# 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 Preparation

Devices are required for the digital version of the activity Graphing Areas and Scale Factors.

### Student Facing

• I can use square root graphs and do calculations to interpret the relationships between scale factors and areas.

Building Towards

### Glossary Entries

• axis of rotation

A line about which a two-dimensional figure is rotated to produce a three-dimensional 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 three-dimensional 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 three-dimensional 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 three-dimensional 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 three-dimensional figure formed by rotating a two-dimensional 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 three-dimensional figure in which all cross-sections in every direction are circles.

### Print Formatted Materials

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