MAFS.7.G.1.2

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
General Information
Subject Area: Mathematics
Grade: 7
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. (Additional 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

  • Assessment Limits :
    Given conditions should not focus on similarity or congruence or that the sum of angles in a triangle is 180 degrees. Be aware of the scoring capabilities for the GRID tool when designing these items. To distinguish from other grades, conditions should include factors other than parallel/perpendicular lines and angle measure, such as symmetry and side length.
  • Calculator :

    Neutral

  • Context :

    Allowable

Sample Test Items (3)

  • Test Item #: Sample Item 2
  • Question: Nathan wants to draw a triangle. He knows that two of the side lengths are 5 inches and 7 inches.

     What is a possible length for the third side?

  • Difficulty: N/A
  • Type: EE: Equation Editor

Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205050: M/J Grade 7 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101010: M/J Two-Dimensional Studio Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101020: M/J Two-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101040: M/J Three-Dimensional Studio Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101050: M/J Three-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond)
0101025: M/J Two-Dimensional Studio Art 2 & Career Planning (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond)
0101005: M/J Exploring Two-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101026: M/J Two-Dimensional Studio Art 3 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101035: M/J Exploring Three-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101100: M/J Visual Art 1 (Specifically in versions: 2015 - 2022, 2022 and beyond)
0101110: M/J Visual Art 2 (Specifically in versions: 2015 - 2022, 2022 and beyond)
0101120: M/J Visual Art 3 (Specifically in versions: 2015 - 2022, 2022 and beyond)
0104100: M/J Drawing 1 (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0104110: M/J Drawing 2 (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0104200: M/J Painting (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0110100: M/J Printmaking (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.G.1.AP.2a: Construct or draw plane figures using properties.

Related Resources

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

Formative Assessments

Sides of Triangles:

Students are asked to determine if given lengths will determine a triangle.

Type: Formative Assessment

Drawing Triangles SSS:

Students are asked to draw a triangle with given side lengths, and explain if these conditions determine a unique triangle.

Type: Formative Assessment

Drawing Triangles SSA:

Students are asked to draw a triangle given the lengths of two of its sides and the measure of a nonincluded angle and to decide if these conditions determine a unique triangle.

Type: Formative Assessment

Drawing Triangles SAS:

Students are asked to draw a triangle given the measures of two sides and their included angle and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Drawing Triangles ASA:

Students are asked to draw a triangle given the measures of two angles and their included side and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Drawing Triangles AAS:

Students are asked to draw a triangle given the measures of two angles and a non-included side and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Drawing Triangles AAA:

Students are asked to draw a triangle with given angle measures, and explain if these conditions determine a unique triangle.

Type: Formative Assessment

Image/Photograph

Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Type: Image/Photograph

Lesson Plans

Coding Geometry Challenges #1-7, 14 & 15:

This set of geometry challenges focuses on creating a variety of polygons 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

Coding Geometry Challenge # 16, 18 & 19:

This set of geometry challenges focuses on creating a variety of polygons using the coordinate plane 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

Triangle Inequality Investigation:

Students use hands-on materials to understand that only certain combinations of lengths will create closed triangles.

Type: Lesson Plan

Designing Geo-World: A Geometry based theme park:

In this lesson, students will investigate a contextual problem in which they will need to construct a 2-dimensional polygon, compute actual lengths and areas and then reproduce a scale drawing of the figure at a different scale. Students will also use the free application, GeoGebra (see download link under Suggested Technology) to help them design their parks.

Type: Lesson Plan

Perspectives Video: Professional/Enthusiast

Mathematically Optimizing 3D Printing:

Did you know that altering computer code can increase 3D printing efficiency? Check it out!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Kites, Geometry, and Vectors:

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Tutorials

Construct a Right Isosceles Triangle:

This video discusses constructing a right isosceles triangle with given constraints and deciding if the triangle is unique.

Type: Tutorial

Construct a Triangle with Given Side Lengths:

This video demonstrates drawing a triangle when the side lengths are given.

Type: Tutorial

Virtual Manipulative

Congruent Triangles:

This manipulative is a virtual realization of the kind of physical experience that might be available to students given three pieces of straws and told to make them into a triangle. when working with pieces that determine unique triangles (SSS, SAS, ASA). Students construct triangles with the parts provided. After building a red and a blue triangle, students can experience congruence by actually moving one on the top of the other.

Type: Virtual Manipulative

MFAS Formative Assessments

Drawing Triangles AAA:

Students are asked to draw a triangle with given angle measures, and explain if these conditions determine a unique triangle.

Drawing Triangles AAS:

Students are asked to draw a triangle given the measures of two angles and a non-included side and to explain if these conditions determine a unique triangle.

Drawing Triangles ASA:

Students are asked to draw a triangle given the measures of two angles and their included side and to explain if these conditions determine a unique triangle.

Drawing Triangles SAS:

Students are asked to draw a triangle given the measures of two sides and their included angle and to explain if these conditions determine a unique triangle.

Drawing Triangles SSA:

Students are asked to draw a triangle given the lengths of two of its sides and the measure of a nonincluded angle and to decide if these conditions determine a unique triangle.

Drawing Triangles SSS:

Students are asked to draw a triangle with given side lengths, and explain if these conditions determine a unique triangle.

Sides of Triangles:

Students are asked to determine if given lengths will determine a triangle.

Student Resources

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

Tutorials

Construct a Right Isosceles Triangle:

This video discusses constructing a right isosceles triangle with given constraints and deciding if the triangle is unique.

Type: Tutorial

Construct a Triangle with Given Side Lengths:

This video demonstrates drawing a triangle when the side lengths are given.

Type: Tutorial

Virtual Manipulative

Congruent Triangles:

This manipulative is a virtual realization of the kind of physical experience that might be available to students given three pieces of straws and told to make them into a triangle. when working with pieces that determine unique triangles (SSS, SAS, ASA). Students construct triangles with the parts provided. After building a red and a blue triangle, students can experience congruence by actually moving one on the top of the other.

Type: Virtual Manipulative

Parent Resources

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

Image/Photograph

Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Type: Image/Photograph

Virtual Manipulative

Congruent Triangles:

This manipulative is a virtual realization of the kind of physical experience that might be available to students given three pieces of straws and told to make them into a triangle. when working with pieces that determine unique triangles (SSS, SAS, ASA). Students construct triangles with the parts provided. After building a red and a blue triangle, students can experience congruence by actually moving one on the top of the other.

Type: Virtual Manipulative