Understanding Dilation in the Coordinate Plane

Objective:

Students will be able to understand and apply the concept of dilation in the coordinate plane by multiplying each coordinate by a given scale factor.

Assessment:

Students will demonstrate their mastery of dilation in the coordinate plane through a worksheet where they will dilate different shapes on a coordinate grid by a specified scale factor.

Key Points:

• Definition of Dilation: Dilation in the coordinate plane involves multiplying each coordinate by a scale factor, known as mapping.

• Mapping: Mapping is a procedure where points on a coordinate grid are plotted to observe the behavior of a function.

• Dilation Formula: For any dilation, the mapping of a point (x, y) will be (kx, ky).

Opening:

• Introduce the concept of dilation by discussing how resizing images can change their appearance.

• Ask students to think about how resizing an image on a screen works and what happens to the coordinates of each point.

Introduction to New Material:

• Explain the concept of dilation using real-world examples such as enlarging or reducing a map scale.

• Show visuals of shapes being dilated on a coordinate grid.

• Anticipated misconception: Students may confuse dilation with translation. Emphasize the difference by highlighting that dilation involves scaling while translation involves moving.

Guided Practice:

• Provide examples of shapes on a coordinate grid and guide students through dilating them by a scale factor.

• Scaffold questioning from simple dilations to more complex ones to ensure understanding.

• Monitor student performance by circulating the classroom, observing their work, and providing immediate feedback.

Independent Practice:

• Assign students a worksheet with various shapes to dilate on a coordinate grid using different scale factors.

• Require students to label each point before and after dilation to demonstrate their understanding.

Closing:

• Have students share their answers and explain how they performed the dilations.

• Summarize the key points of the lesson and ask students to reflect on how dilation changes the appearance of shapes.

Extension Activity:

• For early finishers, provide a challenge task where they have to dilate irregular shapes on a coordinate grid based on both fractional and whole number scale factors.

Homework:

• As homework, students can research real-life applications of dilation in architecture or art and write a short paragraph explaining how dilations are used in those fields.

Standards Addressed:

• 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 inputs and give other points as outputs. ((Note: CCSS.MATH.CONTENT.HSG.CO.A.2 standards will be tailored to the grade level with the appropriate rigor and detail)

• CCSS.MATH.CONTENT.HSG.CO.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of corresponding angles and the proportionality of corresponding sides.