In this lesson, students will learn methods for identifying congruent and similar figures. They will use the relationship between corresponding parts to make decisions regarding pairs and sets of figures. Students will use the concept of scale factor to consider the changes in figures as they are reduced and enlarged. Students will:

- identify congruent and similar polygons.
- explain the characteristics that determine similarity and congruence.
- discover the relationship between scale factor, perimeter, and area.
- graph figures and their images (including congruent, similar, and non-similar).
- write and use rules for reducing and enlarging figures, such as (
*x*,*y*) → (2*x*, 2*y*). - consider congruence and similarity of circles.
- apply congruence and similarity concepts to solve problems with missing values.
- apply the concept of scale factor to scale drawings and maps.

- How can we use the relationship between area and volume to help us draw, construct, model, and represent real situations and/or solve problems of area and volume?

**Congruent:**Having the same shape and size.**Corresponding:**Parts of a figure, such as sides and angles, which are in the same relative position in two different figures.**Similar:**Having the same shape, but a different size which is proportional to another figure.**Scale Factor:**The ratio of the lengths of the corresponding sides in similar figures, the number multiplied by the side length measures of one figure to create a reduced or enlarged image.**[IS.1 - Preparation]**

180–210 minutes **[IS.2 - All Students]**

Prerequisite Skills haven't been entered into the lesson plan.

- student copies of Vocabulary Journal pages (M-7-6_Vocabulary Journal.docx)
- ¼ inch or centimeter grid paper
- shape sets (M-7-6-3_Shape Set.docx), cut apart and place each set in an envelope or zipper bag, one set for each group of 2–4 students
- student copies of the Shape Set Record sheet (M-7-6-3_Shape Set Record Sheet.docx), one record sheet per group or per student
- one copy or transparency of the Shape Set sample responses (M-7-6-3_Shape Set Sample Record.docx)
- student copies of the Scale Factor and Similarity Labsheet and one copy or transparency of the answer key (M-7-6-3_Scale Factor Labsheet and KEY.docx)
- student copies of the Similarity Applications sheet, and 1 copy or transparency of the answer key (M-7-6-3_Similarity Applications and KEY.docx)
- 18 x 24 inch drawing paper or poster paper, 1 for each pair or small group
- markers or colored pencils for group use
- rulers, centimeter/inch
- optional: chart paper with grids for demonstration purposes
- a variety of road maps, U.S. geography maps, or local city maps (could be printed from Internet sources, pages from an old atlas, folded road maps)
- student copies of the Exit Ticket for Lesson 3 (M-7-6-3_Exit Ticket Lesson 3 and KEY.docx)
- student copies of the Rethinking Congruence and Similarity page (M-7-6-3_Rethinking Similarity and KEY.docx)
- student copies of the Size 6 Grid (M-7-6-3_Grid Size 6.docx)
- student copies of Morph Your Character record tables (M-7-6-3_Morph Your Character.docx)
- additional similarity exercises, if needed (M-7-6-3_More Work with Similarity and KEY.docx)

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

- student copies of Vocabulary Journal pages (M-7-6_Vocabulary Journal.docx)
- ¼ inch or centimeter grid paper
- shape sets (M-7-6-3_Shape Set.docx), cut apart and place each set in an envelope or zipper bag, one set for each group of 2–4 students
- student copies of the Shape Set Record sheet (M-7-6-3_Shape Set Record Sheet.docx), one record sheet per group or per student
- one copy or transparency of the Shape Set sample responses (M-7-6-3_Shape Set Sample Record.docx)
- student copies of the Scale Factor and Similarity Labsheet and one copy or transparency of the answer key (M-7-6-3_Scale Factor Labsheet and KEY.docx)
- student copies of the Similarity Applications sheet, and 1 copy or transparency of the answer key (M-7-6-3_Similarity Applications and KEY.docx)
- 18 x 24 inch drawing paper or poster paper, 1 for each pair or small group
- markers or colored pencils for group use
- rulers, centimeter/inch
- optional: chart paper with grids for demonstration purposes
- a variety of road maps, U.S. geography maps, or local city maps (could be printed from Internet sources, pages from an old atlas, folded road maps)
- student copies of the Exit Ticket for Lesson 3 (M-7-6-3_Exit Ticket Lesson 3 and KEY.docx)
- student copies of the Rethinking Congruence and Similarity page (M-7-6-3_Rethinking Similarity and KEY.docx)
- student copies of the Size 6 Grid (M-7-6-3_Grid Size 6.docx)
- student copies of Morph Your Character record tables (M-7-6-3_Morph Your Character.docx)
- additional similarity exercises, if needed (M-7-6-3_More Work with Similarity and KEY.docx)

Instructional videos haven't been assigned to the lesson plan.

DRAFT 10/10/2011

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