Active Learning Math and Computer Science

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover the relationships between the sides of 30-60-90 and 45-45-90 right triangles Students will create and then measure the sides of each type of triangle. Prerequisites 1. Students understand the basic concepts of triangles 2. Students have learned the basics of functions 3. Students are familiar with angles an

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover when a polynomial function is even or odd Prerequisites 1. Students have learned the basics of functions 2. Students have learned functional notation 3. Students have been introduced to polynomial functions 4. Students know how to graph a function by hand given a table of values The Process Students are presented wit

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover the meaning of a radian by manipulating the central angle of a circle and comparing the length of the radus to the intercepted arc. Students will be using an online visual tool, Desmos, in order to aid them in their discovery. Prerequisites 1. Students understand the basic concepts of circles 2. Students h

This activity is designed to have the students practice finding the inverse of a function for specific values from graphs or tables. In this way students can gain a better understanding of inverse functions. Prerequisites 1. Students have learned the basics of functions 2. Students have learned functional notation 2. Students understand the definition of inverse functions 3. Students know how to read graphs. 4. Students know how to graph by hand 5. Students know to to find the c

Students learn best when discovering patterns on their own. This activity is designed to lead students to discover that logarithms are the inverse of exponential functions. Students are asked to graph the inverse of the graphs of several exponential functions. They are then asked a series of questions that will lead them to discover a new type of function, logarithms! For each graph students are asked to: graph the inverse of the functionfind the equation, domain and range of the original g

Students will use an online graphing tool called Desmos to investigate the changing the amplitude of the graphs of trigonometric functions as the value of A is changed in the functions: y = Asin(x) and y = Acos(x) This will be an active learning exercise where students will discover patterns for themselves. They will have some practice problems as well. Students who discover relationships for themselves have better problem solving skills and they retain the subject matter because it is not a m

Students will use an online graphing tool called Desmos to investigate the vertical transformation of the graphs of trigonometric functions as the value of D is changed in the functions: y = sin(x) + D and y = cos(x) + D. This will be an active learning exercise where students will discover patterns for themselves. They will have some practice problems as well. Students who discover relationships for themselves have better problem solving skills and they retain the subject matter because it is

This activity is designed to have students practice graphing exponential and log functions. The questions are designed so that students will have to think about the transformations that are taking place. Students are given a series of either exponential or log functions. For each function, they are asked to identify the parent functionto explain in words what transformation of the parent function is taking placeto graph the functionto identify the domain and range of the functionPrerequisites

Students will use an online graphing tool called Desmos to investigate the horizontal shifting of the graphs of trigonometric functions as the value of C is changed in the functions: y = sin(x-C) and y = cos(x-C) This will be an active learning exercise where students will discover patterns for themselves. They will have some practice problems as well. Students who discover relationships for themselves have better problem solving skills and they retain the subject matter because it is not a me

Students will use an online graphing tool called Desmos to investigate the changing the period of the graphs of trigonometric functions as the value of B is changed in the functions: y = sin(Bx) and y = cos(Bx) This will be an active learning exercise where students will discover patterns for themselves. They will have some practice problems as well. Students who discover relationships for themselves have better problem solving skills and they retain the subject matter because it is not a memo

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover how to graph inverse functions and how to determine the equation of inverse functions Prerequisites 1. Students have learned the basics of functions 2. Students have learned functional notation 3. Students know how to graph a function by hand given a table of values 4.. Students have been introduced the definitio

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover how changing the equation of an exponential function changes its graph into a growth or decaying exponential function. Prerequisites 1. Students have learned the basics of functions 2. Students have learned functional notation 3. Students know how to graph a function by hand given a table of values 4.. Students h

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover how to graph inverse functions as reflections across the line y=x. It also leads students to discover the relationship between the domain and range of inverse functions. Finally students will learn how to determine when functions do not have inverses. Prerequisites 1. Students have learned the basics of functions 2.

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover the rules for the shifting the graphs of functions horizontally by discovering them on their own. Students will be using an online visual tool, Desmos, in order to aid them in their discovery. Students can just as well use a graphing calculator if they own one. Prerequisites 1. Students have learned the basics of

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover the rules for shifting the graphs of functions vertically by discovering them on their own. Students will be using an online visual tool, Desmos, in order to aid them in their discovery. Students can just as well use a graphing calculator if they own one. Prerequisites 1. Students have learned the basics of func

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover the rules for the reflecting of graphs across the axes by discovering them on their own. Students will be using an online visual tool, Desmos, in order to aid them in their discovery. Students can just as well use a graphing calculator if they own one. Prerequisites 1. Students have learned the basics of function

This handout contains all of the important properties of the eight parent functions. This includes: the equation, domain and range, and a picture of the graph. The parent functions are the main functions that are to be used when students are taught to transform functions: move up, move down, move left, move right, stretch and shrink. Teachers should first have students discover these properties on their own and then give them this handout.

This activity has students practicing adding, subtracting, multiplying and dividing functions using function notation. Students are asked to perform these operations from equations, tables and graphs. Giving students the opportunity to combine functions from these three perspectives will enhance students understanding of the undlerlying concepts. Prerequisites Students have learned the basics of functions Students have learned functional notation

Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover the shape of sinusoidal functions with the aid of a Ferris Wheel Students will collaborate with each other as they discuss the various patterns involved with the path of a seat on a moving Ferris Wheel Prerequisites 1. Students have learned the basics of functions 2. Students are familiar with domain and

Reference Angles are an important concept that students must learn before they can go on to understanding the unit circle. In this discovery activity students manipulate an online unit circle in order to understand the meaning of reference angles. This is an active learning worksheet where students must discover the information for themselves. Students can do this by themselves or in a cooperative environment.