This unit builds on the previous two units as students expand their understanding of transformations to include similarity transformations. This unit also connects with studentsâ€™ prior work with scale drawings and proportional reasoning (7.G.1, 7.RP.A.2) These understandings are applied in unit 7 as students use similar triangles to explain why the slope, m, is the same between any two distinct points on a nonvertical line in the coordinate plane (8.EE.B.6)
Key Concepts:
 A dilation of a twodimensional figure produces a figure that is smaller than, larger than, or the same size as the original figure.
 The figure resulting from a transformation (dilations, rotations, reflections, or translations) is similar to the original figure because certain attributes are preserved (angle measures).
 The figure resulting from a series of different transformations (dilations, rotations, reflections, or translations) is similar to the original figure because certain attributes are preserved.
Prior Knowledge Needed:
 Solve problems involving scale drawings; 7.G.A.1
 Recognize and represent proportional relationships between quantities; 7.RP.A.2
 Recognize the properties of rotations, reflections, and translations; 8.G.A.1
 Understand congruence in twodimensional shapes; 8.G.A.2
Units on the Horizon:
 Use similar triangles to explain slope; 8.EE.6
 Understand similarity in terms of similarity transformation; G.SRT.1
 Determine if two shapes are similar; G.SRT.2
Lessons

Lesson objective: Understand that a dilation of a twodimensional shape produces a shape that is smaller than, larger than, or the same size as the original shape. Students bring prior knowledge of proportionality from 7.RP.A.2. This prior knowledge is ...

Lesson objective: Understand that shapes with the same name are not necessarily similar. To be similar, the shapes must have the same scale factor or ratio when comparing dimensions. Students bring prior knowledge of proportionality from 7.RP.A.2. This ...

Lesson objective: Apply understanding that a dilation of a twodimensional shape produces a shape that is smaller than, larger than, or the same size as the original shape by drawing a diagram of a farm. Students bring prior knowledge of proportionality...

Lesson objective: Identify similarity in shapes with the same name. This lesson helps to build fluency with identifying attributes of similar shapes. A coordinate plane is used here because it allows students to determine lengths either by the numbers o...

Lesson objective: Understand that similarity between shapes can be proven by identifying two pairs of congruent corresponding angles. Students bring prior knowledge of the attributes of dilated shapes from 8.G.A.3. This prior knowledge is extended to pr...

Lesson objective: Fluently determine similarity in triangles by identifying equivalent relationships of the sides or identifying two pair of congruent corresponding angles. This lesson helps to build fluency with the attributes of similar shapes. Triang...

Lesson objective: Apply knowledge of similarity in triangles by identifying equivalent relationships of the sides or identifying two pair of congruent corresponding angles. This lesson helps to build fluency with the attributes of similar shapes. Triang...

Lesson objective: Understand that an image resulting from a series of different transformations (dilations, rotations, reflections, or translations) is similar to the original shape because the corresponding lengths have a common scale factor and the co...

Lesson objective: Fluently understand that an image resulting from a series of different transformations (dilations, rotations, reflections, or translations) is similar to the original shape because the corresponding lengths have a common scale factor a...

Lesson objective: Apply the understanding that an image resulting from a series of different transformations (dilations, rotations, reflections, or translations) is similar to the original shape because the corresponding lengths have a common scale fact...
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