Math Playbook Review Sheet v2
Math Playbook
IA3 Championship Review
Player:
Date:
"Success is where preparation and opportunity meet." Follow the Coach's Play for guidance, then execute the Player's Play on your own!
ZONE 1: Rational Numbers
Coach #1
Evaluate the expression:
\( -2\frac{2}{3} - 1.25 + \frac{5}{6} \)
Modeling Space
Player #1
Evaluate the expression:
\( -1\frac{3}{4} + 0.5 - \frac{1}{8} \)
A) \( -1\frac{3}{8} \)
B) \( -1\frac{1}{8} \)
C) \( -1\frac{5}{8} \)
D) \( -2\frac{3}{8} \)
ZONE 2: Expressions
Coach #2
Simplify the following expression:
\( \frac{2}{5}(15x - 30y) + 10x \)
Player #2
Simplify the following expression:
\( \frac{3}{4}(12x - 8y) + 5x \)
A) \( 14x - 6y \)
B) \( 14x - 8y \)
C) \( 9x - 6y \)
D) \( 17x - 6y \)
ZONE 3: Proportions
Coach #3
What is the constant of proportionality (\(k\)) shown in the relationship (\(x, y\)): (2, 18), (5, 45)?
\( k = \) ____________
Player #3
What is the constant of proportionality (\(k\)) shown in the relationship (\(x, y\)): (2, $3.50), (4, $7.00)?
A) 1.75
B) 0.57
C) 3.50
D) 2.00
ZONE 4: Equations
Coach #4
Case Study:
Becky spent $97. She bought 3 gourmet pies for $22 each and 5 pineapples for \(x\) each. Solve for the cost of each pineapple.
Final Price: $____________
Player #4
The Play:
Daniela rented a snowboard for $35, then took lessons that cost $7 per hour. If her total cost to rent and take lessons was $73.50, how many hours of lessons did she take?
Show Your Work
Hours: ____________
ZONE 5: Percents
Coach #5
A $450 camera has a 40% discount. After the sale, the price increases by 40% of the NEW sale price. What is the final price?
Final Cost: $____________
Player #5
Appliances are on sale for 30% off the $500 price. Isaiah has a coupon for an 18% discount on the sale price. How much will he pay? Show work.
Calculations
Final Amount: $____________
ZONE 6: Circles
Coach #6
A circle has a diameter of 26 units. What is the area of the circle to the nearest hundredth of a square unit?
A = π r²
Area: ____________
Player #6
A circular dartboard requires approximately 78.5 square inches of fabric to cover it. What is the best estimate for the radius?
A) 5 in
B) 10 in
C) 12.5 in
D) 25 in
ZONE 7: Inequalities
Coach #7
"Ms. Hernandez has $100 to spend. Parking costs $7. Admission is $15.50 per person. Write an inequality for the maximum number of people (\(p\))."
Inequality Setup: ________________
Player #7
Jake has at most $40 to spend. He buys one $10 ticket and some snacks for $5 each. Which inequality represents the snacks (\(s\))?
A) \( 5s + 10 \le 40 \)
B) \( 5s + 10 \ge 40 \)
C) \( 10s + 5 \le 40 \)
D) \( 5s + 10 < 40 \)
Pregame Strategy Notes
IA3 Quick Formulas
- • \( y = kx \) (Proportions)
- • \( A = \pi r^2 \) (Circle Area)
- • \( C = 2\pi r \) (Circumference)
- • \( \% \text{ Change} = \frac{\text{diff}}{\text{original}} \times 100 \)
- • \( \text{Part} = \text{Percent} \times \text{Whole} \)
FINAL SCRIMMAGE: Skills Integration Assessment
The Championship Equipment Order
Review the equipment ordering details below and answer each part of the multi-part question. Show all your work for each step.
Jersey Order Details
- Regular Price: $600.00
- Team Discount: 25% OFF
- Sales Tax: 8.5% (post-discount)
Stopwatch Details
- Item: Pro Stopwatches
- Unit Price: $22.00 each
- Total Budget: $1,200
Coach Hernandez orders jerseys for the track team. The regular price for the jersey order is $600.00. The supplier offers a 25% discount on the regular price. After the discount is applied, an 8.5% sales tax is added to the sale price. What is the total cost of the jersey order? Show your work.
Total Cost: $________________
The track team has a total budget of $1,200. After purchasing the jerseys, Coach Hernandez uses the remaining money to buy stopwatches that cost $22.00 each. Write and solve an equation that can be used to determine the maximum number of stopwatches Coach Hernandez can buy. Show your work.
Stopwatches: ________________
Next week, the price of each stopwatch is expected to increase by 15%. Based on the number of stopwatches purchased in Part B, how much additional money will Coach Hernandez need to purchase the same number of stopwatches at the new price? Show your work.
Additional Funds: $________________
Math Playbook Answer Key
Playbook Key
Teacher Answer Key & Distractor Analysis
IA3 Grade 7 Math
Zone 1: Rational Numbers
#1 (C): \( -3\frac{1}{12} \).
#2 (P): A) \( -1\frac{3}{8} \). Correct decimal calc: \( -1.75 + 0.5 - 0.125 = -1.375 \).
Zone 2: Expressions
#3 (C): \( 16x - 12y \).
#4 (P): A) \( 14x - 6y \). Step: \( \frac{3}{4}(12x) = 9x \), \( \frac{3}{4}(-8y) = -6y \), then \( 9x + 5x = 14x \).
Zone 3: Proportions
#5 (C): \( k = 9 \).
#6 (P): A) 1.75. Distractor B is \(x/y\).
Zone 4: Equations
#7 (C): \( x = \$6.20 \). (Equation: \( 5x + 66 = 97 \)).
#8 (P): 5.5 hours. (Equation: \( 7h + 35 = 73.50 \)).
Zone 5: Percents
#9 (C): $378.
#10 (P): $287. (\( 500 \cdot 0.7 \cdot 0.82 \)).
Zone 6: Circles
#11 (C): 530.93.
#12 (P): A) 5 in. Area \( 78.5 \rightarrow r^2 = 25 \rightarrow r = 5 \).
Zone 7: Inequalities
#13 (C): \( 15.50p + 7 \le 100 \).
#14 (P): A) \( 5s + 10 \le 40 \).
Championship Equipment Order: Official Solution
Part A (NYS Style Percents)
1. Discount: \( 600 \times 0.25 = 150 \). Sale Price: \( 600 - 150 = 450 \).
2. Sales Tax: \( 450 \times 1.085 = \$488.25 \).
Part B (NYS Style Equations)
1. Remaining Budget: \( 1200 - 488.25 = 711.75 \).
2. Equation: \( 22s = 711.75 \) or \( 22s + 488.25 = 1200 \).
3. Solve: \( s = 32.35 \dots \rightarrow \) 32 stopwatches (round down for items).
Part C (NYS Style Percent Change)
1. New Price: \( 22 \times 1.15 = \$25.30 \).
2. New Total for 32: \( 32 \times 25.30 = \$809.60 \).
3. Difference: \( 809.60 - 711.75 = \$97.85 \).
Final Answer: $97.85 additional funds needed.
