Download Lesson Plan - University of Cincinnati

Tantalizing Triangles
Grade Level:
Taught at
10
Hughes High
School
Subject:
Teacher/Bell
Geometry
Richmond/Bells 4 & 5
Prepared By:
Source
Carol Clinton
Original lesson, incorporating
information from references listed at
bottom of lesson plan
Analyze Learners
Overview & Purpose
In this lesson students are exposed to
engineering design fundamentals
using Cincinnati structures as
examples. They gain a physical
understanding of triangle, side, angle
concepts; lines in coordinate system;
congruence, and similarity. They
practice constructing triangles using
Geoboards, dot paper, and paper and
pencil; calculating and measuring
angles; and classifying triangles.
An extra credit extension with
tantagrams was offered.
Education Standards Addressed
Number, Number Sense and Operations Standard –
G. Estimate, compute and solve problems involving real numbers, including ratio, proportion and
percent, and explain solutions.
Measurement Standard –
D. Use proportional reasoning and apply indirect measurement techniques, including right triangle
trigonometry and properties of similar triangles, to solve problems involving measurements.
E. Estimate and compute various attributes, including length, angle measure, to a specified level of
precision.
Geometry and Spatial Sense Standard –
A. Formally define geometric figures.
B. Describe and apply the properties of similar and congruent figures; and justify conjectures involving
similarity and congruence.
C. Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines
and parallel lines.
D. Use coordinate geometry to represent and examine the properties of geometric figures.
E. Draw and construct representations of two- dimensional geometric objects using a variety of tools,
such as straightedge, compass and technology.
F. Represent and model transformations in a coordinate plane and describe the results.
I. Use right triangle trigonometric relationships to determine lengths and angle measures.
Patterns, Functions and Algebra Standard C. Translate information from one representation (words, table, graph or equation) to another
representation of a relation or function.
Select Goals and Objectives
Teacher Guide
Objectives
Students will
 define triangles by Cartesian
coordinates of their vertices;
 Construct triangles on geoboard
 Classify triangles;
 Solve missing angle problems;
and
 Create congruent and similar
triangles.
(Specify skills/information that will
be learned.)
Select Instructional
Strategies –
Information
Student Guide
Direct Instruction – demonstration of
desired behaviors; lecture on key
information
(Give and/or demonstrate
necessary information)
Questioning – during lecture and
during observations of group work
Utilize Technology
Demonstrate use of geoboards and
dot paper
Group Work – collaborative learning
Construct triangles with geoboards.
Draw triangles on dot paper. Use
protractor and ruler to measure
triangle angles and sides. Use
calculator to solve missing angle.
Materials Needed
 Paper
 Pencil
 Geoboards and bands
 Dot Paper
 Protractor
 Ruler
 Handouts
o Pretest
o Bridge sections
o Worksheet
o Post-test
o Tantagrams
Other Resources
(e.g. Web, books, etc.)
Preparing for the OGT in
Mathematics, pages 219 - 309
Require Learner
Participation
Activity
(Describe the independent activity
to reinforce this lesson)
Introduction to objectives and
activities for the day. Show photos of
local bridges, airports and other
landmarks that are based on triangle
geometry.
Catch: Teams of two, one describes a
section of the Brent Spence Bridge
truss, the other draws it based on the
description. Switch. Triangles are
important features of many
engineering structural designs. We
need good ways to describe and
construct them.
Activity:
Distribute pre-test (if not done on prior
day)
Distribute geoboards (give warning
about no rubberband horseplay)
Distribute worksheet and dot paper
Demonstrate constructing triangle
based on vertices, measuring sides
with ruler and angles with protractor.
Demonstrate drawing the triangle on
dot paper.
Review types of triangles: acute,
obtuse, isosceles, right; 30-60, 45-45
Review sum of angle rule
Review rules of congruent and similar
Discuss bisectors
Discuss worksheet
Discuss tantagram handout.
if lesson goes short, discuss altitudes,
medians, demonstrate tantagrams,
discuss tessellations – if lots of time,
calculate slopes of sides, show that
slopes of sides adjacent to right
angles are perpendicular; if more
time, do a problem regarding how
much shore line will be lost for a given
slope if sea level rises
if lesson goes long they will do
worksheet as homework rather than
classwork
Complete worksheet exercises.
1. Construct triangles on geoboard by
plotting specified points by Cartesian
coordinates.
2. Sketch the triangles on dot paper.
3. Classify triangles,
4. Solve missing angles, check on
geoboard with protractor and
ruler.
5. Construct similar and congruent
triangles. Measure side lengths
6. Define angle bisector.
Evaluate (Assessment)
(Steps to check for student
understanding)
Observe students’ classwork,
question them about the work and
give immediate feedback.
Graded classwork
Pre-test/post-test
Graded classwork
Pre-test/Post-test
Additional Notes
Extra credit – define additional
angle bisectors, calculate
triangle altitudes and medians,
construct tantagram figures.
Reflection after teaching this lesson twice:
For the most part, I was pleased with the lesson. The amount of content was pretty good – a few students finished and were able to do extra
credit work. Some didn’t finish. But at least they were all engaged in it and seemed to enjoy the work, The students were mostly enthusiastic. A
few seemed overwhelmed with the concepts and/or terminology, but through working with them one-on-one they got on track. (And best of all, no
problems with flipping rubber bands at each other or other horseplay that my own classmates would have done in the 10 th grade!)
The second time I taught the lesson, I spent more time explaining the worksheet – reading nearly every instruction word for word rather than giving
it a general description and referring to the printed instructions on the worksheet.
Data:
Only partial data is available. Student scores rose an average of 14% from the pre-test to the post test. Roughly half of the students
showed no change. Roughly one third saw increases up to 200%. However, four students actually showed decreased performance on
the post-test (the classroom teacher attributed this to illness and/or distraction of those individual students). A slight positive
correlation was observed between classwork grades and test performance.
Information on student attitudes is not currently available.
References:
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Bass, Laurie E. and Johnson, Art; Prentice Hall Mathematics Geometry, Pearson Education, Inc.; Saddle River, New Jersey;
2004
Andres, Richard J. and Bernstein, Joyce; Preparing for the OGT in Mathematics; Amsco School Publications, Inc.; 2004
Lund, Charles; Dot Paper Geometry With or Without a Geoboard; Cuisenaire Co. of America, Inc.; New Rochelle, NY; 1990
Cech, Joseph P. and Tate, Joseph B.; Geo-board Activity Sheets; Ideal School Supply Company; Oak Lawn, IL; 1971
Dimmerling, Amy; Vice Bowling, Bethany; and Massie, Emma; Brent Spence Bridge STEP lesson; University of Cincinnati,
http://www.eng.uc.edu/STEP/activities/descriptions/brent_spence_bridge.htm; 2004