Standard #: MAFS.8.G.1.3 (Archived Standard)


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Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.


General Information

Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software. (Major 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 - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    Coordinate values of ?? and ?? must be integers. The number of transformations should be no more than two. In items that require the student to draw a transformed figure using a dilation or a rotation, the center of the transformation must be given.
    Calculator :

    Neutral

    Context :

    Allowable



Sample Test Items (3)

Test Item # Question Difficulty Type
Sample Item 1 Triangle ABC is translated 5 units to the right to create triangle A’B’C’. 

Use the Connect Line tool to draw triangle A’B’C’.

N/A GRID: Graphic Response Item Display
Sample Item 2

Quadrilateral ABCD is rotated 90° clockwise about the origin to create quadrilateral A’B’C’D’.

Use the Connect Line tool to draw quadrilateral A’B’C’D’.

N/A GRID: Graphic Response Item Display
Sample Item 3

A pentagon is shown.

The pentagon is translated 5 units to the left and then reflected over the x-axis.

Use the Connect Line tool to draw the pentagon after its transformations.

 

N/A GRID: Graphic Response Item Display


Related Courses

Course Number1111 Course Title222
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
7912115: Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))


Related Resources

Educational Software / Tool

Name Description
Transformations Using Technology

This virtual manipulative can be used to demonstrate and explore the effect of translation, rotation, and/or reflection on a variety of plane figures. A series of transformations can be explored to result in a specified final image.

Formative Assessments

Name Description
Translation Coordinates

Students are asked to translate two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

Rotation Coordinates

Students are asked to rotate two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

Reflection Coordinates

Students are asked to reflect two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

Dilation Coordinates

Students are asked to dilate two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

Lesson Plans

Name Description
Coding Geometry Challenge #10 & 11

This set of geometry challenges focuses on scaled drawings and area 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.

Coding Geometry Challenge #23 & 24

This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. 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.

Slide to the Left... Slide to the Right!

Students will identify, review, and analyze transformations. They will demonstrate their understanding of transformations in the coordinate plane by creating original graphs of polygons and the images that result from specific transformations.

Exploring Rotations with GeoGebra

This lesson will help students understand the concept of a geometric rotation. The teacher/students will use a GeoGebra applet to derive the rules for rotating a point on the coordinate plane about the origin for a 90 degree, 180 degree, and a 270 degree counterclockwise rotation.

Problem-Solving Tasks

Name Description
Reflecting Reflections

In this resource, students experiment with successive reflections of a triangle in a coordinate plane.

Point Reflection

The purpose of this task is for students to apply a reflection to a single point. The standard asks students to apply rigid motions to lines, line segments, and angles. Although this problem only applies a reflection to a single point, it has high cognitive demand if the students are prompted to supply a picture. This is because the coordinates of the point (1000,2012) are very large. If students try to plot this point and the line of reflection on the usual x-y coordinate grid, then either the graph will be too big or else the point will lie so close to the line of reflection that it is not clear whether or not it lies on this line. A good picture requires a careful choice of the appropriate region in the plane and the corresponding labels. Moreover, reflections of lines, line segments, and angles are all found by reflecting individual points.

Triangle congruence with coordinates

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Student Center Activity

Name Description
Edcite: Mathematics Grade 8

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Tutorial

Name Description
Scaling Down a Triangle by Half

This video demonstrates the effect of a dilation on the coordinates of a triangle.

Virtual Manipulative

Name Description
Rotation of a Point

This virtual manipulative is an interactive visual presentation of the rotation of a point around the origin of the coordinate system. The original point can be dragged to different positions and the angle of rotation can be changed with a 90° increment.

Student Resources

Educational Software / Tool

Name Description
Transformations Using Technology:

This virtual manipulative can be used to demonstrate and explore the effect of translation, rotation, and/or reflection on a variety of plane figures. A series of transformations can be explored to result in a specified final image.

Problem-Solving Tasks

Name Description
Reflecting Reflections:

In this resource, students experiment with successive reflections of a triangle in a coordinate plane.

Point Reflection:

The purpose of this task is for students to apply a reflection to a single point. The standard asks students to apply rigid motions to lines, line segments, and angles. Although this problem only applies a reflection to a single point, it has high cognitive demand if the students are prompted to supply a picture. This is because the coordinates of the point (1000,2012) are very large. If students try to plot this point and the line of reflection on the usual x-y coordinate grid, then either the graph will be too big or else the point will lie so close to the line of reflection that it is not clear whether or not it lies on this line. A good picture requires a careful choice of the appropriate region in the plane and the corresponding labels. Moreover, reflections of lines, line segments, and angles are all found by reflecting individual points.

Triangle congruence with coordinates:

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Student Center Activity

Name Description
Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Tutorial

Name Description
Scaling Down a Triangle by Half:

This video demonstrates the effect of a dilation on the coordinates of a triangle.

Virtual Manipulative

Name Description
Rotation of a Point:

This virtual manipulative is an interactive visual presentation of the rotation of a point around the origin of the coordinate system. The original point can be dragged to different positions and the angle of rotation can be changed with a 90° increment.



Parent Resources

Problem-Solving Tasks

Name Description
Reflecting Reflections:

In this resource, students experiment with successive reflections of a triangle in a coordinate plane.

Point Reflection:

The purpose of this task is for students to apply a reflection to a single point. The standard asks students to apply rigid motions to lines, line segments, and angles. Although this problem only applies a reflection to a single point, it has high cognitive demand if the students are prompted to supply a picture. This is because the coordinates of the point (1000,2012) are very large. If students try to plot this point and the line of reflection on the usual x-y coordinate grid, then either the graph will be too big or else the point will lie so close to the line of reflection that it is not clear whether or not it lies on this line. A good picture requires a careful choice of the appropriate region in the plane and the corresponding labels. Moreover, reflections of lines, line segments, and angles are all found by reflecting individual points.

Triangle congruence with coordinates:

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.



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