Match-up: Solving equations

Sample Student Workbook Intermediate Algebra: Puzzles for Practice

Written by Maria H. Andersen Muskegon Community College

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Prepared by Ann Ostberg

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Grace University

Table of Contents: Intermediate Algebra Puzzles for Practice

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RNUM: Real Numbers Match Up on Fractions……………………………………………………….. Signed Numbers Magic Puzzles……………………………………………. ALG: Algebraic Expressions Follow the Multiplication Road………………………………………………. Match Up on Like Terms and Distribution………………………………….. EQN: Solving Linear Equations and Inequalities Stepping Stones..............................................……………………….……… Tic-Tac-Toe with Inequalities………………………………………………… ABS: Absolute Value Equations and Inequalities Matching Up the Different Cases…………………....……………….……… LINE: Lines and More Match Up on Slopes.…………………..………………………………………. Tic-Tac-Toe on Inequality Solutions ………………………………………… SYS1: Solving Systems Following the Clues Back to the System of Equations.……………………. Tic-Tac-Toe on Inequalities…………………………………………………... SYS2: More on Solving Systems Tic-Tac-Toe on Row Echelon Form……..…………………………………... Rowing to Freedom……………………………………………………………. EXP: Exponent Rules Match Up on Basic Exponent Rules……..………………………………….. Escape the Matrix with Ten Power..…………………………………………. POLY: Simplifying Polynomials Caught in the Net......………………………………………………………….. Match Up on Polynomial Division…………………………………………… FACT: Factoring and More The First Factoring Matchup…………..……..……………………….……… Escape the Matrix by Solving Quadratic Equations……………….……… RAT: Rational Expressions and Equations Tic-Tac-Toe on Complex Fraction Pieces………………………………….. Match Up on Simple Rational Equations…………………………………… RAD: Radical Expressions and Equations Escape the Rational Exponent Matrix..………………..……………………. Sail Into the Pythagorean Sunset…………………………………………… QUAD: Quadratics Square Isolation Tic-Tac-Toe..……………………………………………….. Match Up on the Discriminant……………………………………………….. EXPF: Exponential Functions Exponential Workout……………………..…….……………………….……. LOG: Logarithms and More Paint by Equivalent Equations………………………….…………………… Escape the Logjam…………………………………………………….……… CNC: Conics Name that Conic!…………..…………………………….………………….... SEQ: Sequences and More Paint by Factorials…………………………………………………………….

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Student Activity Match Up on Fractions Match-up: Match each of the expressions in the squares of the table below with its simplified value at the top. If the solution is not found among the choices A through D, then choose E (none of these).

3 4

B

C

7 8

D 0

E None of these

7 4 ÷ 6 3

7 ÷0 8

15 −1 8

⎛1⎞ 6⎜ ⎟ ⎝6⎠

2 8 ÷ 3 9

1 3 + 2 8

1 8 + 5 10

1 2 + 2 2

1 5 2 − 8 4

0÷

3 4

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⎛ 3 ⎞⎛ 1 ⎞ ⎜ ⎟⎜ ⎟ ⎝ 2 ⎠⎝ 2 ⎠

19 5 − 12 6

3 ( 0) 4

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A 1

1 1 ÷ 3 3

I thought we shared a common denominator, but he was only a fraction of the person I thought he was. 3 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 2012.

Student Activity Signed Numbers Magic Puzzles Directions: In these “magic” puzzles, each row and column adds to be the same “magic” number. Fill in the missing squares in each puzzle so that the rows and columns each add up to be the given magic number.

Magic Puzzle #1 −2

Magic Puzzle #2

8

4

−9

−5 8

4

Magic Number = 5

−6

Magic Number = 0


Magic Puzzle #3 2 12

2 14 −2 12

1 4

Magic Number =

−2 8

9 −9 −4

−7 4 −5

−6 Magic Number = 1

Magic Puzzle #5

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Magic Puzzle #4

1 2

−8

−3

8

−11 −2

7 2

6 −7

Magic Number = − 2

4 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 2012.

Student Activity Follow the Multiplication Road Match-up: Find your way from start to finish along the multiplication road by shading in matching pairs of algebraic expressions. The first pair has been shaded for you!

START

12a

2 ( 3x ) 3

1 ( 2a ) 12

6x

( 0.8 x )( −2 )

1.6x

( 5t )( −4 )

12a

−20t

( −5t )( −4 )

5 ( −2x )

−10x

4 (4x) 3

x 3

4x ( 4) 3

z 5

2x

− x ( −9 )

−9x

⎛2z ⎞ 5⎜ ⎟ ⎝ 5 ⎠

9x

9− x

⎛5z ⎞ 5⎜ ⎟ ⎝ 2 ⎠

4x2 5x2


7a

4 x2 5

4 2 (x ) 5

8x

5z

−3 ( −4a )

−7a

4 ( 4x )

4x 2

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3 ( 4a )

−9t

2 (12t 2 ) 3

9t

3 2 (8 t ) 4

6t 2

1 2 x 7

2

( )

x2 7 x2

x2 7

FINISH


Student Activity Match Up on Like Terms and Distribution Match-up: Match each of the expressions in the squares of the lower table with an equivalent expression from the top. If the solution is not found among the choices A through D, then choose E (none of these). A 4 x + 16 − 12 y

B 5 + 4x + 6 y

C x+ y−z

D 3x + 3 y + 3z

E None of these

5 + 2x + 6 y + 2x

3y + 3( x + z )

2 (8 + 2 x − 6 y )

( x − z) + y

4 ( x − 3 y + 4)

4 ( x + 3 y ) + 16

6 y + 5 + 4x

4 ( x + 4 ) − 12 y

2 ( 2x + 8 − 6 y )

(5 + 6 y ) + 4x

1 ( −3z + 3 y + 3x ) 3

2 ( 2 x + 8) + 6 y

5 x + 3 y + 3z − 2 x

2y − ( z + y) + x

3x + 3 ( z + y )

6 y + 5 + 4x

4 x + 12 y − 16

Please! We realize you are all in the same Parentheses! Hang on and you will each get one!

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5 + 2 (3 y + 2x )


3( x + y ) + z

6x + 6 y − 3( x + y − z )

x − ( z − y)

( z + y) − z

4 x − (12 y − 16 )


( 4 x + 16 ) − 12 y

Student Activity Stepping Stones Directions: Shade pairs of equivalent expressions to create a path of stepping stones from Start to Finish.

5

⎛ 3x ⎞ 8⎜ ⎟ ⎝ 2 ⎠

12 x

⎛ z⎞ 6⎜ − ⎟ ⎝ 3⎠

3z

8x

15 x

−12 x

−3z

−2z

2z

⎛ 3x ⎞ 4⎜ ⎟ ⎝ 2 ⎠

−15 x

⎛ 5⎞ 24x ⎜ − ⎟ ⎝ 8⎠

12

⎛4⎞ 9⎜ ⎟ ⎝3⎠

36

6x

3⎛1⎞ ⎜ ⎟ 2⎝ x⎠

⎛ 3x ⎞ 5⎜ ⎟ ⎝ 10 ⎠

3x 2

x 2

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Start ⎛1⎞ 10 ⎜ ⎟ ⎝2⎠

⎛1⎞ 3⎜ ⎟ ⎝4⎠

1 12

⎛ 1⎞ x⎜− ⎟ ⎝ 7⎠

⎛ 2⎞ −6u ⎜ − ⎟ ⎝ 3⎠

4u

⎛2⎞ 4⎜ ⎟ ⎝u⎠

x 7

2x ⎛ 3 ⎞ ⎜ ⎟ 3 ⎝2⎠

x

Finish

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−4u

9u


Student Activity Tic-Tac-Toe with Inequalities Tic-tac-toe #1: If the inequality in the square is true, then put an O on the square. If it is false, then put an X on the square. 8>8

−6 > −2

2 − 3 < −1

1 1 < 2 3

7≤7

a≥a

0 < −4

−3 >1

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−5 < −1

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Tic-tac-toe #2: If the number in the square is a solution to the inequality, then put an O on the square. If it is false, then put an X on the square. x−2 4− x

−x < 4

2 x + 3 < 3x

−5

−3

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−2 x < 4


Student Activity Matching Up the Different Cases Directions: Begin by isolating the absolute value in each of the equations and inequalities below. Then categorize the problem as one of the four cases or a special case. The first one has been done for you. Let k be a positive constant and let X , X 1 , and X 2 be mathematical expressions. Case 2:

X =k

X1 = X 2

x −3 < 2 CASE 3

x + 4 = 2x − 2

−2 4 y < 10

5− x+ 4 = 2

Case 4: X >k

X ≤k

X ≥k

Special Case: If the constant is negative or zero.

x−3 −4 ≥ 2

2a − 3 + 5 > 3

x −2= 4 3

1 = 2t − 4 + 4

5 − 2x < 2

4 x +3 −3 ≤ 2

3x − 4 ≤ −2 −6

1> 3−b −6

2x = x + 3

6−2 x+4 ≤ 0

x−4 +5 =5

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2 x−3 < 4

Case 3: X y+4

x≤5

⎛1 1⎞ ⎜ , ⎟ ⎝ 2 3⎠

( 4, 0 )

( 4,9 )


x+ y