Unit 6: Extreme Fractions

Unit 6: Extreme Fractions

Unit 6: Extreme Fractions Banner

Overviews

Fractions Diagram

Unit 6: Extreme Fractions

This unit will illustrate the difference between shape and size as they relate to the concepts of congruency and similarity.

Unit Focus

Reading Process

Vocabulary Development

  • The student will use new vocabulary that is introduced and taught directly.
  • The student will listen to, read, and discuss familiar and conceptually challenging text.
  • The student will relate new vocabulary to familiar words.

Algebra Body of Knowledge

Radical Expressions and Equations

    • Simplify algebraic ratios.
    • Solve algebraic proportions.

Vocabulary

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Lesson 1: Ratios and Proportions

Lesson 1: Ratios and Proportions Banner

Lesson Overview

Rations and Proportions Image

Lesson 1: Ratios and Proportions

We should be able to see that changing the size of a geometric figure can occur without changing the shape of a figure. Working with ratios and proportions will help us understand the relationship between congruence and similarity.

Reading Process

Vocabulary Development

  • The student will use new vocabulary that is introduced and taught directly.
  • The student will listen to, read, and discuss familiar and conceptually challenging text.

Algebra Body of Knowledge

Radical Expressions and Equations

    • Simplify algebraic ratios.
    • Solve algebraic proportions.

Lesson Reading

Video

 

Click Image to View Video on Ratios and Proportions

Click Image to View Video on Ratios and Proportions

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Lesson 2: Similarity and Congruence

Lesson 2: Similarity and Congruence Banner

Lesson Overview

Proportion Definition and Example

Lesson 2: Similarity and Congruence

Similarity and congruence are concepts used to describe relationships between geometric figures.

  • Similarity: Similarity refers to the property of two geometric figures having the same shape but possibly different sizes. In similar figures, corresponding angles are equal, and corresponding sides are proportional. Symbolically, if two figures are similar, they are often denoted by the symbol '∼'.

  • Congruence: Congruence, on the other hand, describes the property of two geometric figures being identical in shape and size. In congruent figures, all corresponding angles are equal, and all corresponding sides have the same length. Congruent figures can be obtained by translations, rotations, reflections, and combinations of these transformations. Congruence is typically denoted by the symbol '≅'.

Understanding similarity and congruence is fundamental in geometry, as these concepts are used to prove theorems, solve problems, and analyze relationships between geometric objects. They play a significant role in various fields, including architecture, engineering, physics, and computer graphics.

 

Reading Process

Vocabulary Development

  • The student will use new vocabulary that is introduced and taught directly.
  • The student will listen to, read, and discuss familiar and conceptually challenging text.
  • The student will relate new vocabulary to familiar words.

Algebra Body of Knowledge

  • Radical Expressions and Equations
  • Solve algebraic proportions.

Lesson Reading

Video

Click Image to View Video on Similarity and Congruence

Click Image to View Video on Similarity and Congruence