References: This lesson should teach to one of the topics in either Everyday Math or Impact Math that leads to a regents question. I have also listed a sample Regents Question from Baron’s (page, year and question number), which the lesson addresses.
My Mathematics Lesson Plan 2
Special Education Class
Lesson Topic: Exploring the Interior Angles of a Triangle
I have chosen the above mathematics topic from our class text: Barons Regents Review Math ”A”. This lesson is geared towards teaching to the following lesson in Barons Math A
Lesson: Triangle Angle Sum (pages 127-132)
(Page , 129 Question 1 ).
At the end of this lesson plan I will describe how this lesson is in alignment with the Impact Math approach.
Lesson Overview
Title: Exploring the Interior Angles of a Triangle
Author: Tracy Boyer
Subject: Mathematics
Area: Geometry
Grade Level(s): 5th grade
Duration: 50 minutes
Unit Description
Throughout this unit, students will explore angles, how to measure angles, classify, compare, and identify relationships between measures of angles. Students will measure and draw angles using protractors. Students will apply estimation to identifying angles. Students will be able to use multiple forms of representation to explore and represent mathematical thinking and relationships. Students will be able to discover the relationship among the interior angles of a triangle and draw conclusions on the sum of their angles. Students will be able to solve for the missing angle of a triangle. Students will be able to classify triangles by their angles and sides.
Lesson Description for the Day
This lesson focuses on students exploring the relationship among the interior angles of a triangle to draw conclusions on the sum of the interior angles. Students will use a variety of representations to uncover and represent the relationship among the interior angles of a triangle. Students will measure angles of triangles using protractors.
State Standards
New York State Learning Standards: Mathematics, Science, and Technology Standards:
Standard 1: Analysis, Inquiry, and Design
*1.1: Abstraction and symbolic representation are used to communicate mathematically.
Standard 3: Mathematics
*3.1: Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.
*3.4: Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
*3.5: Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.
Goals
Unit Goals:
Students will be able to:
*classify triangles by their angles and sides.
*explore the relationship among the angles of a triangle using multiple representations.
*represent mathematical thinking and relationships using multiple representations.
*draw conclusions on the sum of the interior angles of a triangle.
*measure and draw angles using a protractor.
*apply estimation to classifying and identifying angles.
*find the missing angle in a triangle.Bottom of Form
Lesson Goals:
Students will be able to:
*use a variety of representations to prove the relationship among the measures of the interior angles in a triangle.
*draw conclusions on the sum of the interior angles of a triangle.
*represent the relationship among the angles of a triangle using multiple representations.
*measure the angles of a triangle.
Methods
Anticipatory Set:
1.) Students take a math bin from front table and place it at seat (contains materials for the math lesson).
2.) Present the problem of the day: a review of estimating and measuring angles using a protractor (to be completed in mathematics journals).
3.) Review and discuss the problem of the day.
Introduce and Model New Knowledge:
1.) Lesson Essential Question (LEQ): What is the relationship among the interior angles of a triangle?
2.) Demonstration: carefully tear off angles: A, B, C. Place each of the angles on the straight line that is provided with common sides together (students do at seat with materials from math bin).
3.) Ask questions:
*What do you notice about the interior angles of a triangle?
*What conclusion can we draw about the sum of the interior angles of a triangle?
4.) Demonstration 2: use a protractor to measure each of the angles of the triangle. Add the measurements to find the sum of the angles.
5.) Apply algebra to represent the sum of the interior angles of a triangle algebraically (mathematical statement). Draw conclusion based on findings.
6.) Demonstration 3: apply understanding of geometry to explore the relationship among the angles of a triangle to determine the sum of the interior angles.
Teacher presents the problem to students (students have this in math packet)
This demonstration draws on recognizing special pairs of angles (corresponding and alternate interior angles) and parallel lines.
7.) Questions to ask:
*What do we know about angles A and D? (alternate interior angles)
*What is true about the measurement of these angles? (congruent)
*What can we conclude about angle A? (angle A=angle D)
*What do we know about angle F and angle C? (alternate interior angles)
*What do we know about angle C? (angle C=angle F)
*What can we conclude about angle D + angle B + angle F? (form a straight lineà180 degrees)
*What can we conclude about the interior angles of triangle ABC? (sum is 180 degrees)
Provide Guided Practice:
1.) Students further explore the relationship among the interior angles of a triangle using manipulatives (triangles), measuring angles with a protractor (measure and add interior angles of a triangle), and by applying geometry and algebra. Students have the option of working independently or with a partner on guided practice. At the beginning of guided practice, we will work on the same section together but students will have the opportunity to work it out on their own or with a partner before discussing as a whole group.
2.) Guided questions (make references to the following topics):
*how to use protractor correctly
*relationship among the interior angles of a triangle
*the steps used in measuring angles and how to find the sum of the angles
*representing the relationship among the angles and their sum algebraically
*vocabulary terms: alternate interior angles, parallel lines, straight lines
*vocabulary terms: alternate interior angles, parallel lines, straight lines Bottom of Form
Provide Independent Practice:
1.) Students complete an independent task: Angles of a Triangle sheet. The teacher will provide the appropriate accommodations/modifications to address individual learning needs on the independent task.
2.) The teacher will address learning needs in small groups or one-on-one using the data collected on the observation checklist during the lesson.
3.) Math centers: when students complete the independent task they can choose one of the four math centers (centers to be introduced to students prior to going to special):
A.) technology: students explore the sum of the interior angles of a triangle through an interactive website (http://www/edumedia-sciences.com/en/a379-angles-triangle).
B.) hands-on: students engage in a variety of activities exploring triangles using various manipulatives, resources, tools, and materials.
C.) movie: students watch a movie exploring the sum of the interior angles of a triangle and do activity to follow along with video.
D.) exploration: students explore triangles by drawing and measuring the interior angles of triangles.
Wrap-Up
Conclude this lesson by bringing students together to have a class discussion.
1.) Present Lesson Essential Question (LEQ): What is the relationship among the interior angles of a triangle?
2.) Students answer the LEQ in their mathematics journals and provide an example to demonstrate understanding (students can draw or write)
3.) Discuss and share student responses to the LEQ.
Assessment
Formative/Ongoing Assessment:
Informal Observation (checklist)
*Discussions: whole-group, small-group, one-on-one
*Demonstration: demonstrate understanding of the relationship among the interior angles of a triangle and answers questions
Summative/End Of Lesson Assessment:
Mathematics Journal Entry:
*Students answer the lesson essential question (LEQ) in their mathematics journal and provide an example to demonstrate understanding.
Angles of a Triangle sheet
Materials
*Student math bins: triangles (varying sizes and colors labeled by letters), straight line, ruler, protractor, colored pencils, and math packet (outline of lesson, graphic organizer (geometry terms), student sheets for instruction, and Angles of a Triangle sheet).
*Teacher materials: variety of triangles (different sizes and colors: correspond to students triangles), protractor, poster board, markers, ruler, scissors, tape, strips for math vocabulary terms, and poster (LEQ).
*Student materials: mathematics journals, pencil, and eraser.
*Audiocassette: taping of the lesson, independent task, cassette player, and headphones.
*Technology center: direction sheet (visual and written directions) student computers, internet accessibility, and headphones for computers.
*Movie center: television, VCR, movie: Sum of the Angles of a Triangle (by: Miss Boyer), materials to do the interactive components of the movie (paper, scissors, and pencils).
*Hands-on center: activities for students to explore the sum of the interior angles of a triangle using manipulatives (various sized triangles), poster on the sum of the interior angles of a triangle, scissors, tape, paper, protractors, rulers, and colored pencils.
*Exploration center: paper (various colors), scissors, rulers, protractors, pencils, colored pencils, markers, glue, and poster size paper (white).
*Small group instruction or one-on-one materials: triangles (various sized and colors), poster displaying different theorems, computer, internet, and projection screen (to display the website that addresses the relationship of the interior angles of a triangle), activity materials (paper, pencil, and markers).
References:
EduMedia. (2008). Angles/Triangle. Retrieved February 19, 2010 from http://www/edumedia-sciences.com/en/a379-angles-triangle
Leff, L. (2003). Let’s review: Math a, 2nd. ed. United States of America: Barron’s Educational Series, Inc.
Mankus, M. (1998). What is the sum of my angles? Retrieved on February 19, 2010 from http://mason.gmu.edu/~mmankus/tripoly/tri.htm
Mathematics Open Reference (2009). Interior angles of a triangle. Retrieved February 19, 2010 from http://www.mathopenref.com/triangleinternalangles.html
The State Education Department. (1996). Learning standards. The University of the State of New York. Retrieved on April 1, 2008 from http://www.emsc.nysed.gov
Van De Walle, J. (2007). Elementary and middle school mathematics: Teaching developmentally, 6th ed. New York: Pearson Education, Inc.
Alignment with Impact Mathematics:
This lesson aligns with Impact Mathematics in a variety of ways. For example, this lesson provides students with plenty of opportunities to practice the concept being learned. Guided practice, independent practice, and the mathematics centers provide learners with numerous opportunities to apply and develop their understanding of the mathematical concept being learned. This lesson also incorporates the use of manipulatives to support students in developing an understanding of the relationship among the interior angles of a triangle. This lesson introduces the theorems on the sum of the interior angles of a triangle. The manipulatives help students to visualize the angles and their relationship to draw important mathematical conclusions. This understanding is critical to the proceeding lessons within this unit. This geometry unit is organized by mathematical content with interconnecting lessons in which students make connections among mathematical ideas and apply and build on prior knowledge. This unit addresses four of the five mathematical content standards and all five process standards. As a result, students are able to learn, apply, develop, and extend their mathematical thinking and understanding through an integrated approach to mathematics.