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
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.
CK-12 Foundation
Arithmetic Sequences: Paying of a Loan
How long does it take to pay off a loan? Pupils use a graph to model the sequence associated with paying off a loan. Using the graph, learners determine the initial value and the common difference of the arithmetic sequence. The learners...
CK-12 Foundation
Finding the nth Term Given the Common Ratio and the First Term: Dominoes
Topple misunderstandings of geometric sequences. Using a context of creating ever-increasing sizes of dominoes, pupils develop a geometric sequence. The scenario provides the size of the first domino and the common ratio between...
CK-12 Foundation
Geometric Sequences: Bacteria Colony
Show budding mathematicians how to model a diminishing bacteria colony two ways—graphically and algebraically. Using the coordinate axis, pupils create a graph to represent the decay of a bacteria colony. They determine the number of...
CK-12 Foundation
Division of Decimals by Whole Numbers: Lemonade Stand
After a full day of selling lemonade, three friends split the cost of the profit money. If the total profit was $34.20, how much will each friend get?
CK-12 Foundation
Volume by Disks: The Vase Case
Finding the volume is an integral characteristic of a vase. Using the idea that summing the areas of cross-sectional disks will calculate the volume of a rotational solid, pupils find the volume of a vase. Scholars determine the interval...
CK-12 Foundation
Logarithm Properties: The Log Properties
Roll a log into an equivalent expression. Given four expanded logarithmic expressions, pupils write an equivalent condensed expression. They identify which properties allows for the simplification.
CK-12 Foundation
Sequence of Partial Sums: Partial Sums
Have some fun building squares out of triangles. Pupils investigate the partial sums of odd numbers. Using the sum of the first four odd numbers, learners see that it can be rewritten as a sum containing a triangular number. Simplifying...
CK-12 Foundation
Sums of Finite Arithmetic Series: Triangular Numbers
Using a slider, scholars build triangular numbers and their associated rectangles and use the geometric display to find the pattern to determine the next triangular number. They then relate that number to the area of the rectangle to...
CK-12 Foundation
Parabolas: Invisible Graph
Envision the function as the point swings. Given a point connected to another point and a line, pupils trace through an invisible graph. Learners identify the name of the given point and the line and determine the type of conic section...
CK-12 Foundation
Hyperbolas
Hyperbolas—practice thinking outside of the box. Pupils alter the end behavior box to create various graphs of hyperbolas. They determine formulas to find the distance from the origin to the foci. Using that information, scholars...
CK-12 Foundation
Equations of Circles: The Sea of Happiness
Map this! Help your young mathematicians draw a circular island on a map. Given specifics of the location and size of an island on a map, pupils transform a circle to meet the given requirements. They then determine the location of the...
CK-12 Foundation
Parametric-Inverses: Graph Matching
Perform a switch to find the inverse of a parametric equation. Pupils match four parametric functions with the graph of the their inverses. Using the graphs, learners determine whether particular points are on the original parametric...
CK-12 Foundation
Two-Dimensional Vectors: River Ferry and Current Vectors
Fight against the current. Pupils explore the resulting path when they are crossing a river while being pushed downstream by the current. Using vector notation, learners express the speed and direction of a ferry. They finish by...
CK-12 Foundation
Existence: One-to-One Functions and Inverses
One-to-one means the answer is simple, right? Given four graphs, pupils use a vertical line to test each graph to find out if they are one-to-one. By using the resource, learners realize that not all one-to-one relations are functions....
CK-12 Foundation
Change of Base: River Logs
Using the answers to the challenge questions, class members work through simplifying a complex logarithmic expression that requires changing bases. Pupils drag values to fill in the steps to arrive at a numerical equivalent expression.
CK-12 Foundation
Solving Logarithmic Equations
Pupils follow a chain of reasoning in deconstructing a logarithmic equation step by step. Using their knowledge of logarithms, learners compare the solutions of logarithmic equations when the bases are changed.
CK-12 Foundation
Recursive Formulas: Fibonacci Sequence
Explore the building blocks of the Fibonacci Sequence. Given the lengths of sides of squares, pupils deduce the pattern to determine the lengths of two more squares. Learners continue to work with recursive formulas to generate numerical...
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 2)
What does it mean if young mathematicians cannot put the squeeze on a sequence? Learners investigate a divergent sequence and find the formula for the nth term. Using the definition of a limit of a sequence, pupils try to find the limit...
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 4)
Take a look at another alternating sequence. The resource provides a graphical display of a sequence that alternates between two values. Pupils use the display to determine whether the sequence has a limit. Given a theory of limit,...
CK-12 Foundation
Circles Centered at the Origin: The Map of the Beta Solar System
Calculate galactic orbits in a far-out resource. Pupils drag a point on a circle to graph the orbit of a fictional planet. Using the equation, they find points through which the orbit passes. To finish the simulation, users determine the...