Illustrative Mathematics
Velocity vs. Distance
At the end of this activity, your number crunchers will have a better understanding as to how to describe graphs of velocity versus time and distance versus time. It is easy for learners to misinterpret graphs of velocity, so have them...
Mathematics Vision Project
More Functions, More Features
Learners tackle a wide range of intimidating topics in this comprehensive unit that spans piecewise functions, absolute value of functions, and inverse functions (among other topics). Investigative group work alternates with more...
Curated OER
Worksheet 2: Graphs, Functions and Derivatives
In this math worksheet, learners answer 7 questions having to do with graphing derivatives of functions, rectilinear motion, speed and distance.
Curated OER
Calculus 10.2 day 2 - Vector Valued Functions
Looking for a lesson on vectors? Here is a PowerPoint that has six examples for finding velocity, acceleration, speed and direction of motion. One of the examples demonstrates the use of the TI-89 Graphing Calculator to solve a problem.
Mathematics Vision Project
Module 6: Trigonometric Functions
Create trigonometric functions from circles. The first lesson of the module begins by finding coordinates along a circular path created by a Ferris Wheel. As the lessons progress, pupils graph trigonometric functions and relate them to...
Curated OER
Worksheet 3 - Velocity, Movement
In this velocity worksheet, students determine the distance traveled when an object is moving in a straight line. Students graph functions and determine the slope of the line. This two-page worksheet contains six multi-step problems.
Curated OER
Worksheet 22 - Functions
In this function worksheet, students use functions to identify an electron traveling along a path. They examine the velocity vector and compute the directional derivative. This two-page worksheet contains six multi-step problems.
EngageNY
The Concept of a Function
Explore functions with non-constant rates of change. The first installment of a 12-part module teaches young mathematicians about the concept of a function. They investigate instances where functions do not have a constant rate of change.
Curated OER
Position, Distance, Velocity
Learners calculate the position, distance and velocity using functions in this calculus lesson. They investigate horizontal motion through the derivative of functions and use the TI to create a visual of their function.
Flipped Math
Calculus AB/BC - Connecting a Function, Its First Derivative, and Its Second Derivative
Uncover what the first and second derivatives reveal about the function. Pupils move beyond sketching graphs to determine what derivatives tell about the function itself. The video reminds learners about particle motion and how to...
Curated OER
Functions
In this functions worksheet, students solve and complete 5 different sets of problems that include determining functions on intervals. First, they define a definite integral and the Fundamental Theorem of Calculus. Then, students draw a...
Curated OER
Position, Velocity & Acceleration vs. Time
In this motion worksheet, students use a graph showing the velocity of an object over time to describe the motion of the object and to determine the position of the object at different intervals. Then students create speed vs. time and...
Curated OER
Graphing Calculator Investigation - Second Degree Polynomial Functions
High schoolers solve quadratic functions. In this solving quadratic functions lesson, students determine the height of an object at a given time. High schoolers determine the time at which an object hits the ground. Students answer...
Shmoop
Functions Worksheet 5
To the point and deeper thinking are both types of questions included in the worksheet. Begin the practice of solving quadratics and then finish with five questions asking quadratic and exponential application problems.
Curated OER
Reading Graphs
Working independently or in teams, your class practices connecting graphs, formulas and words. This lesson includes a guided discussion about distance vs. time graphs and looking at how velocity changes over time.
Illustrative Mathematics
Distance across the channel
Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...
Curated OER
Elevator Height as Integral of Velocity
Pupils investigate integrals and their relationship to velocity in this calculus lesson plan. They use the idea of a moving elevator to explore vertical motion and use the TI to help them create a visual.
Curated OER
Fitting Periodic Functions-Distant Planets
In this periodic functions worksheet, students use given data of the speed of a star and find the best fit periodic function that follows the trend in data. They determine the amplitude, offset phase and the formula for the angle. They...
Curated OER
Rotation Velocity of a Galaxy
In this orbit of stars in galaxies worksheet, students are given an equation that models the orbital speeds of stars as they relate to their distance from the nucleus of a galaxy. Students solve 5 problems using this equation and...
Curated OER
Calculating Arc Lengths of Simple Functions-I
In this calculating arc lengths instructional activity, students are given 4 simple functions and they use the Pythagorean Theorem and the basic techniques of calculus to find the arc-length formula in order to find the arc-length.
NASA
Ascent: 50 Seconds to MECO
All systems go! With a video and a Google Earth tour as background, pairs investigate two graphs. The graphs display acceleration vs. time and velocity vs. time of a space shuttle launch. Using graphing calculators, the pairs take a...
Kenan Fellows
Using Motion Sensors to Explore Graph Sketching
Get moving to a better understanding of graphs of derivatives. Using motion sensors, scholars vary their velocities to create graphs of the first derivative of a function. The activity challenges groups to first create a script of the...
Curated OER
The Function Elevator
Students solve and graph functions. In this precalculus lesson, students use piecewise function to relate real life scenarios. They analyze the graphs and identify the vertex and intercepts.
Curated OER
Velocity
Students explore the concepts of velocity, acceleration, distance and football. They collect data on the velocity of a football and they determine the distance and height of a football when it is thrown. Students compare their findings...