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 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.

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.

Students investigate the basic graphs of parent functions for powers, rational powers, exponents, logarithms, reciprocals, greatest integer and absolute value. The investigation involves completing t-charts, graphing the functions and answering questions about the graph differences within each category (for example, with the power function the differences in the graph as the power increases).

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.

Students investigate relations vs functions, the different representations of functions, the vertical line test, function notation, locating f(x) values from a graph, domain and range of graphs and equations and graphing a function by hand. This could be used as an introduction or a review.

Students investigate quadratic functions in terms of standard, vertex and factored form and what those forms tell us about the graph and solutions to quadratic equations. Students write equations from graphs and vice versa. Also included is the second constant term using finite differences, the general pattern of all quadratic graphs, domain and range, how to find the vertex from standard form without completing the square, and solving equations in the form of 0 = x^2 and those requiring the qua

Throughout these 8 pages, students identify quadrant names, review ordered pairs, look at x- and y-intercepts, slope, explore slope-intercept form, standard form and transforming between these two forms. Emphasis is placed on graphing as well as algebraic manipulation. Each topic is explained and then followed by practice problems. This can be used as a note sheet or a group activity, with the teacher available to consult and guide.

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.