CCSS.Math.Content.HSG-CO.A

CCSS.Math.Content.HSG-CO.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSG-CO.A.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 ...

• CCSS.Math.Content.HSG-CO.A.2

  Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as...

• CCSS.Math.Content.HSG-CO.A.3

  Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

• CCSS.Math.Content.HSG-CO.A.4

  Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

• CCSS.Math.Content.HSG-CO.A.5

  Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. ...

01

What Students Need to Do

Students move figures using translations, rotations, and reflections, both on paper and on a coordinate plane. They describe each move precisely and track what happens to points, lengths, angles, and orientation.

02

What Mastery Looks Like

Students accurately draw and label images after translations, rotations, and reflections. They can describe a transformation or sequence that maps one figure onto another and explain which lengths, angles, and orientations are preserved or changed.

03

Common Misconceptions

Students often reverse clockwise and counterclockwise turns or reflect across the wrong line. They may apply coordinate rules without checking the diagram, change side lengths during rigid motions, or mismatch corresponding vertices.

04

How to Assess It

Give students triangle A(1, 2), B(4, 2), C(2, 5). Ask them to rotate it 90 degrees counterclockwise about the origin, list the new coordinates, and name two preserved properties.

1. 01

   Cut a scalene triangle from tracing paper, translate, rotate, and reflect it on a grid, then trace each image and label corresponding vertices.

2. 02

   Show two congruent polygons and ask, "What sequence of moves maps the first onto the second, and how can you verify it?"

3. 03

   Play transformation bingo with coordinate rules, diagrams, and names, requiring students to match equivalent representations and justify each match.

4. 04

   Photograph a tile pattern, identify its translations, rotations, and reflections, then mark the centers, vectors, and mirror lines.

• CCSS.Math.Content.HSN-VM.C.12

  (+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

• CCSS.Math.Content.8.G.A.1

  Verify experimentally the properties of rotations, reflections, and translations: