CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 2)
What does it mean if young mathematicians cannot put the squeeze on a sequence? Learners investigate a divergent sequence and find the formula for the nth term. Using the definition of a limit of a sequence, pupils try to find the limit...
Chapman University
Proof of L’Hospital’s Rule
Understanding how calculus formulas were derived connects learners to the idea that the study of mathematics is continuous and cumulative. Learners will also develop a deeper appreciation for the derivative's application in simplifying...
Chapman University
Derivative of sin x
Direct and to the point (the slope at a point that is) describes this one-page proof of the derivative of the sin(x). The definition of a derivative using a limit is the first step in this sequential, algebraic, explanation of how the...
Illustrative Mathematics
Equal Area Triangles on the Same Base II
A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...
Curated OER
Application of Delta-Epsilon Definition of the Limit
Students create a Hexaflexagon using a formula. For this calculus lesson, students apply the definition of delta epsilon as it relates to limit to create a shape using creases. They relate the same rule to triangles and investigate angles.
Curated OER
Application of Delta-Epsilon Definition of the Limit
Pupils investigate the concept of a Limit and how it is used in a variety of problematic situations. They fold paper to help illustrate how to form equilateral triangles and explain how all the angles are the same. The lesson includes a...
Old Dominion University
Introduction to Calculus
This heady calculus text covers the subjects of differential and integral calculus with rigorous detail, culminating in a chapter of physics and engineering applications. A particular emphasis on classic proof meshes with modern graphs,...
Curated OER
The Product and Quotient Rules
In this produce and quotient rule learning exercise, students identify the values of given limits. They justify given proofs and explore the derivative of the sine and tangent functions. This three-page learning exercise contains...
College Board
Differentiability of Piecewise Defined Functions
Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...
EngageNY
Proving the Area of a Disk
Using a similar process from the first lesson in the series of finding area approximations, a measurement resource develops the proof of the area of a circle. The problem set contains a derivation of the proof of the circumference formula.
School Improvement in Maryland
Court Proceedings Civil Cases
What's the difference between civil and criminal law? How do the court proceedings differ in these two types of trials? How do the standards of proof differ? Why do these differences exist? As part of their examination of the US court...
Science Matters
Earthquake Building/Shaking Contest
Japan is one of only a handful of countries that constructs buildings that are almost earthquake proof. The 13th lesson in the 20-part series challenges scholars to build structures to test against earthquakes. With limited materials and...
Curated OER
What Proof is There to Support Biological evolution?
Students identify who developed the theory of evolution. The concepts of adaptation and development are discussed. The age of the earth is explored in relationship to the development of various species. The condition of the environment...
Curated OER
Failure-Proof Writing: Assignments for the Student Who Can't/Won't Write
Students with learning disabilities are introduced to the techniques of proper writing. After completing a warm up, they practice writing about what they saw to determine where they are at in the process. In groups, they complete a set...
Curated OER
Proof It
Fourth graders complete a worksheet. In this spelling lesson, 4th graders complete a timed activity where they identify misspelled words and write their correct spelling.
Inside Mathematics
Rhombuses
Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...
Noyce Foundation
The Shape of Things
Investigate the attributes of polygons. A thorough set of lessons presents problem scenarios for elementary through high school classes. The first lessons focus on basic characteristics of polygons, including the line of symmetry. As the...
Curated OER
Epsilon-Delta Window Challenge
Students graph functions and analyze them. In this calculus lesson, students define limit formally using Epsilon-Delta. They use the TI to graph the function and analyze it.
Curated OER
Government Lesson Plan: Lesson Plan 9
Students examine and compare/contrast the steps of criminal and civil cases. They define key vocabulary terms, develop an outline of a criminal and civil trial, and analyze the differences in standards of proof in legal cases.
EngageNY
The Inscribed Angle Alternate – A Tangent Angle
You know the Inscribed Angle Theorem and you know about tangent lines; now let's consider them together! Learners first explore angle measures when one of the rays of the angle is a tangent to a circle. They then apply their newfound...
College Board
Why Variances Add - And Why It Matters
Why is adding variance important? A lesson outline defines a variance theorem and how it affects the data statistics. The instruction shows scholars the importance of considering the variance of data and why it requires independence.
Curated OER
A.P. Calculus Integration Test
In this A.P. Calculus learning exercise, students complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields. Some of the problems are multiple choice, while others...
Curated OER
The U.S. Constitution Power Grab Game
Learners study the powers and limitations of the three branches of the American government. They explain how the system of "checks and balances" protects the individual citizens. They explain how the amendments to the Constitution...
Curated OER
Mistakes that English Native Speakers Make 2
In this ESL worksheet, students proof read 20 sentences to find the mistakes. They label each sentence as to the mistake using the key at the top of the page which includes the misuse of articles, commas, apostrophes, and capital letters.