Teams can use the storyboard tools from Google Docs, available also on Curriki. Depending on resources, teams may also use other formats, such as paper/pen, whiteboard, MSWord, or MS PPT.

Teams should save all work in folder or digitally on Geometry with Friends site or in class Learning Management System.

Have each team review the presentation section of the Project Rubric [link] to guide them.





Focus: Introduce concept of translations.

1. Provide examples of transformation, (Trees through season, flip or rotate dominoes, etc.)

2. Provide examples of rigid motions (Isometries: Preimage to image)

3. Have students view three main transformations.

4. Have students practice rotations using this unit on Curriki Geometry resources.

5.. Introduce key terms. [link]

  • Composition
  • Image
  • Isometry
  • Preimage
  • Rigid motion
  • Transformation
  • Translation


6. Introduce the Mathematical Practices rubric and highlight how the eight practices will apply during the project.




To build on the key terms and vocabulary.


Highlight Mathematical Practice 7, Look for and Make Use of Structure, on the Mathematical Practices rubric. Can students begin to discern patterns and structures around them?







Focus: Continue translations.

1. Begin day with short quiz on key terms.

2. Introduce angles using this Khan Academy video.

3. Discuss angles in the real world. Follow with video, Where are angles in the real world?

4. Practice naming images and preimages by having students match corresponding points, sides, and angles.


As much as practical, intersperse videos and instruction with team discussions rather than whole class discussion.




Focus: Incorporate translations into draft ideas for presentations.

1. Teams identify examples of translations and their importance.

2. Teams brainstorm three bullet points for a message marketing translations to teens.

3. Each team shares bullet points with one other team and receives feedback.




Have teams begin to track their progress on the Project Milestones form [link].

If using Geometry with Friends, set up notification system for team members.

Teach teams to use a modified form of the Critical Friends Protocol [link] to encourage high quality feedback:


    “I like…”

    “I wonder…”

    “I suggest…”




Focus: Introduce Reflections

1. Introduce reflection as key term.

2. Have students work in pairs or triads from their team and view three videos on reflections (they may choose, or you may to choose for them.). Have them discuss and generate three questions about reflections, then share and answer questions together. Collect any questions that can’t be answered for guide to teaching..

3. Have teams define reflections in real world.

4. Students practice drawing reflections or generating pictures of reflections.



Use to discuss variations of ‘reflection.’

Highlight Mathematical Practice 1, Make sense of problems and persevere in solving them, and Mathematical Practice 6, Attend to precision, on the Mathematical Practices rubric.





Focus: Second draft of presentation

1. Teams create a second draft of presentation, incorporating reflections.

2. Teams use Circle of Viewpoints or other protocol from Visible Thinking Routines [link] to receive feedback and improve draft before submitting.

2. Collect second draft for feedback and/or grading.

3. Create presentation schedule and have teams sign up for time slots.

4. Identify and invite other math teachers, parents, or adult experts to be members of the audience for the presentations.



This is a critical milestone in the project. Have teams offer and receive feedback on their draft presentation. Have them analyze the draft product according to the rubric standards. Is it compelling for teens? Convincing? Does it reference historical significance of Geometry? Does it show/teach concepts for this unit?


Teams should enter progress on Project Milestones form.




Focus: Introduce Rotations

1. Explain Positive/negative rotation.

2. Introduce key terms:

  •        Center of a polygon
  •         Rotation

3. Have students practice rotating a triangle around a point using Sketchometry or Geometer’s Sketchpad.



Highlight Mathematical Practices 1, Use appropriate tools strategically, on Mathematical Practices rubric.


See this Curriki Geometry unit for ideas on designing the lessons for days 9 & 10.




Focus: Continue Rotations

1. Have students practice rotating objects in a coordinate plane.

2. Provide examples of rotations.






Focus: Rotating an object by x0  or Y0

1. Teach Key concept: Rotating an object x0  and then by Y0 differs from rotating an object Y0 and then by x0

2. Students practice rotations in pairs or individually.






Allow teams/students time to generate questions and prepare for quiz.


Students can build and share their own practice quiz for terms and definitions using





Focus: Quiz and Summation Day

1. Students perform three transformations using Geometer’s Sketchpad or Sketchometry, and submit shapes on projector or directly to teacher for grading.

2. Students take preimage and create an image based on rules, then submit image for grading.











Focus: Progress/evaluation check on team performance and Mathematical Practices rubric.

1. Have students individually self-evaluate their progress on the Mathematical Practices rubric by highlighting one strength and one area of challenge. Collect for review and feedback with student.

2. Have teams self-evaluate themselves on teamwork rubric.

3. Have teams share results online and do online critique as homework.



Students can post results on blogster, Google Docs, or your Learning Management system. Guide the critique with appropriate questions or directions (these will depend on the status and progress of your students.)


Teams should enter progress on Project Milestones form [link].




Focus: Introduce symmetry

1. Introduce topic withThe World Runs on Symmetry’ video.

2. Discuss everyday examples of rotational or reflectional symmetry.

3. Introduce key terms:

  •         Symmetry
  •         Reflectional symmetry
  •         Line symmetry
  •         Rotational symmetry
  •         Point symmetry

4. Prepare short vocabulary quiz for following.




Teams identify examples of symmetry in classroom or on campus. This can be a brief field trip around campus, if time permits.


Highlight Mathematical Practice 7, Look for and make use of structure, on Mathematical Practices rubric.





Focus: Prepare second draft of presentation and incorporate symmetry.

1. Hand back all feedback/ comments on Draft 1.

2. Review and coach teams on draft product.




Teams may take video or pictures of symmetry examples to incorporate into presentations.


At this point, teams may divide tasks by assigning roles of editor, photographer, researcher, etc.


Use storyboard or similar tool to capture second draft.


Teams should enter progress on Project Milestones form [link].




Focus: Dilations and isometries

1. Teach students to understand scale factors.

2. Introduce key terms:

  •          Dilation
  •          Enlargement
  •          Reduction

3. Provide exemplars, such as car models or apple seeds.

4. Students practice dilations using Sketchometry or Geometer’s Sketchpad.



See this Curriki Geometry lesson for ideas on teaching dilations and isometries.


Highlight Mathematical Practice 7, Look for and make use of structure, on Mathematical Practices rubric.


If time permits, have students brainstorm other dilations, then meet in triads and offer one-minute presentation on why dilations matter.




Focus: Compositions of Isometries

1. Introduce additional key terms:

  •         Isometry
  •         Glide reflection

2. Have students view examples of isometries.

3. Teach students the cncept of Composition of Reflection across parallel/intersecting lines.

4. Teach students to recognize isometries by having them prepare a short lesson using ShowMe, then presenting to class or other teammates.



After students create their Show Me lesson, critique by highlighting  Mathematical Practice 6, Attend to precision, on Mathematical Practices rubric.





Focus: Tesellations

1. Introduce examples of tessellations, eg. Escher.

2. Introduce key terms:

  •       Tesellation
  •         Transformational symmetry
  •             Glide reflectional symmetry

3. Have teams begin to investigate tessellations online and choose a design of their own.



Use this lesson for ideas on teaching glide reflection.

Highlight Mathematical Practice 3, Construct viable arguments and critique reasoning of others, on Mathematical Practices rubric.

Direct students to the Cool Math site for help in investigating tessellations.  

Students can use the ‘tesssellation’  site to design their tessellation.




Focus: Tesellations

1. Teams draw own tessellation examples to be included in presentation, using Sketchometry or Geometer’s Sketchpad.

2. Conduct a Digital Gallery Walk by having students view each other’s drawings.

3. Reflect and discuss: Why are tessellations compelling? What do they reveal about geometric structures?



Teams should enter progress on Project Milestones form [link].








Focus: Exam

1. This is a comprehensive exam on Geometry content learned in the project to date.


Suggested exam.




Focus: Complete final draft of presentation (website, poster, or other public presentation.

1. This is a work day. Introduce tasks and remind students of timeline for preparing for final presentations.

2. Near end of period, teams work in tandem to review drafts of presentations and score on rubric.



Teams should enter progress on Project Milestones form [link]. Revise as necessary to prepare for project completion.


Highlight Mathematical Practice 7,    Model with mathematics, on Mathematical Practices rubric. Students should be able to state how transformations are used in practical ways in the world and show the importance of Geometry to real-world applications.






Focus: Preparation for presentations.

1. Review requirements for presentation, including the Presentation rubric. [link].

2. Have teams practice their presentation at least twice to another team. Have the listening team score the presenters on the rubric and provide feedback.



If teams are not prepared by the end of the period, they will need to meet after school or online to complete the preparation.




Focus: Presentation Day

1. Videotape presentations for feedback and posting.



Teams present. 10 minutes each.




Focus: Presentation Day

1. Videotape presentations for feedback and posting.



Teams present. 10 minutes each.




Focus: Reflection Day

1. Use your preferred method from Reflection Matrix to review project. [link]

2. Post webinar or other presentations on Geometry with Friends website.

3. Offer ideas/additions on this project on Geometry with Friends website.


Students can also reflect online using blog posts or other collaborative tools.


Use volunteers or extra credit to have students post materials if time is lmited.






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