This activity practices solving incomplete quadratic equations by taking square roots. Almost all of the equations are in standard form. Solutions are rational (integers and fractions) and irrational numbers. The fun part is finding an idiom corresponding to each solution sets of the partners’ quadratic equations labeled with one and the same small alphabetic letter. Activity Directions: Students start solving their own set of twelve equations by the square root method. They are given tables to use. Using table 2, each partner finds which two words correspond to each solution set of his equations. At last partners together rearrange the words corresponding to their equations labeled with one and the same small alphabetic letter and find out an idiom. They find out 12 different idioms and write them in table 3. Answer keys are included.

In this activity, students will practice solving rational equations resulting in linear and quadratics using three types methods for solving: Cross Multiplying Multiplying by the LCD Factoring to find the LCD This activity includes monomial, binomial, and trinomial denominators. The equations have only rational roots. The problems have a varying degree of difficulty. Activity Directions: There are 20 problems total, separated into two sets. Partners start solving their own set of ten equations by the most appropriate method and check for extraneous solutions. They must determine the common root between each two partners’ corresponding equations. ( For instance, the equations (1a) and (1b) are corresponding and have one common root, similarly the equations (2a) and (2b)… ). Partners record their answers and mark the common roots in a table given OR they record each common root in the area of each pair of intersecting ellipses on a figure given. Student recording sheets are provided for partners to show all work. An answer key is included.

This activity practices solving quadratic equations. The half of the equations are in standard form and set to zero and the other half have one term on the right side of the equation. There are also included incomplete quadratic equations. Solutions are only rational numbers. Activity Directions: Partners will each have their own set of 8 quadratic equations. They solve the first four of them by factoring and the rest – by the most appropriate method they choose. Then they search for the numbers they have found on the “balloons board” - a set of balloons given with numbers and words on them. When students find their answers written on some of the balloons, they “burst”(strike-through) it. The word written on this balloon is eliminated too. Partners continue solving still that way and at last they will have some balloons “survived” inseparably with the words written on them. They arrange all these words to make a proverb. I have designed THREE DIFFERENT VARIANTS of “balloon boards” so the groups playing different versions to find out other proverbs.(The problems are the same.) All answer keys are included. I hope your students enjoy “eliminating balloons” and searching for wisdom sayings.

This activity practices solving quadratic equations.The half of the equations are in standard form and set to zero and the other half have one term on the right side of the equation. There are also included incomplete quadratic equations. Solutions are only rational numbers. Activity Directions: Partners will each have their own set of 8 quadratic equations. They solve the first four of them by factoring and the rest – by the most appropriate method they choose. Then they search for the numbers they have found on the “balloons board” - a set of balloons given with numbers and words on them. When students find their answers written on some of the balloons, they “burst” (strike-through) them. The words written on these balloons will be eliminated too. Partners continue solving still that way and at last they will have some balloons “survived” inseparably with the words on them. They can arrange all these words remained to make a proverb. All answer keys are included. I hope your students enjoy “eliminating balloons” and searching for wisdom sayings.

This activity is designed to be used for groups of 4 members! It practices solving quadratic equations by factoring. The most of the equations have one or two terms on the right side and need to be reduced in their standard form. The leading coefficient is 1. Solutions are only integers. Activity Directions: Partners will each have their own set of 8 quadratic equations. They start solving and write down the solutions of the problems on the recording sheet provided. Then students look for the answers they have found on the “skittles board” – set of “pairs of skittles” given with numbers on them. They will find that all their solution sets are written on these pairs. Each player must cross out or mark the pairs of skittles which represent the solution sets of his equations. The group which has solved all the equations correctly and has “knocked down all the skittles” first, wins. Answer keys are included.

This product contains 40 trigonometric expressions with their detailed SOLUTIONS. The problems are separated into five groups/quizzes. EACH GROUP OF PROBLEMS REQUIRES APPLYING OF SPECIFIED IDENTITIES TO BE SOLVED as follows: • Double - Angle Identities • Half - Angle Identities • Angle – Sum and - Difference Identities • Sum Identities • Product Identities The problems have varying degrees of difficulty. The product can be divided into parts and used in a variety of ways to aid learners in reasoning and increase their ability to simplify trigonometric expressions: in class practice(teacher can show the solutions to some of the examples to assist students in completing the rest successfully) as partner activity or group activity (students can assist one another throughout simplifying the expressions) an assessment or homework Student recording sheets are provided and full solutions to the problems as well.

This is a set of two trigonometry mazes to practice proving and disproving trigonometric identities using the fundamental trigonometric identities ( Pythagorean, reciprocal, quotient identities). Students are given 24 statements. They will need to determine whether some of these statements are true or false, prove or disprove them and use their answers to navigate through the maze. Not all boxes are used in this maze to prevent students from just guessing the correct route. Recording sheets are provided for students to show all work. Answer keys and FULL SOLUTIONS to the problems are included. This maze could be used as: a way to check for understanding, a review, cooperative learning, homework, individual practice, partner activity, before a quiz on the topic, and more.

This activity practices proving and disproving trigonometric identities using • double - anlge formula • half – angle formula • angle - sum and - difference formulas • sum - to - product formulas • product - to - sum formulas The activity aims to stimulate students interest in history of math and physics as well. Students are given a set of 16 cards each with two statements written on it – one statement concerns a fact about famous mathematicians and physicists, and the other is a trigonometric identity. The statements are both true or they are both false. Thus, students are challenged to find one and the same answer to two different type questions. If they already know the answer to the text statement on a card, then they have a hint – to prove or disprove the relevant to it trigonometric identity. In case students don’t know whether the stated as a fact on the card is true, verifying the identity will help them in searching the right answer. After students prove or disprove the trigonometric identities, they sort the cards into two groups - “TRUE” and “FALSE”. Recording sheets are provided for students to show all work. Answer keys and FULL TYPED SOLUTIONS (proofs) to the problems are included. The cards could be used in class practice as a way to check for understanding, a review, cooperative learning, individual practice, partner or group activity, before a quiz on the topic, and more.

This product contains 50 trigonometric expressions with their detailed typed solutions. The problems are separated into five groups/quizzes. EACH GROUP of expressions REQUIRES APPLYING OF SPECIFIED IDENTITIES to be simplified as follows: • The fundamental Pythagorean identity • Quotient identities • Reciprocal identities • Pythagorean identities • Co-function identities The problems have varying degrees of difficulty. The product can be divided into parts and used in a variety of ways: in class practice (teacher can show the solutions to some of the examples to assist students in completing the rest successfully) as partner activity or group activity (students can assist one another throughout simplifying the expressions) an assessment or homework Student recording sheets are provided and full solutions to the problems as well.

In this activity, students will practice simplifying 24 trigonometric expressions using fundamental identities such as reciprocal identities, quotient identities, Pythagorean identities and cofunction identities. The problems are carefully thought out so that 23 of them have one and the same exact value and ONE HAS NOT THE SAME VALUE AS THE OTHERS. Students simplify and evaluate each of the expressions given. They must find out the different expression. (The problems have varying degrees of difficulty.) The product is designed to be used in class practice, as partner activity, group activity, an assessment or homework. Student recording sheets are provided. SOLUTIONS TO ALL THE PROBLEMS are included.

The activity contains more challenging problems on different types of trigonometric equations. Students will practice solving trigonometric equations by factoring, the quadratic formula and the square root method. The equations require the use of fundamental trigonometric identities double - and half- angle, angle - sum and - difference, sum - to- product and product - to -sum identities There are four sections, each containing four different equations. Students find the general solutions to each of the equations in a section. Then they must determine which of the equations have a given general solution as their own solution. Thus students find groups of trigonometric equations having a common general solution. This quiz can be used in class practice or as a group activity (groups of 4). It can be used for enrichment/extra practice, review, as an assessment or homework as well. All answer keys are included.

Students will practice solving trigonometric equations by the square root method with this activity. This includes 12 cards and 12 problems that require students to be skillful at solving basic trigonometric equations. The focus is on finding the primary solutions of a trigonometric equation on the interval (0, 2π]. Activity Directions: Partners work cooperatively to match each equation with its private solutions written on a card. They are instructed to record the equation in the middle of a card presenting its solutions. Then pupils should find cards with equivalent equations. They use the cards to determine three fours of equations having the same private solutions on the interval given and sort the cards into groups. A recording sheet is provided for students to give accountability to the teacher. All answer keys are included.

This resource includes multiple-angle trigonometric equations for your students to solve on the interval [0, 2π). There are four sections, each containing three different equations. The equations included in each section involve respectively double, triple, half and quadruple angle. No identities are required other than the reciprocals of the six basic trigonometric functions. Students will only need to use algebraic manipulations to isolate the trigonometric function on one side of the equation. Activity Directions: There are given three equations and a set of radians in each section. Students start solving the equations on the specified interval. Then they must determine which one of the equations has the given set as its own private solutions. The possible answers are – one, two or not even one of the equations has the given set as its own private solutions. This activity can be used as individual practice or in a small group. It can be used as an assessment as well. An answer key is included.

Students will practice solving trigonometric equations by factoring with this quiz game. This includes multiple - choice questions with nine equations that require the use of Pythagorean, reciprocal, quotient and double angle identities. The focus is on finding both the general and specific solution of a trigonometric equation. Problems range in difficulty. At first, students solve all the problems. (After that they will need their answers to find out the configuration of a constellation). Students are also given a figure with shapes of a circle, called “stars”. Nine of them form the configuration of a constellation. These nine “stars” are labeled with the correct answers of students’ questions. Students connect the “stars” of the constellation with straight lines in a specified sequence. At last, they try to identify the constellation. Recording sheets are included for students to show work. An answer key is included as well. This activity can be used as individual practice or in a small group of three. It could also be used as an assessment .

This activity practices solving trigonometric equations of quadratic type. It includes multiple - choice with twelve equations and a brief story about the history of trigonometry to be completed. The equations require the use of Pythagorean, reciprocal, quotient, double angle identities and the quadratic formula. Problems range in difficulty. Activity Directions: Students must solve all the problems and find specific solutions. The answers they get will give them pieces of a brief story about history of trigonometry. Studying the history of trigonometry will throw light on the nature of the discipline. It will help students gain a deeper understanding of the trigonometry they have already studied by seeing how it was developed over time. Recording sheets are provided for students to show all work. An answer key is included. This activity can be used as individual practice, as a partner activity (each partner will get a sheet that has only six equations to solve) or in small groups of 3. It could also be used as an assessment.

This activity practices solving basic trigonometric equations. Students must find their primary solutions in the specific interval (0 ; 2π] and give answers in radian form. The process of solving involves only the use of the reciprocal identities and algebraic manipulation (such as collecting like terms) to isolate the trigonometric function on one side of the equation. Partners will each have their own set of fourteen equations. All the equations are well thought so the solutions of each equation on the specified interval are only two. The amusing part of this activity is creating compound words corresponding to each solution set of the trigonometric equations given. Partner A’ s equations are equivalent to partner B’ s equations, so the compound words made by one partner will be the same as the words made by the other partner. Thus, partners will be satisfied to know that they both have worked correctly and will be encouraged to collaborate. Activity Directions: Partners start solving individually their own problems. Once they have found the solution set of each equation, they are given two tables to use. There is a word corresponding to each radian written in table 1 . Using this table, students find which two words correspond to each solution set of their equations and make compound words. They record the solution set of each trigonometric equation and write down the compound word corresponding to it in table 2 . Students show detailed solutions on student recording sheets specially designed for this activity or they can solve the problems on a separate sheet of notebook paper. All answer keys are included.