Flipped Math
Calculus AB/BC - The Fundamental Theorem of Calculus and Accumulation Functions
Connect integrals with differentiation. The beginning of the video introduces the definition of an accumulation function. Scholars learn about the relationship between integrals and derivatives. Using what is commonly known as Part Two...
Flipped Math
Calculus AB/BC - Interpreting the Behavior of Accumulation Functions Involving Area
Accumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...
Curated OER
Accumulation Functions as Antiderivatives
In this accumulation functions worksheet, students describe the graph of an accumulation function for a constant function. Students describe the link between the slope of the graph of the accumulation function and the value of the function.
Curated OER
Graphing Accumulation Functions
In this accumulation function worksheet, students find the graphical relationship between two functions. They describe the relationships between the graphs of a function when accumulation begins at 0 and at 2.
Curated OER
More On Accumulation Functions
In this math worksheet, students investigate using the accumulation method to solve for the functions. They also review using Riemann Sums.
Flipped Math
Calculus AB/BC Mid-Unit 6 Review: Integration and Accumulation of Change
Accumulate the content so far. Learners review the content from the first five lessons dealing with accumulation functions. The eight problems go over finding maximums, minimums, concavity, points of inflection, and intervals of increase...
Curated OER
Fundamental Theorem of Calculus
High schoolers, with the assistance of their TI-84 Plus / TI-83 Plus calculators, explore and assess the connections between an accumulation function, one defined by a definite integral, and the integrand. They summarize that the...
Curated OER
Accumulation Functions and Definite Integrals
In this accumulation functions worksheet, students write expressions that involve the definite integral of a given function. They use a graph to find given values of areas of the line. Students follow guiding questions to determine the...
Curated OER
Cardiac Output, Rates of Change, and Accumulation
Students explore rates of change. In this cardiac output lesson, students measure the amount of blood being pumped by a heart. They explore the flow rate and complete an accumulation and concentration problem. They analyze data, flow...
Flipped Math
Calculus AB/BC - Exploring Accumulation of Change
Add up area to find total change. Pupils learn what it means to find the area under a curve and how to calculate it geometrically. They first find the accumulation of change given a rate of change function. Scholars then apply that...
Curated OER
Evaluating Definite Integrals Using Accumulation
In this integral learning exercise, students sketch functions and use their graph to evaluate functions. This two-page learning exercise contains four multi-step problems.
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Lab 2: Euler's Method and Riemann's Sums
In this Euler's Method and Riemann's Sum worksheet, students identify the best situation in which to use Euler's Method and Riemann's Sum. They identify the initial value of a problem and use the accumulation formula to determine the...
Illustrative Mathematics
Two Wheels and a Belt
Geometry gets an engineering treatment in an exercise involving a belt wrapped around two wheels of different dimensions. Along with the wheels, this belt problem connects concepts of right triangles, tangent lines, arc length, and...
Curated OER
Applied Fundamental Theorem of Calculus
Students apply the Fundamental Theorem of Calculus. In this calculus lesson, students identify the graphical connections between functions and accumulation functions. They use a TI to represent the functions.
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Integrated Algebra Practice: Exponential Growth
For this exponential growth worksheet, learners solve 10 multiple choice and short answer problems. Students find the interest of an amount of money given the rate, time, and times compounded.
Cornell University
Scaling Down: Effects of Size on Behavior
Two activities explore the concept of size, especially small sizes down to the nano. Scholars practice determining volume, mass, and density and calculate exponential increases and decreases. They then predict and test the effect of size...
Curated OER
Exploring the Various Regions of Boyle Heights: Continuity and Change
Student study the local landscape of Boyle Heights, California and draw a sketch of the area. Students use map making skills in this activity. Studient make a portfolio of information and photographs they accumulate over time on the area.
Curated OER
Applying the Fundamental Theorem of Calculus
In this fundamental theorem worksheet, students identify the anti-derivative and write equations as an explicit function. This two-page worksheet contains two multi-step problems.
Curated OER
Interesting Interest Rates
Your young bankers compare earning interest accumulated yearly and monthly to decide which method most increases their balance. Using an exponential function to model the bank balance affords the learners more practice connecting these...
Curated OER
Inflation and Money
Students examine the relationship between inflation and money. Defining key terms, they define money in terms of its functions and give examples of money. They discover what happens when inflation occurs unexpectedly. They also examine...
Curated OER
Discussion Sheet 7: Exponential Growth
In this exponential growth worksheet, students determine the population of a country. They set up an integral which represents the mass of an abject and determined the total accumulation of snow in a region. This one-page worksheet...
Curated OER
Examining the Effects of Space Flight on the Heart, Lungs, and Blood Vessels
Students are able to identify the components of the cardio-vascular system. They are able to describe the way the heart works to pump the blood. Students are able to explain the function of the cardio-vascular system. They are able to...
Curated OER
Structure of the Nephron
In this nephron worksheet, students color the parts of the nephron and answer five questions about the structures and functions of the parts of the nephron.
Curated OER
Plant Structure and Growth
This plant structure and function PowerPoint addresses the main organs and the factors that affect its development as well as going into detail about the specializations at a cellular level. The cell functions and system adaptations...