CK-12 Foundation
Logistic Functions: Fab Fitness
Strengthen your understanding of logistic functions. Young mathematicians change the carrying capacity of a logistic function and see how function values change. The function models the number of members in a gym over time.
CK-12 Foundation
Compound Interest per Period: Credit Card Payment
Credit cards can be convenient, but are they worth it? Future consumers learn about compound interest and credit card payments. They use an interactive to create a table that shows the remaining balance after each month.
CK-12 Foundation
Continuous Interest
Continue teaching your financial scholars about interest. A slider interactive has users investigate the growth of an account earning continuous interest. A set of challenge questions has them solve problems given a variety of situations.
CK-12 Foundation
APR and APY: APR vs. APY
Who wins the battle of the interest rates? Scholars use an interactive to investigate three different bank rates. Comparing APR and APY lets them see how nominal and effective rates differ.
CK-12 Foundation
Even and Odd Functions and Function Symmetry: Even and Odd Functions
Even, odd, or neither? Pupils study even and odd functions using a well-balanced interactive. They determine whether a given function is even or odd from its graph.
CK-12 Foundation
Even and Odd Functions and Function Symmetry: Even and Odd Functions (Symmetry)
Even money states that the resource is good to use. Scholars manipulate an interactive to adjust the portion of a graph to the left of the y-axis. The interactive allows them to switch between even and odd modes that show the right side...
CK-12 Foundation
Find Imaginary Solutions: Imaginary Zeros
The resource is the real deal. Individuals investigate the imaginary zeros of f(x) = x^2 + 1. They accomplish this task by using an interactive that shows input values x = a + bi and output values x^2 + 1 on a complex plane.
CK-12 Foundation
Concept of Limit
There's no limit to how useful the resource can be. Scholars use a slider interactive to investigate limits from graphs. They take both one-sided and two-sided limits into consideration.
CK-12 Foundation
Concept of Limit: Limit Notation
Limits to infinity are simple to find if you can compare numerators and denominators. Users of the interactive drag expressions to match with their limit as x approaches infinity. A set of challenge questions assesses their groupings.
CK-12 Foundation
Linear, Quadratic, and Cubic Models: The Box Model
Models make math manageable. Individuals investigate a cubic function that models the volume of a cube through the interactive.
CK-12 Foundation
Area Sums: Estimation with Rectangles
The more rectangles, the better the estimate. Using the interactive, pupils explore estimating the area under a curve using left-hand sums. Learners respond to challenge questions on how to get better estimates using the same technique.
CK-12 Foundation
Properties of Definite Integrals
Close your eyes and visualize a definite integral. An interactive provides a visualization of a function and definite integral on a closed interval. Pupils move one point of the interval in either the positive or negative direction....
CK-12 Foundation
Trapezoidal and Midpoint Approximations: Area of a Skirt
When are trapezoids better than rectangles? Using trapezoids pupils approximate the area of fabric defined by a function. Just like with rectangles, learners realize the more trapezoids the more accurate the approximation. Scholars use...
CK-12 Foundation
Area Between Curves: Income and Expenses
Use the area of polygons to calculate the area between curves. Pupils calculate areas under income and expense curves by filling the space with squares and right triangles. Using that information, they determine the profit related to the...
CK-12 Foundation
Method of Cylindrical Shells
Approximate the volume of a solid of revolution. Using a method similar to approximating the area under a curve, pupils investigate the volume of a solid of revolution. The learners use a given definite integral to find the volume of...
CK-12 Foundation
Length of a Plane Curve
Challenge your class to use straight lines when estimating the length of a curve. An engaging interactive allows individuals to place line segments one after another along the arc. Learners determine that the more lines used, the better...
CK-12 Foundation
Work and Force: Lifting a Bucket
How much work does it take to lift a bucket? An interactive presents a problem of lifting a bucket from the ground to the top of a building. Using their knowledge about work and integrals, pupils calculate the amount of work required to...
CK-12 Foundation
Inverse Functions
Provide a graphical view of inverses. Pupils manipulate points on a line and see the relationship of the graph with the graph of its inverse. Using the relationship between the graphs, scholars respond to questions concerning inverses...
CK-12 Foundation
Inverse Functions: Definition of Inverse Functions
Is the inverse of a function also a function? Pupils manipulate the graph of a function to view its inverse to answer this question. Using a horizontal and vertical line, class members determine whether the initial function is...
CK-12 Foundation
Vector Sum and Difference: The Country of Dreams
Find your way around using vectors. Scholars use an interactive to learn about vector addition. They answer a set of questions about modeling a route on a map using vectors.
CK-12 Foundation
Vector Projection
Two words summarize the interactive: vector projector. An easy-to-use resource lets users investigate vector projections on the coordinate plane. Given the components of two vectors, they determine the projection of one vector onto the...
CK-12 Foundation
Vector Projection: Hitting a Baseball
Hit a home run with a resource that is all fun and games. Learners apply an interactive to determine the horizontal component of the distance a baseball travels. They must consider vector projections for this task.
CK-12 Foundation
Explicit Formulas: Tiles for Writing nth Term in a Sequence
Build an explicit formula using tiles. Pupils develop a tile representation of a term within a sequence given figures of previous terms. Using the diagrams, learners develop the explicit formula by recognizing the common difference and...
CK-12 Foundation
Sum Notation and Properties of Sigma: Cracking the Code
Help your class develop an understanding of sigma notation. Pupils match the sigma notation with the sums. Using the expanded sums, learners evaluate the summations. The scholars move on to prove a property of sums.