Lesson 1: Areas of Triangles

Abstract

This study guide contains a series of lessons that could be used as a unit or partial unit on geometric shapes and their properties. Several of the lessons are concerned with basic concepts of shapes in the plane such as perimeter and area. Another lesson looks at interior angles of polynomials. The Pythagorean Theorem is covered in some depth to include distance in a coordinate plane. These lessons are designed to be taught in a 7^th or 8^th grade Mathematics class but are also suitable for review in the 9^th grade. Throughout the lessons an emphasis is placed on mathematics as its own language. While teaching mathematical concepts, one must also teach students to communicate effectively in this new language. Exit tickets, and vocabulary exercises are used extensively throughout this guide with other techniques used as appropriate.

Table of Contents

Abstract 2

Introduction. 4

Lessons. 5

Lesson 1: Areas of Triangles. 5

Lesson 2 Area of a Rectangle / Area Addition Postulate. 8

Lesson 3: Area of a Trapezoid. 11

Lesson 4: Area of a Regular Polygon. 14

Lesson 5: Surface Area and Volume of a Right Prism.. 17

Lesson 6: Perfect Squares and Irrational Number 20

Lesson 7: Pythagorean Theorem.. 24

Lesson 8: Distance Lesson Plan. 29

Lesson 9: Proportion and Scale. 32

Lesson 10: Proportion Measuring Height Indirectly. 34

Conclusions. 38

References. 39

Introduction

The lessons presented in this guide are based on lessons that have been given in our classrooms over the last two years. They can be used as one or more units or partial units in geometry. While the lessons are primarily aimed at 7^th and 8^th grade students, they could also be used in the 9^th grade for review. They have been modified to include some of the techniques that we have studied in this course.

As we worked on this guide and reviewed various lessons for inclusion, we realized that Mathematics is truly its own language. We struggle on a daily basis not just to help our students to comprehend English but also to teach them an entirely new way of looking at the world along with a new and complex vocabulary to describe this new world view. We are continuously translating from English to Math symbology as well as providing new definitions for common words applied to a mathematical setting.

As a result of this need to teach the language, vocabulary is a key part of most of our lessons either directly or indirectly. A word wall is a feature of our classrooms that is constantly updated. We use many activities to emphasis the meaning of various terms and symbols such as tables, 8 page books, flowcharts, etc. Exit tickets are used frequently to check for understanding. We use both expression and equation type exit tickets as well as “think and explain” type tickets in our various lessons. While this guide is concerned primarily with geometric shapes and principles, the techniques used can readily be applied to other lessons. The key is to use various methods to help students to understand the concepts and the language of math rather than just have them memorize procedures to “plug and jug” answers.

Lessons

Lesson Component	Description of Component For This Lesson
Lesson Opening   (10 minutes)     Introduction of New Material (5 minutes)	Objective: To calculate the area of different types of triangles. SWBAT: (1) identify types of triangles and their component parts (2) identify the height of a triangle, or construct the height. (3) calculate the area and perimeter of a triangle   Do Now: Refresh the Pythagorean Theorem, factoring, radical expressions. Find the roots of: y2 +4y – 12 = 0 Solve for x: x2 - 2y2 = 2z2, where y=3, z=5   Homework posted on board as students enter [HW] Pg. 431, No. 1, 2, 5, 6, 10, 11, 12, 15, 16   (1) Mini-lesson I will describe the characteristics of different triangles: right, obtuse, acute, and isosceles. I will identify the height in each case. I will review the proper formula for calculating the area of a triangle and constructing the height of each type plus define all variables (Area A, height h, base b and perimeter p). I will define perimeter.   A = ½bh, p = ∑ [sides] (2) Engagement I will demonstrate an example using a right triangle, identifying the component parts and calculating the area and perimeter each time. I will show how each leg could represent the base, b, in this case. Repeat with the different triangles and different components missing (Area, height, base or perimeter).
Student Practice of New Material (20 minutes)	(3) Exploration/Application Students will identify the base and height in several triangles and decide how to apply the Area formula to solve for the unknown component of the triangle in a table. Students will apply the Area formula to complete the table in their notebooks. Students will compute the perimeters for each triangle.
Summary (5 minutes)	(4) Assessment An exit ticket to assess, hand out index cards. Students will express, in words, the proper method for calculating the area, A, of triangle ABC where angle BCA is a right angle. (more than one answer exists!) Submit index card before departing class.

Lesson 1: Areas of Triangles

Part 3. Complete the table below in your notebook using the formula for the Area and perimeter of a triangle. Title the entry “Area of a Triangle”.

Exit Ticket (describe how to find Area, A) :

B

C A

Homework

Date: 2015-12-24; view: 776