Students will be able to understand and apply the concept of dilation, including identifying the center, determining the scale factor, and recognizing similarities between dilated figures and the original figure.
Students will be assessed through a worksheet that includes various figures for dilation. They will need to identify the center of dilation, calculate the scale factor, and determine the dilated image's dimensions based on a given scale factor.
Dilation: An enlargement or reduction of a figure that preserves shape but not size. All dilations are similar to the original figure.
Center and Scale Factor: Dilations have a center and a scale factor. The center is the point of reference for the dilation, and the scale factor (k) tells us how much the figure stretches or shrinks.
Formula for Dilation:
If the center of dilation is at point O and the scale factor is k:
The coordinates of the dilated point A' are given by:
A' = k * OA
The distances between points are all multiplied by the scale factor k.
Introduction of the topic with real-world examples of dilation (e.g., resizing images on a computer)
Engage students with a teaser question: "How can we change the size of a shape without changing its shape?"
Explain definition of dilation and give examples
Introduce the concept of a center of dilation and its significance
Provide examples of calculating scale factor in dilations
Common misconception to anticipate: Confusing scale factor with the actual measurements of the dilated figure
Demonstrate how to find the center of dilation and calculate the scale factor with guided examples
Scaffold questioning from basic to complex, allowing students to practice identifying the key components of dilation
Monitor student performance by circulating the classroom and providing feedback as needed
Assign a worksheet with figures for dilation where students need to identify the center, calculate the scale factor, and determine the dimensions of the dilated figure
Encourage students to work independently and ask for assistance if needed
Review key concepts of dilation by asking students to share one thing they learned about dilations today
Challenge early finishers to create their own set of dilated figures using a given scale factor and center of dilation. They can then swap with a partner to solve each other's dilation problems.
For homework, students should practice dilating different figures at home and come prepared to discuss their findings in the next class.
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, and parallel lines.