MAFS.912.G-CO.4.13

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Make geometric constructions. (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
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
    Assessed with:
    MAFS.912.G-CO.4.13

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)
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)
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022 (current), 2022 and beyond)
0101355: Creating Two-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0101365: Creating Three-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 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.4.AP.13a: Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.

Related Resources

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

Assessments

Sample 4 - High School Geometry State Interim Assessment:

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

Type: Assessment

Sample 2 - High School Geometry State Interim Assessment:

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

Type: Assessment

Formative Assessments

Regular Hexagon in a Circle:

Students are asked to construct a regular hexagon inscribed in a circle.

Type: Formative Assessment

Equilateral Triangle in a Circle:

Students are asked to construct an equilateral triangle inscribed in a circle.

Type: Formative Assessment

Construct the Center of a Circle:

Students are asked to construct the center of a circle.

Type: Formative Assessment

Square in a Circle:

Students are asked to construct a square inscribed in a circle.

Type: Formative Assessment

Lesson Plans

Construction of Inscribed Regular Hexagon:

A GeoGebra lesson for students to become familiar with computer based construction tools. Students work together to construct a regular hexagon inscribed in a circle using rotations. Both a beginner and advanced approach are available.

Type: Lesson Plan

Inscribe Those Rims:

This lesson will engage students with an interactive and interesting way to learn how to inscribe polygons in circles.

Type: Lesson Plan

Construction Junction:

Students will learn how to construct an equilateral triangle and a regular hexagon inscribed in a circle using a compass and a straightedge.

Type: Lesson Plan

Inscribe it:

This activity allows students to practice the construction process inscribing a regular hexagon and an equilateral triangle in a circle using GeoGebra software.

Type: Lesson Plan

Construct Regular Polygons Inside Circles :

Students will be able to demonstrate that they can construct, using the central angle method, an equilateral triangle, a square, and a regular hexagon, inscribed inside a circle, using a compass, straightedge, and protractor. They will use worksheets to master the construction of each polygon, one inside each of three different circles. As an extension to this lesson, if computers with GeoGebra are available, the students should be able to perform these constructions on computers as well.

Type: Lesson Plan

Construct This:

In this lesson, students will construct a square inscribed in a circle using the properties of a square and determine if there is more than one way to complete the construction.

Type: Lesson Plan

Paper Plate Origami:

This lesson highlights a hands-on activity where students construct inscribed regular polygons in a circle using models. Through guided questions, students will discover how to divide a model (paper plate) into 3, 4 and 6 parts. Using folding, a straightedge and compass, they will construct an equilateral triangle, a square and a regular hexagon in their circles.

Type: Lesson Plan

Crafty Circumference Challenge:

Students identify, find, and use recycled, repurposed, or reclaimed objects to create "crafty" construction tools to partition the circumference of a circle into three, four, and six congruent arcs which determine vertices of regular polygons inscribed in the circle.

Type: Lesson Plan

St. Pi Day construction with a compass & ruler:

St. Pi Day construction with compass

This activity uses a compass and straight-edge(ruler) to construct a design. The design is then used to complete a worksheet involving perimeter, circumference, area and dimensional changes which affect the scale factor ratio.

Type: Lesson Plan

Original Student Tutorials

A Square Peg in a Round Hole:

Learn how to construct an inscribed square in a circle and why certain constructions are used in this interactive tutorial.

Type: Original Student Tutorial

Designing with Hexagons:

Learn how to construct an inscribed regular hexagon and equilateral triangle in a circle in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Inscribing a hexagon in a circle:

This problem solving task challenges students to inscribe equilateral triangles and regular hexagons on a circle with a compass and straightedge.

Type: Problem-Solving Task

Tutorial

Constructing Polygons Inscribed in Circles:

Click "View Site" to open a full-screen version. Geometric constructions using tools such as a compass and straightedge can help students better understand geometric concepts and the underlying principles that govern their relationships. The focus in this tutorial is on the construction of an equilateral triangle, square, and regular hexagon inscribed in a circle.

Type: Tutorial

Virtual Manipulative

Inscribe a Regular Hexagon in a Circle:

This geogebratube interactive worksheet shows the step by step process for inscribing a regular hexagon in a circle. There are other geogebratube interactive worksheets for the square and the equilateral triangle.

Type: Virtual Manipulative

MFAS Formative Assessments

Construct the Center of a Circle:

Students are asked to construct the center of a circle.

Equilateral Triangle in a Circle:

Students are asked to construct an equilateral triangle inscribed in a circle.

Regular Hexagon in a Circle:

Students are asked to construct a regular hexagon inscribed in a circle.

Square in a Circle:

Students are asked to construct a square inscribed in a circle.

Original Student Tutorials Mathematics - Grades 9-12

A Square Peg in a Round Hole:

Learn how to construct an inscribed square in a circle and why certain constructions are used in this interactive tutorial.

Designing with Hexagons:

Learn how to construct an inscribed regular hexagon and equilateral triangle in a circle in this interactive tutorial.

Student Resources

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

Original Student Tutorials

A Square Peg in a Round Hole:

Learn how to construct an inscribed square in a circle and why certain constructions are used in this interactive tutorial.

Type: Original Student Tutorial

Designing with Hexagons:

Learn how to construct an inscribed regular hexagon and equilateral triangle in a circle in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Inscribing a hexagon in a circle:

This problem solving task challenges students to inscribe equilateral triangles and regular hexagons on a circle with a compass and straightedge.

Type: Problem-Solving Task

Virtual Manipulative

Inscribe a Regular Hexagon in a Circle:

This geogebratube interactive worksheet shows the step by step process for inscribing a regular hexagon in a circle. There are other geogebratube interactive worksheets for the square and the equilateral triangle.

Type: Virtual Manipulative

Parent Resources

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

Problem-Solving Task

Inscribing a hexagon in a circle:

This problem solving task challenges students to inscribe equilateral triangles and regular hexagons on a circle with a compass and straightedge.

Type: Problem-Solving Task