Lesson 5
Scaling and Unscaling
Lesson Narrative
In this lesson, students practice working with areas of scaled figures, connecting them to cross sections and encountering a common misconception.
Then, they create a graph representing \(y=\sqrt{x}\) and use it to answer questions about a situation. They analyze the shape of the graph to better understand the relationship between an area and the scale factor needed to achieve it.
When students consider two arguments (one of which includes a common misconception) and decide which is correct, they are critiquing the reasoning of others (MP3).
Learning Goals
Teacher Facing
 Describe (using words and other representations) the relationships between scale factors and areas using square root graphs and calculations.
Student Facing
 Let’s examine the relationships between areas of dilated figures and scale factors.
Required Materials
Required Preparation
Devices are required for the digital version of the activity Graphing Areas and Scale Factors.
Learning Targets
Student Facing
 I can use square root graphs and do calculations to interpret the relationships between scale factors and areas.
CCSS Standards
Glossary Entries

axis of rotation
A line about which a twodimensional figure is rotated to produce a threedimensional figure, called a solid of rotation. The dashed line is the axis of rotation for the solid of rotation formed by rotating the green triangle.

cone
A cone is a threedimensional figure with a circular base and a point not in the plane of the base called the apex. Each point on the base is connected to the apex by a line segment.

cross section
The figure formed by intersecting a solid with a plane.

cylinder
A cylinder is a threedimensional figure with two parallel, congruent, circular bases, formed by translating one base to the other. Each pair of corresponding points on the bases is connected by a line segment.

face
Any flat surface on a threedimensional figure is a face.
A cube has 6 faces.

prism
A prism is a solid figure composed of two parallel, congruent faces (called bases) connected by parallelograms. A prism is named for the shape of its bases. For example, if a prism’s bases are pentagons, it is called a “pentagonal prism.”

pyramid
A pyramid is a solid figure that has one special face called the base. All of the other faces are triangles that meet at a single vertex called the apex. A pyramid is named for the shape of its base. For example, if a pyramid’s base is a hexagon, it is called a “hexagonal pyramid.”

solid of rotation
A threedimensional figure formed by rotating a twodimensional figure using a line called the axis of rotation.
The axis of rotation is the dashed line. The green triangle is rotated about the axis of rotation line to form a solid of rotation.

sphere
A sphere is a threedimensional figure in which all crosssections in every direction are circles.
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