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 cut apart individual triangles to match functions with their derivatives to form a large triangle. Includes square roots and rational functions. (Their are no chain rule, product or quotient rule problems.)

Students work in groups of two or three to match the graph of a function, the graph of the first derivative, the graph of the second derivative, information from the first derivative (increasing, decreasing & horizontal tangent locations) and information from the second derivative (concavity & inflection points).

Students cut out triangles which they match to form a diamond shape. Matches involve evaluating in exact value inverse trig function to it's angle measure. This puzzle uses mostly sine, cosine and tangent. There are some expressions that involve evaluating the trig function of and inverse trig function. Some of the latter require drawing a right triangle on a coordinate system.

Two-page note sheet which includes an activity for looking at the different reasons for which differentiability fails interpreted graphically.

Students play the game of War with equivalent definite integrals. Integrals are mostly the power rule. Negative answers are obtained by switching the limits on integrals.

Students work in groups of two or three to match the function equation on a specified interval with the absolute maximum and absolute minimum of the function on the interval.

This contains a series of questions involving the graphs of functions and the graphs of their derivatives. Students must make connections between critical points on one and what they mean on the other for the same function. This can be used as a group activity or a whole class demonstration.

Students match graphs which are the result of transformations of a given graph to the equations that create the transformations. Includes horizontal and vertical stretch and shrink, horizontal and vertical shift, absolute value inside and outside the function, and negative x and negative f(x).

This is an outline with all that students need to know to graph and write equations for Polynomial (Linear, Second Degree and Higher Degree), Rational, Radical and Transcendental (Trig and Log) Relations. Includes Conic Sections. I give this to my Calculus students at the beginning of the year and use parts of it for Pre-Calculus. My students have expressed that it is very useful, so I offer it here.

Students cut apart individual triangles to match basic integrals with their solutions to form a large triangle. Includes power rule, sums and trig functions. A few basic trig identities are needed.

In pairs, students create identities involving 1, 2, 3, 4 and 5 steps and then ask other pairs to prove them. Play continues until time is called. Student should have done some identity proving prior to this activity.

Given equations, students sketch graphs using a graphing calculator. Then, they cut apart the individual graph/equation squares. Next they categorize and generalize about the types of graphs. After that they indicate how the type of graph is related to the type of equation. Finally they indicate special features are involved with each type of function. Types of functions involved are polynomial, rational, radical and exponential.

Practice worksheet wherein students graph polynomials in factored form or find the roots using the factor theorem, synthetic division and the quadratic formula as necessary without using a calculator. Y-axes are unnumbered.

This includes a series of functions of rational, square root, absolute value and piecewise functions that are plotted by hand. It is a good review for advanced classes or a learning experience for lower level classes.

Each student gets one or two cards with a question and an answer. Play goes around the room as students answer questions. This is a whole class activity. Includes Mean Value Theorem, Related Rates and Max-Min Applications. NOTE: If these cards do not exactly match your curriculum, cut the card pair(s) you want to eliminate in half and tape the halves you want to keep together before you laminate.

Students write down what happens with each type of function graph transformation and then use that information to plot transformations of a given graph. Includes reflections over both axes and absolute value. This can be used as a review of transformations in Precalculus or Calculus.

Students match a function, it’s critical points, where the function is at a minimum and/or maximum, where the function is increasing and/or decreasing and the sign chart for the first derivative. This activity has been revised.

The content includes limits of linear, absolute value, radical, greatest integer, rational, trig and log/exponential functions. This is a set that can be printed on card stock or regular paper and laminated. Run off as many copies as needed to make a set of cards for a group of two or three and cut them apart. Original has cards in correct order. If a topic does not exactly match your curriculum, simply cut the pair of dominoes in half, remove the item you don't want and tape the other halves t

The content includes properties of logarithms, derivatives and integrals of logs and exponents, and limits. This is a set that can be printed on card stock or regular paper and laminated. Run off as many copies as needed to make a set of cards for a group of two or three and cut them apart. Original has cards in correct order. If a topic does not exactly match your curriculum, simply cut the pair of dominoes in half, remove the item you don't want and tape the other halves together before you l