Tools of Geometry

12 Components
Initial Task
Transformer
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Representing & Combining Transformations
Re-engagement
Re-engagement for Unit 1
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources for GEO Unit 1 Find aligned Regents questions with Quiz Banker
Geo U1: Tools of Geometry
Unit Outline
Initial Task
Transformer
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Representing & Combining Transformations
Re-engagement
Re-engagement for Unit 1
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources for GEO Unit 1 Find aligned Regents questions with Quiz Banker
None
Geo U1:

Tools of Geometry

What does it mean for geometric figures to be congruent?
6 weeks
See Standards
Common Core: Major Standards:
G-CO.B.6

Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-CO.B.7

Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

G-CO.B.8

Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Common Core: Supporting Standards:
G-CO.A.1

Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-CO.A.2

Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.A.3

Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Clarification: Trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.”

G-CO.A.4

Experiment with transformations in the plane. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G-CO.A.5

Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.D.12

Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

G-CO.D.13

Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Unit one is about using tools to explain the congruence within and between polygons, focusing on triangles and regular polygons. Students will strategically use a variety of tools, including constructions and transformations, to justify the congruent relationships of sides, angles, and polygons. Developing fluency in construction is NOT an end in and of itself—it must connect to conceptual understanding.

Essential Questions:

  • What does it mean for geometric figures to be congruent?
  • How are constructions and transformations used to understand and be more precise about congruence?
  • How are constructions used to understand and be more precise about rigid motion transformations?
Printable Unit Plan
  • Geometry Unit Plan for Unit 1
    Resource:
    Geometry Unit Plan for Unit 1

    This is a printable version of the entire unit plan. You can make a copy of it and edit it or download and print it as needed.

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Unit Outline

12 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 5 itemsHide 5 items

Formative Assessment Lesson See 1 itemHide 1 item

Re-engagement See 1 itemHide 1 item

End of Unit Assessments See 4 itemsHide 4 items