Hill City 
Introduction to Limits 
912 
4 days 
Math, Calculus 

John Hoag 
John.Hoag@k12.sd.us 
6/6/2002 12:40:22 PM 
6/24/2002 3:44:47 PM 

Math 

Cory Ginsbach 
Cory.Ginsbach@k12.sd.us 

This unit will cover what the definition of a limit is and how it can be associated to the real world. There will be extensive use of calculators to find the limit graphically and by using tables.

Students will understand the definition of a limit. Students will be able to find the limit of an equation, a graph or from numerical data that is presented to them. Students will be able to find the limit of an equation, a graph or from numerical data as a variable approaches + or  infinity. Students will be able to use their ti83+ calculators to determine the limit graphically or by using a table.


Math Students will use the language of algebra to explore, describe, represent, and analyze number expressions and relations that represent variable quantities. Students will develop and use number sense to investigate the characteristics of numbers in a variety of forms and modes of operation. Students will discover, analyze, extend, and create patterns, relations, or functions to model mathematical ideas in a variety of forms.

GOAL 1: ALGEBRA Indicator 1: Analyze procedures to transform algebraic expressions. Indicator 2: Use a variety of algebraic concepts and methods to solve problems.
Goal 4  NUMBER SENSE Indicator 2: Apply number operations with real numbers and other number systems. Indicator 4: Analyze the concept of value, magnitude, and relative magnitude of real numbers.
Goal 5  PATTERNS, RELATIONS, AND FUNCTIONS Indicator 1: Analyze and describe the properties and behaviors of relations, functions, and related inverses. Indicator 3: Analyze the applications of the concept of mathematical limit.

GOAL 1: ALGEBRA Indicator 1: 9 – 12 Benchmarks: c. transform algebraic expressions and analyze the changes in graphs. Indicator 2: 9 – 12 Benchmarks: c. use the graphs of functions to solve problems.
Goal 4  NUMBER SENSE Indicator 2: 9 – 12 Benchmarks: analyze algebraic expressions Indicator 4: 9 – 12 Benchmarks: c. create generalizations discovered through investigations of finite and infinite sets of numbers.
Goal 5  PATTERNS, RELATIONS, AND FUNCTIONS Indicator 1: 9 – 12 Benchmarks: a. analyze the relationship between dependent and independent variables. Indicator 3: 9 – 12 Benchmarks: c. demonstrate the concept of limit using various geometric, numeric, and algebraic models. 
California Standards Calculus 1.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes onesided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity: 1.2 Students use graphical calculators to verify and estimate limits. 

What are the 3 conditions of a limit? In your own words, describe a limit using anything that is not related to math. (Example: an engine with a governor.) How can you use your calculators to find a limit by only using the graph mode? by the table mode? Give a real world example of a limit as some variable approaches infinity.

After working through the material, the student should be able:
(a)to obtain numerical evidence for the calculation of limits; (b)to determine what appears to be the limit from the numerical evidence; and (c)to become aware of some of the problems in using numerical evidence for the calculation of limits.

Worksheets will be used daily to check for comprehension. A quiz will be given at the end of the week. Tests will be given throughout the year with questions from this unit.

Students will be presented with many different mediums of instruction. These will include flash presentations on the internet, white board lecture, cooperative learning and instruction on the use of the ti83+ calculator with an overhead projector. Students will be presented worksheets that will have riddles answered when they find the appropriate answers to questions.

http://mecca.org/~halfacre/MATH/limits.htm http://archives.math.utk.edu/visual.calculus/1/ http://www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calculus.html 
http://hoager.iscool.net

