MAFS.912.G-CO.1.1

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: Level 1: Recall
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
Assessed: Yes
Test Item Specifications

  • 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 #: Sample Item 1
  • Question:

    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.

  • Difficulty: N/A
  • Type: OR: Open Response

Related Courses

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

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-CO.1.AP.1a: Identify 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.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 1 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 4 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Formative Assessments

Definition of Line Segment:

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

Type: Formative Assessment

Definition of a Circle:

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

Type: Formative Assessment

Definition of Parallel Lines:

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

Type: Formative Assessment

Definition of Perpendicular Lines:

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

Type: Formative Assessment

Definition of an Angle:

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

Type: Formative Assessment

Lesson Plans

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

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Sage and Scribe - Points, Lines, and Planes:

Students will practice using precise definitions and words while they describe and 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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Problem-Solving Tasks

Unit Squares and Triangles:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorials

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.

Type: Tutorial

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.

Type: Tutorial

Identifying parallel and perpendicular lines:

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

Type: Tutorial

Basic Geometry Language and Labels:

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

Type: Tutorial

Video/Audio/Animation

Parallel Lines:

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

Type: Video/Audio/Animation

MFAS Formative Assessments

Definition of a Circle:

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

Definition of an Angle:

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

Definition of Line Segment:

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

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.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Unit Squares and Triangles:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorials

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.

Type: Tutorial

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.

Type: Tutorial

Identifying parallel and perpendicular lines:

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

Type: Tutorial

Basic Geometry Language and Labels:

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

Type: Tutorial

Video/Audio/Animation

Parallel Lines:

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

Type: Video/Audio/Animation

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Unit Squares and Triangles:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task