Mathematics Active Learning

Students match the graph of a quadratic, the x-intercepts, and the equation in standard form. Print out the file on card stock or laminate regular paper. Cut the cards apart to make a set for teams of two or three. The original has the cards that match placed together.

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.

Students cut apart triangles and then match the sides to form a large parallelogram. Students match the standard form of the equation of a line to the slope-intercept form or point-slope form (equal number of each category).

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

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

Given the graph of a quadratic function, students write an equation in vertex form.

Students use a graphing calculator to discover the parents functions of even radicals and odd radicals. They further discover what happens to a parent function if a number is added or subtracted outside the radical sign and if a number is multiplied outside a radical.

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).

Students match the graph of a linear-quadratic or quadratic-quadratic system with its equations and intersection point(s). Includes a couple x = y^2 parabolas and systems with no solution. Cards must be cut apart before they are given to students as the original has the cards arranged with their like cards.

Students work in groups of two or three to match the graph, the domain and range and the equation of a trig function. The first 12 sets involve two transformations and the next six sets involve three transformations. There is an equal number of each of the six trig functions. Does not include negative or absolute value transformations.

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 find the slope between two points while playing the card game War. Includes horizontal and vertical lines.

Given equations of trig functions, students sketch the graph. Equations are given in radians. Most graphs are secant.

Students examine unusual looking function graphs with point-wise plotting to be certain they get a good picture of the graph. Students are exposed to the variety or function graphs (and translations thereof) that exist. Students determine domain, range and continuity of these functions. Included: piece-wise, absolute value, complicated square root, rational, greatest integer, exponential and natural log

Given the graph of a trig function, students write an equation for the function. Graphs are in radians.

Students work in groups of two or three to match the sine graph, its features (shifts, period, amplitude, reflections) and its equation in factored form. Information is given in radians.

Students work in groups of two or three to match up a system graph, the point of intersection and the equations of the two graphs. Matching cards are together on the original. Teacher must print onto card stock or regular paper and laminate. Cards must be cut apart and given to students mixed up. Includes a no solution and an infinite solutions.