EngageNY
Interpreting Rate of Change and Initial Value
Building on knowledge from the previous instructional activity, the second instructional activity in this unit teaches scholars to identify and interpret rate of change and initial value of a linear function in context. They investigate...
EngageNY
Graphs of Linear Functions and Rate of Change
Discover an important property of linear functions. Learners use the slope formula to calculate the rates of change of linear functions. They find that linear functions have constant rates of change and use this property to determine if...
EngageNY
Average Rate of Change
Learners consider the rate of filling a cone in the 23rd installment of this instructional activity series. They analyze the volume of the cone at various heights and discover the rate of filling is not constant. The instructional...
West Contra Costa Unified School District
Average Rate of Change
Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.
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...
Howard County Schools
Constant Rate Exploration
Question: What do rectangles and bathtub volume have in common? Answer: Linear equations. Learn how to identify situations that have constant rates by examining two different situations, one proportional and one not proportional.
NASA
Resolving 2-Plane Traffic Conflicts by Changing Speed—Problem Set E
What do you do to change arrival times of airplanes when a different route is not available? The fifth interactive in a series of six presents problems where pupils must find solutions to conflicts of safety rules. They must decide how...
NASA
Resolving 2-Plane Traffic Conflicts by Changing Route—Problem Set B
Do pilots create appropriate spacing between aircraft by traveling a longer or shorter path? An interactive presents two airplanes that violate safety protocols. Pupils must determine how to change the path of one plane to create the...
NASA
Resolving 3-Plane Traffic Conflicts by Changing Speed—Problem Set F
Get three planes to line up safely. Individuals work through a set of problems to eliminate spacing conflicts between three airplanes in flight. The pupils use their knowledge to change the airplanes' speed or route to meet a...
NASA
Resolving 3-Plane Traffic Conflicts by Changing Route—Problem Set C
Keep the planes from crashing. Pupils work with three airplanes and change their flight paths to keep them at a safe distance from each other. Individuals work through three problems in the third interactive in a set of six with...
Curated OER
Rate of Change
Students observe and calculate slopes. In this algebra lesson plan, students graph equations and determine the pace at which the slope is changing. They use the navigator to see the change as they graph the lines around.
Curated OER
Related Rates
In this algebra instructional activity, students rewrite word problems using algebraic symbols and solve for the related rates. There are 10 word problems involving derivatives and rates.
West Contra Costa Unified School District
Average Rate of Change
The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots of...
Illustrative Mathematics
Video Streaming
Your movie fans will be interested in this resource. They will compare video streaming plans. One plan charges a set rate per month and a reduced viewing fee, and the other has a flat rate per each video viewed. Unfortunately, students...
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...
Curated OER
Worksheet 12: Functions
In this math worksheet, students are given 7 problems in which they differentiate, figure rate of change, determine value, and prove formulas.
Curated OER
Heart Rate Monitoring
Algebra learners like this resource because it is easy to understand and it relates to their lives. Whether you are starting a new workout routine, or just climbing the stairs, your heart rate increases and decreases throughout the day....
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
Dragonfly
The speed of a dragonfly brings math into the real world as your learners collaboratively see the value in calculating unit rates in direct proportion problems. This six-phase lesson plan encourages you, as the teacher, to only ask...
Illustrative Mathematics
Logistic Growth Model, Abstract Version
Here learners get to flex some serious algebraic muscles through an investigation of logistic growth. The properties of the constant terms in the logistic growth formula are unraveled in a short but content-dense activity. Moving...
Curated OER
Mathematical Modeling and constant Rate Equations
In this rates learning exercise, students solve five story (word) problems related to rate and time. In two of the problems students are directed to create a graph of the problem.
Curated OER
Supplementary Related Rates Problems
In this rates worksheet, students read story problems, determine the necessary information, and set up equations to determine the velocity and rates. This two-page worksheet contains two multi-step story problems.
Balanced Assessment
Ford and Ferrari
Which is faster, a Ford or a Ferrari? The short assessment has pupils analyze graphs to determine the rates of change between the two. Individuals interpret the rates of change within the context of speeds of the cars and develop a map...
EngageNY
Introduction to Simultaneous Equations
Create an understanding of solving problems that require more than one equation. The lesson introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of...