EngageNY
Euler’s Number, e
Scholars model the height of water in a container with an exponential function and apply average rates of change to this function. The main attraction of the lesson is the discovery of Euler's number.
Project Maths
Introduction to Calculus
Don't let your class's heart rates rise as you introduce them to differentiation ... an inquiry-based instructional activity helps them keep it in check! The second instructional activity in a three-part series asks learners to analyze...
It's About Time
The Changing Geography of Your Community
Lead your class in exploring their local communities as well as the general environment. As they determine continental distributions by investigating minerals, rocks, and fossils located in their local region, pupils construct a...
Mathematics Vision Project
Quadratic Functions
Inquiry-based learning and investigations form the basis of a deep understanding of quadratic functions in a very thorough unit plan. Learners develop recursive and closed methods for representing real-life situations, then apply these...
Kenan Fellows
Man vs. Beast: Approximating Derivatives using Human and Animal Movement
What does dropping a ball look like as a graph? An engaging activity asks learners to record a video of dropping a ball and uploading the video to software for analysis. They compare the position of the ball to time and calculate the...
Curated OER
Rate of Change
Eleventh graders solve problems dealing with rate of change. In this algebra lesson plan, 11th graders graph their rate of change problems and analyze it comparing their data with each other. They solve problems dealing with percent and...
Chicago Botanic Garden
Historical Climate Cycles
What better way to make predictions about future weather and climate patterns than with actual climate data from the past? Young climatologists analyze data from 400,000 to 10,000 years ago to determine if climate has changed over time....
Nuffield Foundation
Investigating Factors Affecting the Heart Rate of Daphnia
What variables change heart rate? Young scientists observe the beating heart in Daphnia to understand these variables. They make changes in temperature, chemicals, and other factors as they graph the heart rates. Analysis questions help...
CK-12 Foundation
Applications Using Linear Models: Scuba Diving
Dive into this resource on rates of change and linear models. Pupils use two sliders in an interactive to adjust water temperature and depth. They use a given linear equation to calculate the rate of change in water temperature per unit...
Utah Education Network (UEN)
Linear Graphs Using Proportions and Rates
Using a TI-73 or other similar graphing calculator middle school math majors investigate the linear relationship of equivalent proportions. After a brief introduction by the teacher, class members participate in a timed pair share...
Curated OER
Worksheet 14 - Rates
In this rate worksheet, students draw and label given situations, determine the rates and the relationship between them. This two-page worksheet contains 7 multi-step problems.
Curated OER
Physical and Chemical Reactions - Factors Which Affect Reaction Rate
A total of five experiments lead chemistry pros to understand the difference between physical and chemical change. They also experiment with exothermic reaction factors that affect rate of reaction. The procedures are not written in the...
Curated OER
The Global Menu: Changing the Rate of the Voice
Students examine the Windows-Eyes control panel by using dialog boxes, pull-down menus, left and right arrow keys, and shortcut keys. They also change the rate of the screen, keyboard, and mouse voices.
Curated OER
Y-Intercept and Slope Intercept Form
Alegebra amateurs identify the slope and the y-intercept given a linear equation in slope-intercept form by correctly completing some in class problems. They write the linear equation in slope-intercept form that corresponds to the given...
Curated OER
Rate Law Problems
If you need a variety of questions for reactions and rate calculations, this resource is for you. Inspire your students to manipulate values and equations to fit the questions. The word problems are quite involved and require young...
Texas Instruments
Finding Linear Models Part III
Explore linear functions! In this Algebra I lesson, mathematicians graph data in a scatter plot and use a graphing calculator to find a linear regression and/or a median-median line. They use the model to make predictions.
Nuffield Foundation
Investigating Factors Affecting the Breathing Rate of a Locust
Do animals breathe faster when given more oxygen or more carbon dioxide? Young scientists observe the respiration rates of locusts under a variety of gas concentrations to answer that very question. They collect data, analyze the...
EngageNY
Constant Rates Revisited
Find the faster rate. The resource tasks the class to compare proportional relationships represented in different ways. Pupils find the slope of the proportional relationships to determine the constant rates. They then analyze the rates...
Curated OER
Slope, Vectors, and Wind Pressure
A hands-on lesson using the TI-CBR Motion Detector to provide information to graph and analyze. The class uses this information to calculate the slope of motion graphs and differentiate scalar and vector quantities. There is a real-world...
EngageNY
Graphs of Simple Nonlinear Functions
Time to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.
College Board
Reasoning from Tabular Data
Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...
California Mathematics Project
Meteorology
See how estimation is essential to making temperature weather maps. Scholars use ratios and rates of change to estimate temperatures at locations where temperature readings have not been made. They connect this idea to linear functions.
Concord Consortium
Be Well
How much do you spend on healthcare each year? Data shows the expenditures in the US rise significantly each year. Young scholars use the data to calculate a rate of change over a 30-year period and look for—as well as provide— possible...
College Board
1999 AP® Calculus AB Free-Response Questions
Gain an understanding of the test before taking your own. Scholars develop an understanding of how calculus concepts appear on the AP® exam. The six released questions come from across the curriculum and include particle movement and...
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