+
Instructional Video6:15
Corbett Maths

Average Rate of Change

For Students 8th - 12th Standards
Simply find the slope to find the average rate of change. A short video provides the definition of the average rate of change. Using the definition, pupils calculate the average rate of change to solve problems that cover finding average...
+
Lesson Plan
West Contra Costa Unified School District

Average Rate of Change

For Teachers 8th - 10th Standards
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.
+
Lesson Plan
EngageNY

Average Rate of Change

For Students 8th Standards
Learners consider the rate of filling a cone in the 23rd installment of this lesson series. They analyze the volume of the cone at various heights and discover the rate of filling is not constant. The lesson ends with a discussion of...
+
AP Test Prep18:38
1
1
Flipped Math

Calculus AB/BC - Average and Instantaneous Rate of Change

For Students 10th - 12th
Ramp up the average rate of change—instantly. Learners use their knowledge of the formula to find the average rate of change to find the instantaneous rate of change. The presenter shows pupils an interactive that demonstrates finding...
+
Lesson Plan
West Contra Costa Unified School District

Average Rate of Change

For Teachers 9th - 12th Standards
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...
+
Lesson Plan
Curated OER

Instantaneous Rate of Change of a Function

For Teachers 10th - 12th Standards
Pupils draw the graph of a door opening and closing over time. They graph a given function on their calculators, create a table of values and interpret the results by telling if the door is opening or closing and evaluate the average...
+
Interactive
CK-12 Foundation

Average and Instantaneous Rates of Change

For Students 11th - Higher Ed
How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...
+
Worksheet
Curated OER

Exploration 1: Instantaneous Rate of Change Function

For Students 11th - 12th
In this function worksheet, students read word problems and write functions. They determine the instantaneous rate of change and identify intervals. This three-page worksheet contains approximately 20 problems.
+
Lesson Plan
Curated OER

Average Rate of Change, Difference Quotients, and Approximate Instantaneous Rate of Change

For Teachers 9th - 12th Standards
Pupils, with the assistance of their TI-84 Plus / TI-83 Plus calculators, distinguish meanings from right, left and symmetric difference quotients that include rate of change and graphical interpretations. They utilize symmetric...
+
Worksheet
Curated OER

Working with Rates of Change

For Students 8th - 12th
In this calculus worksheet, learners problem solve 8 word problems involving rates of change in association with high school students. Learners work out each problem and give a short explanation of each answer.
+
Activity
1
1
Curated OER

Mathemafish Population

For Teachers 8th - 11th Standards
It's shark week! In this problem, young mathematically minded marine biologists need to study the fish population by analyzing data over time. The emphasis is on understanding the average rate of change of the population and drawing...
+
AP Test Prep8:58
1
1
Flipped Math

Calculus AB/BC - Can Change Occur at an Instant?

For Students 10th - 12th
Be instantly transfixed by the idea of instantaneous rates of change. Scholars watch an informative video that introduces the fathers of calculus, Newton and Leibniz. They then learn about instantaneous rates of change by first...
+
Lesson Plan
Curated OER

Lesson #20 Rates of Change and Velocity

For Teachers 10th - 12th
Students investigate speed. In this rate of change lesson, students complete a rate/time/distance table to determine the average m.p.h. of a given trip. They listen and follow along with the lecture and examples to determine the average...
+
Assessment
1
1
Balanced Assessment

Ford and Ferrari

For Students 9th - 12th Standards
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...
+
Lesson Plan
EngageNY

The Binomial Theorem

For Teachers 11th - 12th Standards
Investigate patterns in the binomial theorem. Pupils begin by reviewing the coefficients from Pascal's triangle. They look at the individual terms, the sums of the coefficients on a row, and the alternating sum of each row. Individuals...
+
Lesson Plan
EngageNY

Euler’s Number, e

For Teachers 9th - 12th Standards
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. 
+
Lesson Plan
EngageNY

The Concept of a Function

For Students 8th Standards
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.
+
Assessment
1
1
Balanced Assessment

On Averages and Curves

For Students 11th - 12th
Determine the average on a curve. The class finds graphical representations of averages and expresses them both symbolically and on the graph. The assessment requires class members to justify using average to describe graphs.
+
Worksheet
Curated OER

The Babylonian Algorithm, Limits and Rates of Change

For Students Higher Ed
In this successive approximations worksheet, students use the Babylonian algorithm to determine the roots of given numbers. They identify the limits of a function, and compute the rate of change in a linear function. This two-page...
+
Assessment
CCSS Math Activities

Smarter Balanced Sample Items: High School Math – Target L

For Students 9th - 12th Standards
Functions are for forming context models. A PowerPoint file contains 11 questions for learners to answer. It covers the high school SBAC Claim 1 Target L item specifications and requires interpreting functions, determining appropriate...
+
AP Test Prep
College Board

2003 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Be integral to the learners in the classroom. Pupils use integrals, differentiation, and limits to solve the free-response questions from an AP® Calculus BC exam. Items cover topics such as area under a curve, particle motion, average...
+
AP Test Prep
1
1
Flipped Math

Calculus AB/BC - Unit 2 Review: Differentiation

For Students 10th - 12th
Tie up everything in one differentiable bow. Pupils work through 20 problems to review the concepts from the unit. The problems range from finding the average rate of change to finding the derivatives of various functions that require...
+
Worksheet
Curated OER

Functions Quiz

For Students 11th - Higher Ed
For this college level algebra worksheet, pupils determine the domain and range of a function, determine the average rate of change given an interval and the function, and graph a polynomial function. The two-page worksheet contains four...
+
Lesson Plan
Curated OER

Climate Change in My City

For Teachers 9th - 12th
Students investigate the climate changes occurring locally, regionally and globally over the last one hundred years. They brainstorm and predict whether the current year's weather was warmer or colder than last year then check the...