
Tricky Triangles 

Patricia Priestas, Educator, Mathematics & Science Center Adapted from Trying Triangles, Pieces and Patterns, A Patchwork in Math and Science, AIMS Activities Grades 59


Developed with funding from Capitol One Financial Services 



Major Understanding 
The sum of the two shorter straws must be greater than the longest straw in order to form a triangle of the straws. 




Grade/Subject 
Math 68; Geometry & Measurement; Statistics 




Objectives 
Determine whether three numbers (which represent lengths of line segments) will form a triangle.



Discover and identify a pattern.



Collect, analyze and
interpret data. 


Compare a whole number to the sum of two whole numbers using concrete materials.



Take a list of all possible outcomes and determine the probability of the occurrence of an event within the list.



Make inferences and predictions based on the analysis of a set of data.


Time 
Anticipatory Set 
5 min 

Background Information 
5 min 

Demonstration 
5 min 

Introduction of Graphing Calculator & Random Integer Generation 
15 min 

Activity I & Tricky Triangles Handout 1 
15 min 


Discussion and Interpretation of Data 
10 min 


Activity II & Tricky Triangles Handout 2 
15 min 


Discussion, Interpretation & Analysis of Data 
10 min 


Ratio Decimal Percent Discussion – Theoretical Probability 
10 min 

Materials 
For each student: 28 Graphing calculators (TI83 or TI83+) 30 Zip bags with sets of pre cut straws (Three 1”, three 2”, three 3”, three 4”, three 5”, three 6”) 3 24” pieces of string and a protractor
For the class: 3 Normal dice 1 Zip bag with set of precut straws, string and protractor
For the teacher: 1 Overhead projector 1 Transparency of Student Handouts 1 and 2 1 Teacher’s model graphing calculator (TI83 or TI83+) 1 View Screen for graphing calculator 1 Laptop, with spreadsheet and graphing software (optional) 1 Computer projection system (optional) 

State and National Correlations 
Virginia Standards of Learning: Grade 6 (6.4, 6.14, 6.20); Grade 7 (7.18)
National Math Education
Standards: Work flexibly with fractions, decimals and percents to
solve problems; Represent, analyze, and
generalize a variety of patterns with tables, graphs, words, and, when
possible, symbolic rules; Use geometric models to represent and explain
numerical and algebraic relationships; Use proportionality and a basic
understanding of probability to make and test conjectures about the results
of experiments and simulations; Build new mathematical knowledge through
problem solving; Make and investigate mathematical conjectures; Organize and
consolidate mathematical thinking through communication; Communicate their
mathematical thinking coherently and clearly to peers, teachers, and others;
Use the language of mathematics to express mathematical ideas precisely. 

Instructional Strategies 
1. Anticipatory
Set 2. Background
Information 3. Demonstrate
4. Activity
I 5.
Introduction of Graphing
Calculator & Random Integer Generation 6.
Activity I 7.
Discussion and Interpretation
of Data 8.
Activity II 9.
Discussion, Interpretation
& Analysis of Data 10. Ratio Decimal Percent Discussion – Theoretical Probability


Practice 
Guided Practice:
Have students conduct a simulated coin toss activity, using the TI83+
graphing calculator and the APPS key, under 6: Prob Sim or using the
following NCTM link: Simulating
Probability Using Box Models. Students first determine the theoretical
probability of tossing heads or tails. Then students, working in pairs, do
the simulation using either the TI83+ or the NCTM link, determining their
experimental probability. Percentages and a class average can be
determined. Discussion of theoretical versus experimental probability. Independent Practice: Students investigate games (board, electronic, computer, graphing calculator or other of their choosing), to determine the probabilities associated with the particular game. For example, Yahtzee uses a set of five (5) dice. Students determine the number of combinations possible and the probability of rolling a specific combination. The following links will be of interest: · Probability of Childhood Games


Closure 
Restate lesson objectives and relate them to the class
experience. Discuss the difference between theoretical and experimental or
simulation 

Extensions 
1.
Using a laptop with spreadsheet and graphing software such as Excel or
ClarisWorks and a computer projection system, place the theoretical
percentages for forming a triangle and for not forming a triangle in a
spreadsheet and display in a graph. Have the students determine the
simulation percentages from Handout 1. Determine a class average and represent
those percentages in a graph on the computer for the number of combinations
that made triangles and for those that did not. Compare the experimental or
simulation probability with the theoretical probability. 2.
Teach the Triple Triangles Lesson and Squared Triangles Lesson. 3. Have students design and create a game for the classroom based on probability.


Assessment 
A sample of items is provided for use in assessing students’ understanding: · PaperPencil Test: Tricky Triangles · Product Task: Poster Showing Straw Combinations · Rubric: Poster Showing Straw Combinations
The following table shows how the assessment items are related to specific objectives.



Objective 
PaperPencil Test 
Product/ 

Determine whether three numbers, which represent lengths of line segments, will form a triangle. 
2 


Discover and identify a pattern. 
6 


Collect, analyze and interpret data. 
3 


Compare a whole number to the sum of a pair of whole numbers. 
1 


Make a list of all possible combinations and determine the probability of the occurrence of an event within the list. 
7, 8, 9 


Make inferences and predictions based on the analysis of a set of data. 
4, 5 


The sum of the two shorter straws must be greater than the longest straw in order to form a triangle of the straws. 


Teaching Tips 
For additional information on teaching this lesson, go to the following links: · Answer Key: PaperPencil Test: Tricky Triangles


References 
AIMS Education Foundation. This site contains integrated handson mathscience activities. Tricky Triangles is adapted from Trying Triangles, a lesson in Pieces and Patterns A Patchwork in Math and Science.
Mathematics & Science Center Visit the Center’s sight to learn all that is new and happening at the Mathematics & Science Center, a regional consortium of K12 school divisions located in central Virginia. Register for student and teacher programs.
MathInScience Visit this educational resource site to acquire webbased lessons and resources for K12 students and teachers. The site is the online educational arm of the Mathematics & Science Center.
National Council of Teachers of Mathematics This site contains the Principles and Standards for School Mathematics. 
