Ohio Resource Center
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Content Supports - Activities and rich problems
Folded Triangle
Discipline
Mathematics
Grades
9, 10, 11, 12
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Professional Commentary

The "Folded Triangle" problem is rich by virtue of its connections to so many different levels of secondary school mathematics. Students in a first-year algebra or geometry course can investigate the problem just as meaningfully as students enrolled in a senior-level calculus course. Moreover, the problem can be modeled inexpensively and conveniently with readily available hands-on manipulatives, namely a standard sheet of 8.5 "x 11" copier paper. The problem has a delightful solution that is completely obvious in hindsight, yet deliciously counter-intutive at first glance. A detailed figure and multiple solutions are included. This mathematically rich problem was developed for the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools proposed by the Ohio Department of Education. (author/sw)


Common Core State Standards for Mathematics
High School - Functions
Building Functions
Build a function that models a relationship between two quantities
HSF-BF.A.1 
Write a function that describes a relationship between two quantities.
  1. Determine an explicit expression, a recursive process, or steps for calculation from a context.
  2. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
  3. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Benchmarks (8–10)
I.
Use right triangle trigonometric relationships to determine lengths and angle measures.
Grade Level Indicators (Grade 9)
2.
Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle sizes in similar figures.
Patterns, Functions and Algebra Standard
Benchmarks (11–12)
A.
Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
Grade Level Indicators (Grade 11)
4.
Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology.
Principles and Standards for School Mathematics
Algebra Standard
Understand patterns, relations, and functions
Expectations (9–12)
analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;
Geometry Standard
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Expectations (9–12)
use trigonometric relationships to determine lengths and angle measures.
Use visualization, spatial reasoning, and geometric modeling to solve problems
Expectations (9–12)
use trigonometric relationships to determine lengths and angle measures.
use geometric models to gain insights into, and answer questions in, other areas of mathematics;