Mathematics Active Learning

Two-page activity which reviews the definition of a logarithm, the inverse nature of exponents and logarithms, graphing logarithm transformations. and transforming between exponents and logarithms (including solving for a variable in the process). Included is a series of questions that ask students to explain why certain properties of logarithms exist (for example "Why does log 1 = 0?")

Students write equations of polynomial functions by looking at their graphs. Graphs include those that cross the x-axis and those that are tangent to the x-axis.

Students match the graph of a polynomial function with the sign of the lead coefficient, the degree and the end behavior.

Students use the TI-84 Calculator to solve systems of equations using the Calculate Function. Systems include rational, linear, quadratic, exponential and absolute value functions. Even if students have not formally studied these functions, the activity works just fine and exposes them to different functions.

Given graphs of rational functions, students write and equation. Graphs include holes, pass through x-intercepts and bounce x-intercepts involving the same factors.

This file may be projected onto a white board or converted to a smart board file. It is an introduction to polynomial function graphs.

This worksheet involves a series of problems involving applications of quadratic functions including projectile motion, area and economics. To complete these problems students should know the quadratic formula and the formula for the x value of the vertex (-b/2a).

Students use sign charts to solve polynomial, rational and radical inequality equations. Includes some absolute value factors.

Students cut apart each small triangle. Then, they match the equation of each function to the equation of its inverse. A diamond shape will be formed. Functions include linear, quadratic, cubic and rational. Two functions that are inverses of themselves are included.

Students explore rational graph behavior at holes and asymptotes. Graphing calculator is used.

Students match cards containing parametric equations, the corresponding table of values and the corresponding graph. Cards are randomized so that students can cut them apart and then match them. Matching cards are presented at the end. This activity should be completed before students are introduced to the procedure for graphing parametric equations on a graphing utility. If not, then this activity will lose its usefulness and will take no time to finish.

Students work in groups of two or three to match the graph, the equation, the asymptote, the table of values and the domain and range of exponential and logarithmic functions Includes exponents and lags with bases of 10, e, 2, and 3. Includes transformations of vertical and horizontal displacement, horizontal and vertical stretch and shrink , negative values of x and y and absolute value.

This is a comprehensive treatment of the following matrix operations: items in the same position are equal when two matrices are equal, addition/subtraction of matrices, multiplication of a matrix by a scalar, multiplication of matrices, finding the inverse of a matrix and mixed operations within one problem. Each new section has a brief explanation of the process before the problem set. This could be used for guided instruction or group work.

Students cut apart small triangles and then match the sides to form a parallelogram. Students match a vector operation with its result. Operations include adding and subtracting, multiplying by a scalar, finding the negative of a vector, and finding the absolute value.

Students cut apart triangles & squares and then match the sides to form a topaz shape. Students match expressions involving reciprocal identities and quotient identities. Transformations involve one or two steps.

Students investigate symmetry to the x-axis, y-axis and origin by looking at graphs, tables of values and observing the ordered pairs of reflected points. They also create graphs of their own. Then students investigate odd and even functions. This is intended as a stand-alone lesson in earlier courses or as the prelude to testing algebraically for symmetry and odd/even functions in more advanced courses.

Provided with graphs, students identify where the functions are constant, decreasing or increasing. Examples include graphs of all functions except trigonometric functions.

Students explore like denominators briefly and then a more in-depth study of unlike denominators. This can be used as a class note sheet, with teacher direction at first. Then students practice in their groups.

This is a short exercise that may be completed as a class or in group work. I have not seen any problems like this and the concepts involved are important: Suppose we have a function f(x) = 7^(2x + 3) Using the properties of exponents, we can re-write this as f(x) = 7^2x × 7^3 Using the properties of exponents, we can re-write this as f(x) = (7^2)^x × 7^3 We can simplify further to f(x) = 49^x × 343 Questions also work the reverse way.

Students investigate transformations of function graphs including translations, stretches & shrinks, reflections and absolute value. May be broken down into smaller units by type of transformation. Some of the explorations are calculator active, but the majority involves translating by hand once the results are known.