Equation Arena Game Slides
Math Tournament Edition
Whole-Class Team Battle
Algebra Showdown • 3 Fast-Paced Rounds + Boss Duel
EQUATION ARENA
Collaborate with your team, conquer simplifying & multi-step equations, and claim the championship trophy!
Team 1 The Solvers
Team 2 The Isolators
Team 3 The Variables
Team 4 The Constants
Arena Rules & Gameplay
Setup: Whiteboard / Scratch Paper
1
Team Huddle
When a problem appears, all teammates work together. Everyone must agree on the final answer and show steps on their board!
Tip: Check negative signs & distribution!
2
Synchronized Reveal
On the teacher's call "3-2-1 BOARDS UP!", each team captain holds up their team's final answer.
No changing answers after boards are raised!
3
Score & Climb
Correct answers earn round points. Bonus points for crystal-clear work and simplified fraction/decimal forms!
Round 1: 100 pts • Round 2: 200 pts • Round 3: 300 pts
Teacher Note: Keep running team scores on the classroom whiteboard between rounds!
Stage 1 of 3
100 Points Per Question
Warm-Up Round
ROUND 1: EXPRESSION EXTRACTION
Target skill: Apply the distributive property, distribute negative signs cleanly, and combine like terms.
Challenge 1.1
Integer Distributive Property
Challenge 1.2
Fractions & Like Terms
Challenge 1.3
Decimals & Multiple Variables
R1 • Q1
Simplifying Expressions
100 PTS
Simplify completely by expanding and combining all like terms:
\( 4(2x - 3) - 3(x - 5) \)
Watch out for the subtraction sign in front of the second set of parentheses!
Team Collaboration: 60 Seconds Write your final simplified expression clearly!
SOLUTION
Round 1 • Question 1 Breakdown
ANSWER KEY
Step 1: Distribute both coefficients
\( 4 \cdot 2x - 4 \cdot 3 = 8x - 12 \)
\( -3 \cdot x - (-3) \cdot 5 = -3x + 15 \)
Step 2: Group and combine like terms
\( (8x - 3x) + (-12 + 15) \)
Official Simplified Form
\( 5x + 3 \)
+100 Points for all teams with \(5x + 3\) !
Teams: Did everyone distribute the negative to make +15?
R1 • Q2
Fractions In Expressions
100 PTS
Distribute the fraction and simplify completely:
\( \frac{3}{4}(8x - 12) + 5x - 7 \)
Remember: Multiply by numerator, then divide by denominator!
Team Collaboration: 60 Seconds Show simplified terms before combining!
SOLUTION
Round 1 • Question 2 Breakdown
ANSWER KEY
Step 1: Distribute \( \frac{3}{4} \)
\( \frac{3}{4} \cdot 8x = 6x \)
\( \frac{3}{4} \cdot (-12) = -9 \)
Step 2: Bring down outside terms
\( 6x - 9 + 5x - 7 \)
Group terms: \( (6x + 5x) + (-9 - 7) \)
Official Simplified Form
\( 11x - 16 \)
+100 Points for \(11x - 16\)
Double check: \(-9 - 7 = -16\). Great job simplifying fractions!
R1 • Q3
Decimals In Expressions
100 PTS
Distribute the decimal coefficient and simplify completely:
\( 2.5(4x + 6) - 1.2x + 8.4 \)
Compute mental math: \(2.5 \cdot 4 = 10\) and \(2.5 \cdot 6 = 15\) !
Team Collaboration: 60 Seconds Line up decimal places when combining constants!
SOLUTION
Round 1 • Question 3 Breakdown
ANSWER KEY
Step 1: Distribute \(2.5\)
\( 2.5 \cdot 4x = 10x \)
\( 2.5 \cdot 6 = 15 \)
Step 2: Combine terms
\( 10x - 1.2x = 8.8x \)
\( 15 + 8.4 = 23.4 \)
Official Simplified Form
\( 8.8x + 23.4 \)
+100 Points for \(8.8x + 23.4\)
Round 1 Complete! Teacher: update scores on the board!
Arena Leaderboard • End of Round 1
Max Possible: 300 PTS
Team 1
The Solvers
[ Score ]
Team 2
The Isolators
[ Score ]
Team 3
The Variables
[ Score ]
Team 4
The Constants
[ Score ]
Level Up Alert: Points DOUBLE in Round 2! Each correct solution is worth 200 PTS!
Stage 2 of 3
200 Points Per Question
Level 2: Target Acquisition
ROUND 2: VARIABLES ON ONE SIDE
Target skill: Solve two-step and multi-step equations where the variable appears on only one side.
Challenge 2.1
Multi-Step with Distributive
Challenge 2.2
Equations with Fractions
Challenge 2.3
Equations with Decimals
R2 • Q1
Solving One-Sided Equations
200 PTS
Solve for the unknown variable \(x\):
\( 3(2x - 7) + 5 = 20 \)
Strategy: Distribute first, combine constants on the left side, then isolate \(x\)!
Team Collaboration: 75 Seconds Write \(x = \_\_\) clearly on your whiteboard!
SOLUTION
Round 2 • Question 1 Breakdown
ANSWER KEY
Step 1: Distribute \(3\)
\( 6x - 21 + 5 = 20 \)
Step 2: Combine constants
\( 6x - 16 = 20 \)
Step 3: Add 16 & divide by 6
\( 6x = 36 \implies x = 6 \)
Official Solution
\( x = 6 \)
+200 Points for \(x = 6\)
Quick Check: \(3(2(6) - 7) + 5 = 3(12 - 7) + 5 = 3(5) + 5 = 20 \checkmark\)
R2 • Q2
Equations With Fractions
200 PTS
Solve for \(x\) in this fractional equation:
\( \frac{2}{5}x - 7 = 9 \)
Hint: Add 7 first, then multiply by the reciprocal \(\frac{5}{2}\)!
Team Collaboration: 75 Seconds Simplify your final answer completely!
SOLUTION
Round 2 • Question 2 Breakdown
ANSWER KEY
Step 1: Isolate the fraction term
\( \frac{2}{5}x - 7 + 7 = 9 + 7 \)
\( \frac{2}{5}x = 16 \)
Step 2: Multiply by reciprocal \( \frac{5}{2} \)
\( x = 16 \cdot \frac{5}{2} = 8 \cdot 5 = 40 \)
Official Solution
\( x = 40 \)
+200 Points for \(x = 40\)
Alternative method: Multiply every term by 5 first to get \(2x - 35 = 45 \implies 2x = 80 \implies x = 40\)!
R2 • Q3
Equations With Decimals
200 PTS
Solve for \(x\) with decimal constants and coefficients:
\( 0.4x + 3.8 = 9.4 \)
Pro Move: Multiply every term by 10 to clear all decimals!
Team Collaboration: 75 Seconds Write down your final value of \(x\)!
SOLUTION
Round 2 • Question 3 Breakdown
ANSWER KEY
Method: Clear decimals by \(\times 10\)
\( 4x + 38 = 94 \)
Step 2: Subtract 38 then divide by 4
\( 4x = 94 - 38 = 56 \)
\( x = \frac{56}{4} = 14 \)
Official Solution
\( x = 14 \)
+200 Points for \(x = 14\)
Decimal check: \(0.4(14) + 3.8 = 5.6 + 3.8 = 9.4 \checkmark\)
Halftime Standings • Round 2 Complete
Max Possible: 900 PTS
Team 1
The Solvers
[ Score ]
Team 2
The Isolators
[ Score ]
Team 3
The Variables
[ Score ]
Team 4
The Constants
[ Score ]
Final Round Ahead: Variables on BOTH sides! Questions are worth 300 PTS each!
Stage 3 of 3
300 Points Per Question
Level 3: The Crossfire
ROUND 3: VARIABLES ON BOTH SIDES
Target skill: Move variables to one side, constants to the other, and master fractions & decimals under pressure.
Challenge 3.1
Integers on Both Sides
Challenge 3.2
Fractions on Both Sides
Challenge 3.3
Decimals & Distribution
R3 • Q1
Variables on Both Sides
300 PTS
Solve the equation for \(x\):
\( 7x - 15 = 3x + 21 \)
Strategy: Subtract the smaller variable term (\(3x\)) from both sides first!
Team Collaboration: 90 Seconds Show both subtraction and addition balance steps!
SOLUTION
Round 3 • Question 1 Breakdown
ANSWER KEY
Step 1: Collect variable terms on one side
\( 7x - 3x - 15 = 21 \)
\( 4x - 15 = 21 \)
Step 2: Collect constants & isolate \(x\)
\( 4x = 21 + 15 = 36 \)
\( x = \frac{36}{4} = 9 \)
Official Solution
\( x = 9 \)
+300 Points for \(x = 9\)
Check: \(7(9) - 15 = 63 - 15 = 48\) and \(3(9) + 21 = 27 + 21 = 48 \checkmark\)
R3 • Q2
Fractions on Both Sides
300 PTS
Solve the equation with fractional coefficients:
\( \frac{3}{4}x - 5 = \frac{1}{2}x + 2 \)
Pro Move: Clear denominators by multiplying the ENTIRE equation by 4!
Team Collaboration: 90 Seconds Don't forget to multiply the constants by 4 too!
SOLUTION
Round 3 • Question 2 Breakdown
ANSWER KEY
Step 1: Multiply all 4 terms by \(4\)
\( 4\left(\frac{3}{4}x\right) - 4(5) = 4\left(\frac{1}{2}x\right) + 4(2) \)
\( 3x - 20 = 2x + 8 \)
Step 2: Subtract \(2x\) and add 20
\( 3x - 2x = 8 + 20 \)
\( x = 28 \)
Official Solution
\( x = 28 \)
+300 Points for \(x = 28\)
Check: \(\frac{3}{4}(28) - 5 = 21 - 5 = 16\); \(\frac{1}{2}(28) + 2 = 14 + 2 = 16 \checkmark\)
R3 • Q3
Decimals & Distribution Both Sides
300 PTS
Solve the decimal equation for \(x\):
\( 1.2(x + 5) = 0.4x + 18 \)
Distribute \(1.2\) on the left first: \(1.2 \cdot x + 1.2 \cdot 5\) !
Team Collaboration: 90 Seconds Show your work carefully before raising boards!
SOLUTION
Round 3 • Question 3 Breakdown
ANSWER KEY
Step 1: Distribute \(1.2\)
\( 1.2x + 6 = 0.4x + 18 \)
Step 2: Subtract \(0.4x\) and subtract \(6\)
\( 1.2x - 0.4x = 18 - 6 \)
\( 0.8x = 12 \implies x = \frac{12}{0.8} = 15 \)
Official Solution
\( x = 15 \)
+300 Points for \(x = 15\)
Check: \(1.2(15 + 5) = 1.2(20) = 24\); \(0.4(15) + 18 = 6 + 18 = 24 \checkmark\)
CHAMPIONSHIP DUEL
The Arena Boss: Grand Synthesis
500 PTS OR TEAM WAGER
Distributive Property • Fractions • Variables Both Sides
\( \frac{1}{3}(6x - 9) + 4x = 2(4x - 5) - 3 \)
Left Side: Distribute \(\frac{1}{3}\) & combine like terms!
Right Side: Distribute \(2\) & combine constants!
Boss Timer: 2 Minutes Teams may wager from 100 to 500 of their earned points!
BOSS SOLUTION
Arena Boss Grand Solution
CHAMPIONSHIP REVEAL
Step 1: Simplify Left Side
\( 2x - 3 + 4x = 6x - 3 \)
Step 2: Simplify Right Side
\( 8x - 10 - 3 = 8x - 13 \)
Step 3: Solve \(6x - 3 = 8x - 13\)
\( -3 + 13 = 8x - 6x \implies 10 = 2x \implies x = 5 \)
Winning Solution
\( x = 5 \)
Full Wager / +500 PTS Awarded!
Check: Left = \(\frac{1}{3}(21) + 20 = 7 + 20 = 27\); Right = \(2(15) - 3 = 30 - 3 = 27 \checkmark\)
Victory Podium & Key Takeaways
Game Completed!
2nd
Runner-Up Team
Mastered negative signs & distributed like pros!
1st Place
Arena Champions
Ultimate equation solvers of the day!
3rd
Bronze Medalist
Cleared fractions and decimals with precision!
1. Distribute clean & watch negative signs
2. Clear fractions with LCD / decimals by 10
3. Keep both sides balanced
