Mathematics Active Learning

Students cut apart triangles and then match the sides to form a triangle square. Students match expressions involving Pythagorean identities, reciprocal identities, quotient identities, odd and even identities and co-function identities. Transformations involve one or two steps.

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 cut apart triangles and match the sides to form one large triangle. Should be completed without a calculator. Includes angle in all four quadrants and an equal distribution between the six trig functions.

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.

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 cut apart triangles and match the sides to form one large triangle. Should be completed without a calculator. Includes angle in all four quadrants and an equal distribution between the six trig functions.

Students work in groups of two or three to arrange steps in the correct order to factor quadratics by splitting the middle term. These involve five steps.

Students cut apart small triangles and then match the sides to form a larger triangle. Students match degree-min-sec measures with decimal degree measures. Students also match degree measures with equivalent radian measures. The questions are half of each type. All d-m-s angles have the same degree measure, but different m and s measures. The radian measures are all within one unit circle revolution and are given as exact values.

Students find the reference angle of angles given in both angles and degrees to play the card game of War.

Students cut apart small squares. Then they match radian angle measures with their ordered pairs on the unit circle. A rectangle will be formed. All angles are within one positive rotation. There is one conversion between radians and degrees to fill out the puzzle.

Students cut apart small squares to form a large square. To accomplish this, they must match polar coordinates to their equivalent rectangular coordinates. All polar coordinates are in radians and involve exact values.

Students work in groups of two or three to arrange steps in the correct order to solve trig equations in linear and quadratic form. Each equation has 5 steps. These work well after students are accustomed to basic operations. Solutions are written for multiple trips around the unit circle. There are some variables of 2x and 3x and some equations which require taking the root of both sides of the equation. Some basic identities are required to solve the problems.

Students cut apart a random group of radian angles. Then they sort the angles by grouping all of the angles that are coterminal. There are sets of five coterminal angles with three positive and two negative angle measures. All angles that represent exact values in a complete trip around the unit circle are represented, plus two angles that involve nine in the denominator.

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 cut apart a 4 by 4 square with functions of the six trig functions that can be matched with their exact values to create a new 4 by 4 square. All functions are given in radian angle measure. Outer edges are blank, so the puzzle is easier.

Students have difficulty observing parameters of polar graphs on calculators by simply plugging in an equation. This exercise involves matching a graph to an equation with the assistance of a graphing calculator. Equations are grouped by type of graph and students are asked to make generalizations about what to expect of each graph type when given an equation by changing variables that change the graph. Graph types included are simple circles, limacons, roses and lemniscates. Students should pra

Students match a series of basic trig identities from start to finish. Included are reciprocal identities, quotient identities, pythagorean identities, odd & even identities and cofunction identities. Cards are in the correct order on the original. Print on card stock or laminate the original and cut apart to make a set. Make as many sets as you need for groups of two or three to work together. If a topic does not exactly match your curriculum, simply cut the pair of dominoes in half, remove t

Students work in groups of two or three to arrange steps in the correct order to simplify trig functions. These all have five steps using the pythagorean and reciprocal identities.

Students play the game of war with cards that include all of the exact values in the first and second quadrants. A set of radian cards and a set of degree cards are included. They may be played separately or mixed.

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