Exponent Showdown

Result: + / − ________

New Bank: ________ pts

ROUND 7 The Boss Battle • Dual Power of Product

Final Wager (Up to All):

Boss Problem Revealed: ____________________________________________________

Multi-Step Show Your Work:

Final Simplified Monomial:

Boss Result: + / − ________

Final Bank: ________ pts

Tie-Breaker Quest: Teacher Reveal • Error Analysis Screen Problem: ____________________

What error was made in the work?

What is the correct simplified form?

Post-Game Scorecard & Strategy Reflection

Accuracy: ___ / 7 Final Bankroll: _________ pts

1. My Wagering Style:

[   ] Conservative (small, safe bets)

[   ] Aggressive (high-stakes wagers)

[   ] Calculated (adjusted by clue)

2. Easiest Exponent Law:

[   ] Product Rule (\(x^a \cdot x^b\))

[   ] Quotient Rule (\(\frac{x^a}{x^b}\))

[   ] Power Rule (\((x^a)^b\))

3. Key Takeaway / Trap Avoided:

Halftime Audit: Pause for 2 minutes. Have students cross-check their current bankroll arithmetic with a neighbor.

Rounds 1–4 Check

Championship Facilitation • Advanced Rounds & Debrief

Order of Operations • Dual Power of Product • Differentiation

Page 2 of 2

Round-by-Round Facilitator Breakdown: Rounds 5 – 7

ROUND 5 P.O.P. & Product

\( (3x^4)^2 \cdot (4x^3) \)

\(36x^{11}\)

Step 1: Expand power: \((3x^4)^2 = 9x^8\).

Step 2: Multiply: \(9x^8 \cdot 4x^3 = (9 \times 4)x^{8+3} = 36x^{11}\).

Trap Alert: Multiplying \(3 \times 4 = 12\) first gives \(144x^{11}\)!

ROUND 6 P.O.P. & Product

\( (2w^3)^4 \cdot (3w^5) \)

\(48w^{17}\)

Step 1: Power first: \(2^4 w^{12} = 16w^{12}\).

Step 2: Multiply: \(16w^{12} \cdot 3w^5 = 48w^{17}\).

Reinforces R5 with a higher outer power (\(2^4 = 16\)).

ROUND 7 Dual P.O.P. Boss

\( (2x^2 y^3)^3 \cdot (3x^4 y)^2 \)

\(72x^{14} y^{11}\)

Step 1 (First P.O.P.): \((2x^2y^3)^3 = 8x^6 y^9\).

Step 2 (Second P.O.P.): \((3x^4y)^2 = 9x^8 y^2\).

Step 3 (Multiply as One): \((8 \cdot 9) x^{6+8} y^{9+2} = 72x^{14} y^{11}\).

TIEBREAKER

\((4x^3)^2 = 8x^5\) (Mistake?)

\(16x^6\)

Two Errors Made: Multiplied coefficient \(4 \times 2 = 8\) (should be \(4^2 = 16\)) and added exponents \(3+2=5\) (should be \(3 \times 2 = 6\)).

Support & Scaffolding (Struggling Learners)

• Law Anchor Strip: Have students keep Slide 3's rule cheat sheet visible at their desks.
• Color Code: Highlight numerical coefficients in yellow and exponents in pink.
• Conservative Betting Tip: Remind risk-averse students that 10-15 pt bets win the game if accuracy is high!

Extensions & Early Finishers (Advanced)

• Quotient Extension: Ask students how Round 7 would change if divided by \(8x^4 y^5\).
• Create-a-Round: Fast finishers draft their own Round 8 Boss Problem with an answer key and trap warning.

Rapid Teacher Reference Matrix Scan student recording sheets at a glance

R1 \(20x^9\)

R2 \(3y^6\)

R3-A \(m^{20}\)

R3-B \(64\) / \(2^6\)

R4 \(27a^{12}b^6\)

R5 \(36x^{11}\)

R6 \(48w^{17}\)

Final Boss (R7): \(72x^{14} y^{11}\)

Tiebreaker: \(16x^6\) (applied \(4 \times 2\) and \(3+2\))

Celebrate Top Bankrolls & Precision Awards!