Constant 19 different words commonly used in solving equations. Help your students quickly master these words via two self-correcting puzzles! Complete with a thorough terminology reference section, instructions, and keys. Ideal for the start of any equations unit or for a detailed review!
Instructions for the teacher If you would like your students to be able to understand and speak the language of algebraic equations, this is the product for you! It can be used as part of any unit on solving simple algebraic equations or as a review of previously learned concepts. It works well in any pre-algebra or algebra class. Through an easy-to-use but detailed review and two different puzzles, it allows students to learn and retain 19 different algebraic equation terms in a fun and memorable way. These key vocabulary words include variable, constant, coefficient, expression, numerical expression, algebraic expression, equation, term, solution, solve, balance, inverse operation, equivalent equation, like terms, positive, negative, isolate, transform, and simplify. Use this review and these puzzles and your students will be correctly using equation terminology and ready to explore equations more fully (more products on solving equations to come soon)! To best utilize Equation Terminology Puzzles, follow the steps below: 1. Use of Equation Terminology Review. There are three methods for using this section: - If you are using the puzzles with students who know nothing of equations, go through the Terminology Review in detail, discussing the various parts of equations and reviewing how they are solved at a high level. Then move to step 2 and have the students do the puzzles in an open note type of fashion, with copies of the Terminology Review at their side as reference material. - If you are using these puzzles near the beginning of an equations unit with students who have had a little exposure to equations, simply distribute the Terminology Review along with the first puzzle, give the instructions in step 2, and then have the students do the puzzles in an open note type of fashion. - If the students are more experienced with equations, you may want to simply distribute the puzzles, allow the students to take a shot at them, and then allow them to use the Terminology Review as reference only if necessary. 2. Explain to the students how to begin work on the first puzzle. Students should be identifying the correct answer to each question from the list of answers in the box below the questions, writing this answer in the blank provided, and then placing the letter (one of the answers will actually be a hyphen) associated with that answer in the appropriate box at the bottom of the page. For instance, the answer to question 1 is Operation. The letter associated with Operation is E. The students should write the word Operation in the blank for question 1 and put an E in the box labeled 1 at the bottom of the page. 3. Set the students to work on the first puzzle, with or without the Terminology Review available as reference material. The puzzle will be self-correcting in that if they do not get the correct answers, the phrase at the bottom of the page will not make sense, so they should keep revising their answers until they get the correct phrase at the bottom. 4. Review the first puzzle solution and the associated terminology in any way that you deem appropriate. 2
Instructions for the teacher (continued) 5. Explain to the students how to begin work on the second puzzle. Students should be identifying the correct answer to each question from the list of answers on the right side of the puzzle sheet, and then placing the letter associated with that answer in the appropriate box at the bottom of the page. For instance, the correct answer for question 1 is 3x + 2 = 5. The letter associated with that answer is O, so the student should write an O in the box labeled 1 at the bottom of the page. If there is a next to the answer on the right, the student should shade that box in at the bottom of the page (it will serve as a space in the phrase that is created). 6. Set the students to work on the second puzzle. Watch what they do closely. They may confuse coefficient and constant, or make other such terminology errors, resulting in incorrect answers at the bottom. Though this puzzle is also self-correcting in that students with incorrect answers will end up with a phrase that does not make sense, they may still need guidance from you if they are far enough off track. 7. Review the second puzzle solution and the terminology used within in it in any way you deem appropriate. 8. Move on to the remainder of your equations unit. More products on solving equations and using them in word problems will be available soon! Good luck with your use of the Equation Terminology Puzzles! 3
Equation Terminology Review Before solving the puzzles we ll do a quick equation terminology review. Let s start with the key components of an algebraic expression: Key Components of an Algebraic Expression: Algebraic Expression - A collection of numbers, variables, and operators (with NO equals sign), packaged into a mathematical phrase. 4x + 3 Coefficient A number that is multiplied by the variable. Variable an unknown quantity, represented by a letter. Terms groups of coefficients, variables, and/or constants, separated by addition and subtraction signs. Constant A number that stands alone (without a variable) in an expression. Operator/Operation addition, subtraction, multiplication, division. A few other things you should know about expressions before moving on to equations: Other Things to Know About Expressions: 1. An expression with no variable in it (numbers and operators only) is called a numerical expression (examples: 4 + 3, 7 8, 8 + 6 2). 2. Positive constants and coefficients are those that are greater than zero. 3. Negative constants and coefficients are those that are less than zero. 4. A constant that is being subtracted in an expression is considered a negative constant. For example, the constant in 4x 2 is -2. 4
Equation Terminology Review (continued) There are several things we can do with an expression, one of them is to simplify the expression by combining like terms. Simplifying Expressions by Combining Like Terms: Like Terms Terms with the same variable raised to the same power. 4x + 6x + 3 10x + 3 We can also set two algebraic expressions equal to each other to form an equation, and then solve the equation step by step: Solving an Algebraic Equation: Equation Two algebraic expressions set equal to each other. Perform Inverse Operations (we want to undo the + 3, so we do so by subtracting 3) Perform Inverse Operations (we want to undo the 4, so we do so by dividing by 4) Combining like terms! When the variable is Isolated (by itself on one side of the equation), the equation has been solved! Simplified Expression (with like terms combined) NOT like terms (different variable!) 4x + 3 = 15-3 -3 4x = 12 4 4 x = 3 3x + 5 + 3 3x + 8 NOT like terms (different power!) 2x + 5y + 4 6x + 4x² + 4 Do Inverse Operations on both sides of the equation to keep it in Balance. Transform the equations into Equivalent Equations. The result (x = 3) is a Solution to the equation. The solution is any value of the variable that makes the equation true. You are now on your way. Now go forth and solve those puzzles! 5
Name: Date: Class: What do you call it when a doctor works on a patient while reciting poetry? Directions: Fill in the blanks by selecting an answer from the selections below. Insert the letter for that answer under the question number at the bottom of the page. When you have finished, you will have answered the question above. (1) A(n) can be either addition, subtraction, division, or multiplication. (2) A number that is greater than 0 is called a(n) number. (3) A(n) is a collection of numbers and mathematical operators. (4) A(n) is an unknown part of an equation, represented by a letter. (5) Two expressions set equal to each other creates a(n). (6) Each group of variables and numbers, separated by addition and subtraction signs, is called a(n) of the equation. (7) We the variable by performing inverse operations on both sides of the equation until it stands by itself. As we solve an equation, we change, or (8) it into a(n) (9). (10) A(n) is a collection of numbers, variables, and mathematical operators. (11) A large land mammal with floppy ears and a long trunk is called a(n). (12) A(n) is a number that stands by itself in an equation. We can (13) an expression by combining (14), which contain the same variable raised to the same power. (15) A(n) to an equation is any value of the variable that makes the equation true. (16) When we perform the same operation on both sides of the equation, the equation stays in. (17) The number that is multiplied by the variable is called the of the variable. P Coefficient S Simplify A Positive O Transform T Isolate E Numerical Expression D Solve E Term R Equivalent Equation I Algebraic Expression I Balance Like Terms N Constant N Elephant U Power R Variable O Equation G Negative V Solution E Operation 16 12 14 15 1 4 13 6 5 17 3 9 2 7 10 8 11 6
Name: Date: Class: What do you call it when a doctor works on a patient while reciting poetry? Directions: Fill in the blanks by selecting an answer from the selections below. Insert the letter for that answer under the question number at the bottom of the page. When you have finished, you will have answered the question above. (1) A(n) operation can be either addition, subtraction, division, or multiplication. (2) A number that is greater than 0 is called a(n) positive number. (3) A(n) numerical is a collection of numbers and mathematical operators. (4) A(n) variable is an unknown part of an equation, represented by a letter. (5) Two expressions set equal to each other creates a(n) equation. (6) Each group of variables and numbers, separated by addition and subtraction signs, is called a(n) term of the equation. (7) We isolate the variable by performing inverse operations on both sides of the equation until it stands by itself. As we solve an equation, we change, or (8) transform it into a(n) (9). (10) A(n) algebraic is a collection of numbers, variables, and mathematical operators. (11) A large land mammal with floppy ears and a long trunk is called a(n) elephant. (12) A(n) constant is a number that stands by itself in an equation. We can (13) simplify an expression by combining (14), like terms which contain the same variable raised to the same power. (15) A(n) solution to an equation is any value of the variable that makes the equation true. (16) When we perform the same operation on both sides of the equation, the equation stays in balance. (17) The number that is multiplied by the variable is called the coefficient of the variable. P Coefficient S Simplify A Positive O Transform T Isolate KEY expression expression E Numerical Expression D Solve E Term R Equivalent Equation I Algebraic Expression I Balance Like Terms N Constant N Elephant U Power equivalent equation R Variable O Equation G Negative V Solution E Operation 16 12 14 15 1 4 13 6 5 17 3 9 2 7 10 8 11 I N - V E R S E O P E R A T I O N 7
Name: Date: Class: What did the variable that had difficulty with English say when he was tardy for a party because he felt sick? Directions: Match each question to an answer on the right. Insert the letter for that answer under the question number at the bottom of the page. When you have finished, you will have answered the question above. 1. I have a coefficient of 3 and a constant of 2. 2. I have four terms on the left side of the equation. 3. The inverse operations that need to be performed to solve me are subtraction and multiplication. 4. The constant on the left side of the equation is 3. 5. I can be transformed into the equivalent equation; x = 6. 6. My solution is x = 15. 7. I have like terms that can be combined to make 5x. 8. The constant on the left side of the equation is -2. 9. I have like terms that can be combined to get 18. 10. I have two constants. One is twice as large as the other. 11. The expressions on the left and right sides both have two terms. 12. I am a one step equation that requires division as the inverse operation and is equivalent to x = 8. J 2x 3 = 5 3x 2 = 5 E 2x + 3 = 12 O 3x + 2 = 5 M 11x + 4 = 8! 7x = 42 L 12x 4 = 8 S 2x + 3x + 4 = 12 5 + 3x 2x = 16 O 11 = 2 9 + 4x + 5x E = 3 4 + 9 + 5 + x = 2x A + 7 = 12 T 7 = 2x + 3 I 9x = 72 P 48x = 6 R 42x = 7 13. The coefficient is 12. 12 8 7 1 9 13 3 11 6 2 10 4 5 8
KEY Name: Date: Class: What did the variable that had difficulty with English say when he was tardy for a party because he felt sick? Directions: Match each question to an answer on the right. Insert the letter for that answer under the question number at the bottom of the page. When you have finished, you will have answered the question above. O A E! E S M T I L 1. I have a coefficient of 3 and a constant of 2. 2. I have four terms on the left side of the equation. 3. The inverse operations that need to be performed to solve me are subtraction and multiplication. 4. The constant on the left side of the equation is 3. 5. I can be transformed into the equivalent equation; x = 6. 6. My solution is x = 15. 7. I have like terms that can be combined to make 5x. 8. The constant on the left side of the equation is -2. 9. I have like terms that can be combined to get 18. 10. I have two constants. One is twice as large as the other. 11. The expressions on the left and right sides both have two terms. 12. I am a one step equation that requires division as the inverse operation and is equivalent to x = 8. 13. The coefficient is 12. J 2x 3 = 5 3x 2 = 5 E 2x + 3 = 12 O 3x + 2 = 5 M 11x + 4 = 8! 7x = 42 L 12x 4 = 8 S 2x + 3x + 4 = 12 5 + 3x 2x = 16 O 11 = 2 9 + 4x + 5x E = 3 4 + 9 + 5 + x = 2x A + 7 = 12 T 7 = 2x + 3 I 9x = 72 P 48x = 6 R 42x = 7 12 8 7 1 9 13 3 11 6 2 I 10 4 5 S O L A T E M E! 9