Geometry Unit 7: Transformations

Unit Driving Question 

How can we manipulate and move objects on the coordinate plane?

Essential Questions 

1. What are the different ways to map a polygon to a congruent polygon on a coordinate plane?

2. How can we change the size of a polygon without changing it’s shape on a coordinate plane?

Launch Task 

Big Ideas for Development Lessons 

Closure & Assessment 

1 Lesson

2 Weeks

2-3 Days 

Click on the links below to see each Big Idea's Lesson Overview (includes links to teacher notes and student activities)

1. Corresponding parts of a polygon map to a congruent polygon under a rotation, reflection or translation.

2. Corresponding parts of a polygon map to a similar polygon under a dilation.

1. Formative Assessment 1 
2. Re-engagement Activity 
3. Unit Assessment

Big Idea 1: Corresponding parts of a polygon map to a congruent polygon under a rotation, reflection, or translation.

OAS-M: G.2D.1.9

Lessons and Additional Activities 

Big Idea 1 Lessons 1-5 Overview (includes links to teacher notes and student activities)

Additional Collaborative Activity:

Stations Activity: Transformations- In this activity, students will work in collaborative groups to complete stations activities that help develop an understanding of transformations.

Evidence of Understanding

Analyze the changes that are made to a polygon when rotating it on the coordinate plane.

• Identify the patterns that are developed when rotating an object 90°,180°, or 270° (clockwise and counterclockwise) about the origin

• Make conjectures to determine what a pre-image will look like after a rotation about the origin.

Analyze the changes that are made to a polygon when reflecting it on the coordinate plane. 

• Identify the patterns that are developed when reflecting a polygon (or single point) across the x-axis, y-axis, line of

• y=x, line y = -x, and any horizontal or vertical line

• Make conjectures to determine what a pre-image will look like after a reflection across:

• The y-axis generalize what happens to each variable in a point as it is reflected across the y-axis: (x,y)(-x,y)

• The x-axis generalize what happens to each variable in a point as it is reflected across the x-axis: (x,y)(x,-y)

• The line y=x generalize what happens to each variable in a point as it is reflected across the line y=x: (x,y)(y,x)

• The line y= -x generalize what happens to each variable in a point as it is reflected across the line y= -x: (x,y)(-y,-x)

• Generalize what happens to each variable in a point as it is reflected across any horizontal or vertical line: Count the distance on both sides.

Analyze the changes that are made to a polygon when translating it on the coordinate plane. 

• Identify the patterns that are developed when translating an object both horizontally and vertically across the coordinate plane

• Make conjectures to determine what a pre-image will look like after a translation across the coordinate plane

Big Idea 2: Corresponding parts of a polygon map to a similar polygon under a dilation. 

Lessons and Additional Activities

Big Idea 2 Lessons 1-2 Overview (includes links to teacher notes and student activities)

Evidence of Understanding

Analyze the changes that are made to a polygon when dilating it on a coordinate plane. 

• Identify the patterns that are developed when dilating an object with a scale factor:

• > 1- increases in size

• < 1- decreases in size

• Make conjectures to determine what a pre-image will look like after it has changed in size

• Recognize that the image and pre-image that are formed from a dilation are similar figures.

• Determine the dilation that has occurred from pre-image to image by writing the scale factor by looking at the graphs or coordinates of the polygon