EngageNY
Writing the Equation for a Circle
Circles aren't functions, so how is it possible to write the equation for a circle? Pupils first develop the equation of a circle through application of the Pythagorean Theorem. The lesson then provides an exercise set for learners to...
Teach Engineering
Discovering Relationships Between Side Length and Area
Consider the relationship between side length and area as an input-output function. Scholars create input-output tables for the area of squares to determine an equation in the first installment of a three-part unit. Ditto for the area of...
Concord Consortium
Bill the Ball Bearing Man
Just how durable could a hollow ball bearing be? Learners model the strength of the walls of a ball bearing as a function of the radius of its cavity. They use their models to make reasonable conclusions about the probability of failure...
Illustrative Mathematics
As the Wheel Turns
Determine the location of a point on a moving wheel. The task challenges groups to determine the horizontal and vertical locations of a point on the edge of wheel that is moving. Teams first determine a function that will model the...
Illustrative Mathematics
Seven Circles III
A basic set-up leads to a surprisingly complex analysis in this variation on the question of surrounding a central circle with a ring of touching circles. Useful for putting trigonometric functions in a physical context, as well as...
Curated OER
Variables, Formulas, Functions, Graphs and Linear Approximations
In this limitations of formulas instructional activity, students answer four essay questions about functions. Two questions refer to the limitations of formulas. They graph one function and explain how it specifies the rule of the function.
Curated OER
Periodic Functions
In this calculus instructional activity, learners identify important rules and properties of the unit circle. They differentiate between polar and complex coordinates. There are 20 questions about the unit circle.
Curated OER
Inverse Trig Functions
Learners solve and graph 10 different problems that are the inverses of various trig functions. First, they determine which equation is equivalent to a given equation. Then, they find an angle of a right triangle, given its leg lengths....
GeoGebra
Getting on the Right Wavelength
Predict an equation that waves up and down. Pupils set the height, radius, and period of a Ferris wheel. The learners write a sine equation to match the graph of the height of a point on the wheel as a function of time. Running the...
Radford University
Maximizing Light Through a Window
Let there be plenty of light. For a perimeter of 10 feet, scholars determine the maximum area of a window composed of a rectangle and a semicircle. They draw diagrams and then write and solve equations to find the height and radius for...
Curated OER
Worksheet 21
In this math worksheet, students find the interval convergence of the series. They also practice writing a series and the functions. Students find the Taylor series about zero.
Curated OER
Solving Problems Involving Chords, Radii, Tangents, Secants and Arcs within the Same Circle
Tenth graders apply their knowledge of angles related to a circle, radii, secants, tangents and chords of a circle. They practice using formulas related to a circle. They also apply what has been practiced to real life situations.
Curated OER
Challenge Discussion Sheet 3
In this function worksheet, students prove given limits, solve differentiate functions, identify points on a graph with tangent lines passing through given points, determine the radius of a largest sphere that can fit inside of a pyramid...
Mathematics Assessment Project
Modeling Motion: Rolling Cups
Connect the size of a rolling cup to the size of circle it makes. Pupils view videos of cups of different sizes rolling in a circle. Using the videos and additional data, they attempt to determine a relationship between cup measurements...
Curated OER
Woody Sine
Students explore the concept of sine. In this sine lesson, students create a sine graph from tooth picks. Students create a unit circle with tooth pick length radius. Students then take the tooth picks from the unit circle and put them...
Mathematics Assessment Project
Sorting Equations of Circles 2
How much can you tell about a circle from its equation? This detailed lesson plan focuses on connecting equations and graphs of circles. Learners use equations to identify x- and y-intercepts, centers, and radii of circles. They also...
Urbana School District
Optics
Don't worry, optics is a light topic! The presentation covers reflection, refraction, fiber optics, mirages, prisms, rainbows, dispersion, mirrors, lenses, telescopes, diffraction, the human eye, and much, much more. Presentation is the...
Curated OER
The Internal Density and Mass of the Sun
In this sun worksheet, students read about calculating the internal density and mass of the sun. Students use a given formula for the internal density of the sun's gases which students use to solve four mathematical problems.
Merck KGaA (Darmstadt, Germany)
EMD PTE
You can't tell by the title, but this is a functional periodic table of elements. Incorporating bright colors, lucid text, and easily operated features, this application serves as a valuable reference tool for your chemistry class.
Curated OER
As the Wheel Turns
This is not your typical Ferris wheel problem. In this exercise, your class will combine their knowledge of sinusoidal functions as well as linear motion to come up with parametric equations that model the position of a point on the edge...
Curated OER
Model Air Plane Acrobatics
Your young airplane enthusiasts will enjoy this collaborative task of graphing an airplane's distance from the ground as it flies in a perfect circle. They will discover that they have graphed a sinusoidal function that comes from the...
Curated OER
Worksheet 3: Graphing Speed and Time
In this graphing speed and time worksheet, students answer 7 questions regarding graphing, speed, distance, derivatives, Newton's method and wheel radius.
Curated OER
The Building Blocks
This PowerPoint is a comprehensive review of all the facts related to an atom's basic structure and function. What makes this unique is that it is geared toward an audience of junior geologists. After introducing the periodic table of...
Curated OER
Telescope #2
Students investigate parabolas as the shape of a telescopic lens. In this Algebra I/Algebra II instructional activity, students explore the relationship between the coefficients of a quadratic function and the shape and position of the...