28 results
Higher education calculus laboratories
Volumes of Solids with Known Cross Sections - An Exploration in Calculus
One of the topics that is difficult for students to grasp is finding the volume of a solid with a known cross section. One reason is that students have difficulty with this topic is that they have difficulty drawing the solid. In this activity the students get to build eight different "solids.”This activity focuses on finding the volume of solids that are built on a two-dimensional surface when cross section cut perpendicular to a known shape. The activity uses the region bounded by the x-axis,
Grades:
10th - 12th, Higher Education
Types:
Also included in: Calculus - Volume using Known Cross Sections Bundle
Calculus - Volume Bundle
This bundle contains seven products that can be purchased separately in my store:· Activity Sheet on the Volume a Solid of Revolution· Activity Sheet on Volume of Solids with Known Cross Sections· Practice Finding the Volume of Solids with Known Cross Sections· Volume Matching Cards· Volume of Solids with Known Cross Sections—An Exploration· Graphic Organizer for Finding Volume· Volume of a Solid with a Known Cross Section—How to Do It Check the description on each individual product for further
Grades:
10th - 12th, Higher Education
Types:
Calculus - Match the Graphs of f, f ', and f "
This set of 100 cards (25 sets of 4) can be duplicated on card stock and then cut apart for a great cooperative learning activity in Calculus. Duplicate the pages in the landscape mode so the cards are slightly larger. Each set of four cards includes:• a graph of a function, • a graph of a derivative of a function, • a graph of the second derivative of a function, and • an algebraic description of a function.Each of the four cards has been numbered with a random number between 1 and 75. A key
Grades:
10th - 12th, Higher Education
Types:
Calculus - Average Value of a Function - An Exploration
As part of the AP Calculus course description students need to understand what it means to find the average value of a function. This activity incorporates the graphing calculator to develop an understanding for the average value of a function. Students draw graph for four functions to view all the function values between two x values. Since students understand that they find an average for a set of numbers by dividing the sum of the numbers by the total number of numbers, this lesson begins by
Grades:
10th - 12th, Higher Education
Types:
Also included in: Calculus - Bundled Lessons on The Average Value of a Function
Calculus Interactive Volume of Revolution y-axis Grapher
This Calculus Interactive Volume of Revolution Surface of Revolution about the y-axis Grapher will wow your kids with LIVE interactive math explorations and animations. My students think this is awesome. This Easy 3D grapher will demonstrate and explore the volume of revolution in your classroom as never before. Incorporate this applet into your traditional lessons, Power Points, or Smart Board lessons or use as a free standing "app" to explore with your class. "What do you think would hap
Subjects:
Grades:
11th - 12th, Higher Education
Types:
Polynomial Labs (Quadratics, Cubics, etc.) including Catapults!
This lab includes two versions of a catapult lab (calculus based and non-calculus based). Students work in groups to collect data on a ball launched using a catapult. Students create regression equations using a graphing calculator or spreadsheet.
Also included is a painted cubes lab that includes 4 types of functions.
Courses: algebra 1, algebra 2, pre-calculus, calculus
Here are links to my other algebra projects:
Click Here to see my project: Indirect Measurement Labs
Click Here to see
Subjects:
Grades:
8th - 12th, Higher Education, Adult Education
Types:
Calculus-Making Observations about the Function and Its Derivatives from Graphs
This discovery activity is made up of 5 part plus a closing question.Part I: Students graph a function and its derivative. From the two graphs students observe that when the graph of the derivative of y1 is positive the graph of y1 is increasing and that when the graph of the derivative of y1 is negative the graph of decreasing. Part II: In part I students studied a function with a minimum. In this part students will repeat the same observations but with a function that has a maximum. Part III:
Grades:
10th - 12th, Higher Education
Types:
Chain Rule Practice Worksheet
** BE SURE TO CHECK OUT MY OTHER WORKSHEETS! **
- *50* Questions!
- *COMPLETE* Solutions!
If you want to move on to more complex mathematics, you need to get certain topics out of working memory. This is my goal in all of my worksheets - to help students learn a particular techniques or topics to the point where it's automatic and they don't have to think about it, so that they can achieve more on the advanced topics.
This is a worksheet that covers one topic - the chain rule in differe
Subjects:
Grades:
10th - 12th, Higher Education, Staff
Types:
Calculus - Continuity
This activity engages the students in understanding the three parts of the definition for a continuous function at a point by asking a series of questions about several functions.You also might be interested in the Activity Sheet on Continuity and the Intermediate Value Theorem that is available in my store. A recent buyer said "Thank you for providing this resource. I appreciate your time and investment in creating a helpful resource."
Subjects:
Grades:
11th - 12th, Higher Education
Types:
Also included in: Calculus - Continuity Bundle
Calculus - Definition of a Derivative - Using the Rule of 4
This activity incorporates the graphing calculator to help students understand the definition of a derivative. Students in AP Calculus and Calculus should be studying the concepts in Calculus graphically, numerically, verbally and analytically ( which is also known as the rule of 4). This activity sheet will help develop the student’s conceptual understanding of the definition of a derivative in these four ways:• Students create graphs and tables of a function and a difference quotient. As th
Subjects:
Grades:
10th - 12th, Higher Education
Types:
Calculus - How Can One Graph Help Describe Another Graph?
This activity incorporates the graphing calculator to help students understand how the behavior of one graph can describe the behavior of another function. Three related equations are entered in y1, y2, and y3 in the graphing calculator. • The original function is entered in y1. • An expression that represents the derivative of y1 is entered in y2. • An expression that represents the derivative of y2 is entered in y3. After graphing y1, y2, and y3 in the same window, a series of questions a
Grades:
10th - 12th, Higher Education
Types:
Calculus - Understanding The Derivative Numerically
This activity incorporates the TI84 and TI84C Graphing Calculator to study how the three difference quotients approach the same limit. Students write equations to match sets of table values as the limit of h approaches zero.
Subjects:
Grades:
10th - 12th, Higher Education
Types:
Also included in: Calculus - Understanding the Derivative Bundle
Calculus - UNDERSTANDING THE DEFINITION OF A LIMIT-1
Students often struggle to understand the formal definition of a limit. This activity sheet has the students build both tables and graphs to see what the definition is saying. In the tabular form, the students keep refining the table to be convinced that as long as they stay very close to a value of a on the x-axis all y values will stay in a close range of a particular number called a limit. The same idea is explored graphically by trying to keep all y values visible when given a particular
Subjects:
Grades:
11th - 12th, Higher Education
Types:
Also included in: Calculus - 3 BUNDLED LESSONS ON UNDERSTANDING THE DEFINITION OF A LIMIT
Calculus - Connecting Continuity with Differentiability
Through this activity students learn the connection between continuity and differentiability of a function. The activity uses either the TI84 or TI84C graphing calculator. Students should understand this concept for AP Calculus.You might also be interested in the Activity Sheet on Continuity and the Intermediate Value Theoremthat is available in my store.
Grades:
10th - 12th, Higher Education
Types:
Also included in: Calculus - Continuity Bundle
Calculus - What is the Slope of a Function at a Point?
This graphing calculator activity engages the students in using two difference quotients and table values to approximate the slope of a function at a point. Students first study y = 2x^2 at the point (1,2). Using the two difference quotients, students find that the slope is 4. The students then explore find the slope of the same function at x = 2, 3, -1, -2, and -3. They then conjecture what the slope will be at A = -4, +4, and 0. Student then move to studying the slope along y = x^3 y =
Subjects:
Grades:
11th - 12th, Higher Education
Types:
PHET Vector Lab (Online Simulator)
I created this lab as an intro into two dimensional motion for my physics classes. The lab uses all the techniques of adding vectors head-to-tail and demonstrates for them that the two vectors being added to make a resultant are the components of that resultant. This lab is great practice and very self-explanatory for grades 11 and 12. I created this lab so that it was an electronic lab so that they could open the lab on their computers, fill out the lab in MS Word, and submit it back to me onli
Subjects:
Grades:
11th - 12th, Higher Education
Calculus - Understanding The Derivative Graphically Using Difference Quotients
Students can used their graphing calculators to build an understanding for the formal definition of a derivative (limit as h approaches zero of (f(x+h)-f(x))/h). Students will set up the forward difference quotient, the backward difference quotient, and the symmetric difference quotient approaching the same limit. Then students will let h equal 1, 0.1, 0.01, and 0.001) to notice that all the difference quotients approach one function. The function they are all approaching will be called t
Subjects:
Grades:
10th - 12th, Higher Education
Types:
Also included in: Calculus - Understanding the Derivative Bundle
Calculus - Using Algebraic and Graphical Methods to Solve Optimization Problems
This activity illustrates for calculus students how they can solve optimization problems using algebraic and graphical methods. Two examples illustrate step by step procedures that can be followed to solve most optimization problems. Both analytical and graphical approaches are used to study the rate of change. After illustrating how two examples can be solved, five additional practice problems with solutions are provided for students to practice.Please check out the Activity Sheet on Optim
Grades:
11th - 12th, Higher Education
Types:
Also included in: Calculus - Optimization Bundle
Pre-Calculus - Maximizing the Volume of a Cone
This hands-on activity engages the students in constructing a cone from a circle,collecting data on the height and radius of the cone, creating a scatterplot, fitting a curve to the data and then estimating the maximum volume of the cone. Many students are surprised that the scatterplot indicates that the volume first slowly increases and then after a maximum volume occurs the volume quickly decreases. By working with a physical model helps students observe how the height, radius, and volume a
Grades:
11th - 12th, Higher Education
Types:
Chain Rule Practice - With Logs and Exponentials, No Trig
** BE SURE TO CHECK OUT MY OTHER WORKSHEETS! **
- *78* Questions!
- *COMPLETE* Solutions!
If you want to move on to more complex mathematics, you need to get certain topics out of working memory. This is my goal in all of my worksheets - to help students learn a particular techniques or topics to the point where it's automatic and they don't have to think about it, so that they can achieve more on the advanced topics.
This is a worksheet that covers one topic - the chain rule in differe
Subjects:
Grades:
10th - 12th, Higher Education, Staff
Types:
Calculus - Slope or Derivative of Inverse Functions
This activity will engage students in discovering the relationship between the slope of two inverse functions. It is designed to be used with the TI84 graphing calculator.There are answers to the investigation and to the 5 problems included in the activity.You might be interested in the Activity Sheet with Derivatives of Inverse Functions that is available in my store.
Grades:
11th - 12th, Higher Education
Types:
Cubic Project
This is a project designed around a specific property of any cubic polynomial. Students will write equations of tangent lines to a given cubic function and then determine areas of resulting bounded regions. By investigating these areas a perplexing property of cubic polynomials will be discovered. There are two parts to the project. In part one students work with a specific cubic and arrive and specific answers. In part two students solve the problem in general for any cubic. CAS methods are
Subjects:
Grades:
11th - 12th, Higher Education
Types:
Pre-Calc: Inverse Relationship Between Logs & Exp (Graph Calc)
This activity uses the graphing calculator to explore the inverse relationship between logs and exponential functions. Students use the table feature of their calculator to generate values for inverse functions and to explore/compare components of each. This is generally an in-class group activity but could be assigned outside of class. Used in PreCalc as a discovery lesson and in Calculus as a review.
Subjects:
Grades:
11th - 12th, Higher Education
Types:
Newton's Law of Cooling Mini-Lab
This is an activity for the differential equations chapter of high school calculus. Students will make their own measurements while a cup of hot water cools in their classroom, they'll generate an equation and draw the graph of an exponential function. It's a really good activity for students to gain a better understanding of how differential equations work and what they can be used for.
Subjects:
Grades:
12th, Higher Education, Adult Education
Types:
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