Standard #: MAFS.912.G-CO.1.1 (Archived Standard)


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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.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
Cluster: Experiment with transformations in the plane. (Geometry - Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :

     None

    Calculator :

    Neutral

    Clarification :
    Students will use the precise definitions of angles, circles,
    perpendicular lines, parallel lines, and line segments, basing the
    definitions on the undefined notions of point, line, distance along a
    line, and distance around a circular arc.
    Stimulus Attributes :
    Items may be set in a real-world or mathematical context

    Items may require the student to analyze possible definitions to
    determine mathematical accuracy.

    Items may require the student to use definitions for justifications
    when choosing examples or nonexamples.

    Items may require the student to use properties of rotations,
    reflections, and translations as steps to a formal definition.

    Response Attributes :

    None



Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1

Kyle defines a circle as "the set of all the points equidistant from a given point."

Explain why Kyle's definition is not precise enough.

Type your answer in the space provided.

N/A OR: Open Response


Related Courses

Course Number1111 Course Title222
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0101340: Three-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0101350: Three-Dimensional Studio Art 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104340: Drawing 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104350: Drawing 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104360: Drawing 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104370: Painting 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104380: Painting 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104390: Painting 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0109310: Portfolio Development: Drawing-Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0109320: Portfolio Development: Two-Dimensional Design Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0109330: Portfolio Development: Three-Dimensional Design Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0114800: Florida's Preinternational Baccalaureate Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0114810: Florida's Preinternational Baccalaureate Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912070: Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 - 2023, 2023 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))


Related Resources

Formative Assessments

Name Description
Definition of Line Segment

Students are asked to draw, label, and give a precise definition of a line segment.

Definition of a Circle

Students are asked to draw, label and give a precise definition of the term circle.

Definition of Parallel Lines

Students are asked to draw, label, and give a precise definition of parallel lines.

Definition of Perpendicular Lines

Students are asked to draw, label, and give a precise definition of perpendicular lines.

Definition of an Angle

Students are asked to draw, label, and give a precise definition of an angle.

Lesson Plans

Name Description
Coding Geometry Challenge # 12 & 13

This set of geometry challenges focuses on creating circles and calculating area/circumference as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor

Basic Definitions in Geometry

A set of basic definitions in geometry (line segment, ray, angle, perpendicular lines, and parallel lines) is addressed. The notation used in naming each defined term is also emphasized.

Musical Chairs with Words and a Ball

This lesson introduces students to concepts and skills that they will use throughout the year. Students will learn that the terms point, and line are considered "undefined." Students will play musical chairs while learning to develop precise definitions of circle, angle, parallel line, and perpendicular line, using counterexamples at different classroom stations. Students will identify models, use notation, and make sketches of these terms.

Pick Your Words Precisely!

Students will develop precise definitions of the terms angle, circle, line segment, parallel line and perpendicular line by completing a graphic organizer under the Frayer model through small and whole group discussion.

Sage and Scribe - Points, Lines, and Planes

Students will practice using precise definitions while they draw images of Points, Lines, and Planes. Students will work in pairs taking turns describing an image while their partner attempts to accurately draw the image.

Building Blocks of Geometry

Students will be introduced to the undefinable concepts of points, lines, and planes that are the building blocks of geometry and recognize that these three terms become the basis for many other geometric definitions. Students will participate in a Building Block Scavenger Hunt, using cameras to photograph examples of specified terms that they find outside of the math classroom. The students will compose a power point to display their photographs of the required terms.
This lesson is adapted from a presentation that included an activity by Dianne Olix, 1995.

Virtually Possible

This is a ray drawing activity to aid students in their understanding of how virtual images are formed by plane mirrors, and how the image size and distance from the mirror compare to those of the object.

Problem-Solving Tasks

Name Description
Unit Squares and Triangles

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Tangent Lines and the Radius of a Circle

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Tutorials

Name Description
Specifying planes in three dimensions

In this tutorial, students are introduced to the concept that three non-collinear points are necessary to define a unique plane.

The language of geometry

Before learning any new concept it's important students learn and use common language and label concepts consistently. This tutorial introduces students to th point, line and plane.

Identifying parallel and perpendicular lines

This tutorial is great practice for help in identifying parallel and perpendicular lines.

Basic Geometry Language and Labels

In this tutorial we will learn the basics of geometry, such as identifying a line, ray, point, and segment.

Video/Audio/Animation

Name Description
Parallel Lines

This video illustrates how to determine if the graphs of a given set of equations are parallel.

Student Resources

Problem-Solving Tasks

Name Description
Unit Squares and Triangles:

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Tangent Lines and the Radius of a Circle:

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Tutorials

Name Description
Specifying planes in three dimensions:

In this tutorial, students are introduced to the concept that three non-collinear points are necessary to define a unique plane.

The language of geometry:

Before learning any new concept it's important students learn and use common language and label concepts consistently. This tutorial introduces students to th point, line and plane.

Identifying parallel and perpendicular lines:

This tutorial is great practice for help in identifying parallel and perpendicular lines.

Basic Geometry Language and Labels:

In this tutorial we will learn the basics of geometry, such as identifying a line, ray, point, and segment.

Video/Audio/Animation

Name Description
Parallel Lines:

This video illustrates how to determine if the graphs of a given set of equations are parallel.



Parent Resources

Problem-Solving Tasks

Name Description
Unit Squares and Triangles:

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Tangent Lines and the Radius of a Circle:

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.



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