Proportions Daily Drills Worksheet Empire State Math Prep
Week 1: Proportions Daily Drills
1 Daily Drills
Name: __________________________________
Monday
Unit Rates
1. A subway train travels 3/4 mile in 1/2 minute. What is the train's speed in miles per minute?
Answer: _________ mi / min
2. A recipe uses 2 1/2 cups of flour for every 1/3 cup of sugar. How many cups of flour per cup of sugar?
Answer: _________ cups
Tuesday
Proportional Tables
Does the table represent a proportional relationship? If yes, find k.
Hours (x) Earnings (y) 2 $30 5 $75 8 $120
Is it proportional?
YES
NO
Constant (k): ______________
Wednesday
Comparison
Store A sells 5 apples for $4.00. Store B sells 8 apples for $6.00. Which store has the better unit price? Show your work.
Better Store: ____________________
Thursday
Multi-step Rates
A car uses 1 1/4 gallons of gas to travel 35 miles. How many miles can the car travel on 1 gallon of gas?
Answer: _________ miles / gal
Friday
NYS Challenge
Which table shows a proportional relationship?
Table A
Table B
Explanation: ____________________________________________________________________
Proportions Power Practice Worksheet 1
Power Practice
Unit Rates & Proportions Review
Standard 7.RP.1 & 7.RP.2
Date: _________________
1 Complex Rates & Unit Prices
1. A landscaping company mows \( \frac{2}{5} \) of an acre in \( \frac{1}{4} \) hour. What is the mowing rate in acres per hour?
Show Work Area
Acres / Hour
2. A grocery store sells a \( \frac{3}{4} \)-pound bag of grapes for $2.40. What is the unit price per pound?
Show Work Area
Price / Pound
2 Identifying Proportions
3. Is the distance proportional to the time? Show unit rates to explain.
Time (hrs) Miles 1.5 18 3 36 4.5 54
Unit Rate Calculations...
Proportional? _________ Reason: __________________________________________
Big Apple Challenge
A food truck sells 45 hot dogs for $157.50 on Monday and 60 hot dogs for $210.00 on Tuesday. Are the sales proportional? What would 150 hot dogs cost?
1. Check Unit Rates
2. Calculate for 150
Proportional?
Yes
No
Total: $_______________
Proportions Answer Key Answer Key
Week 1: Proportions
Teacher Resource
Daily Drills Solutions
Monday
1. \( \frac{3/4}{1/2} = \frac{3}{4} \cdot 2 = \frac{6}{4} = \mathbf{1.5} \) miles per minute.
2. \( \frac{2.5}{1/3} = 2.5 \cdot 3 = \mathbf{7.5} \) cups per cup of sugar.
Tuesday
Proportional? Yes. All ratios \( y/x \) simplify to 15.
Constant of Proportionality (k) = 15 ($15/hr).
Wednesday
Store A: $4 / 5 = $0.80/apple. Store B: $6 / 8 = $0.75/apple.
Better Store: Store B.
Thursday
\( 35 / 1.25 = 35 / (5/4) = 35 \cdot 4/5 = 7 \cdot 4 = \mathbf{28} \) miles per gallon.
Friday (NYS Style)
Correct Table: Choice B.
Reasoning: In Choice B, \( y/x \) is constant (4/2 = 2, 8/4 = 2, 12/6 = 2). Choice A fails at (3, 12) because 12/3 = 4 while others are 5.
Power Practice Solutions
1. Landscaping Rate
\( \frac{2/5 \text{ acre}}{1/4 \text{ hour}} = \frac{2}{5} \cdot 4 = \frac{8}{5} = \mathbf{1.6} \) acres per hour.
2. Unit Price Grapes
\( \$2.40 / 0.75 \text{ lbs} = \mathbf{\$3.20} \) per pound.
3. Cyclist Table
18 / 1.5 = 12. 36 / 3 = 12. 54 / 4.5 = 12.
Conclusion: Yes, it is proportional because the ratio of miles to hours is a constant 12 mph.
4. Charity Walkathon
25 / 2 = 12.5. 62.5 / 5 = 12.5. 125 / 10 = 12.5.
Conclusion: Yes, the constant of proportionality is $12.50 per mile.
The Big Apple Challenge
Rate: $157.50 / 45 = $3.50/hot dog. $210 / 60 = $3.50/hot dog. Proportional? YES.
For 150 hot dogs: \( 150 \cdot \$3.50 = \mathbf{\$525.00} \).
Scoring Guidance
• Award partial credit for correct setups even if arithmetic errors occur.
• Ensure students include units (e.g., "$", "miles", "mph") in final answers.
• For "NYS Style" questions, prioritize the quality of the written explanation.
Graphs Daily Drills Worksheet Empire State Math Prep
Week 2: Graphing the Empire
2 Daily Drills
Name: __________________________________
MONDAY Finding k from Graphs
A graph passes through (0,0) and (4, 12). What is the constant of proportionality (k)?
k = ________
What does k represent?
TUESDAY Equations (y = kx)
A taxi charges $2.50 per mile. Write an equation to represent the total cost (y) for (x) miles.
Work Area
y = _______ x
WEDNESDAY Point (1, r)
A proportional graph contains the point (1, 8.5). What is the unit rate? What would the y-value be when x = 10?
Unit Rate: ___________
When x = 10, y = ___________
THURSDAY Zero-Zero
Why must a proportional relationship pass through the origin (0,0)? Give a real-world example of why this makes sense.
Write here...
FRIDAY Assessment Check
Which point on a proportional graph represents the unit rate?
(0,0)
(1,r)
(x,1)
(r,1)
Explain: ___________________________________________________________________
Graphs Power Practice Worksheet 2
Power Practice
Graphing & Equations Review
Standard 7.RP.2b, 2c, 2d
Date: _________________
Part 1: Graph Analysis
Minutes (x)
Words (y)
(5, 150)
(0,0)
A. Find the unit rate (k):
B. Write the equation (y = kx):
C. What does (0,0) represent here?
Part 2: Multiple Representations
A local library prints copies at a constant rate. 15 copies cost $0.75, and 40 copies cost $2.00.
Copies (x) Cost (y) 15 $0.75 40 $2.00 100 ?
Equation:
y = _________ x
Cost for 100 copies:
$_________
NYS Performance Task:
The graph of a proportional relationship passes through the point \((4, 2)\). Determine if the point \((10, 5)\) is on the same graph. Show your reasoning using two different methods (table, equation, or unit rate).
Method 1
Method 2
Subway Speed Challenge
The speed of the Q-train is represented by the equation \( y = 45x \), where \( y \) is miles and \( x \) is hours. The F-train speed is shown in the table below. Which train is faster? By how many miles per hour?
Q-Train
y = 45x
Hours (x) Miles (y) 2 96 5 240
Faster Train: _______________
Difference in Speed: _________ mph
Graphs Answer Key Answer Key
Week 2: Graphs
Teacher Resource
Daily Drills Solutions
Monday
k = 12 / 4 = 3.
k represents the unit rate (change in y for every 1 unit of x).
Tuesday
Equation: y = 2.50x (or y = 2.5x).
Wednesday
Unit Rate: 8.5. When x = 10, y = 85.
Thursday
Proportionality implies that when there is zero of the input (x), there must be zero of the output (y). Example: 0 miles driven = $0 gas cost.
Friday (Assessment Check)
Point: (1, r).
Explanation: When x = 1, the y-value (r) is by definition the unit rate (amount per 1).
Power Practice Solutions
Part 1: Graph Analysis
A. k = 150 / 5 = 30 words per minute.
B. Equation: y = 30x.
C. (0,0) means that in 0 minutes, 0 words were typed.
Part 2: Multiple Representations
k = 0.75 / 15 = 0.05 (or 2.00 / 40 = 0.05).
Equation: y = 0.05x.
Cost for 100: \( 100 \cdot 0.05 = \mathbf{\$5.00} \).
NYS Performance Task (4, 2) and (10, 5)
Method 1 (k): 2 / 4 = 0.5. 5 / 10 = 0.5. Same k means same graph.
Method 2 (Equation): y = 0.5x. Test (10, 5) -> 5 = 0.5(10) -> 5 = 5. True.
Conclusion: Yes, the point is on the graph.
Subway Speed Challenge
Q-Train speed: 45 mph.
F-Train speed: 96 / 2 = 48 mph.
Faster Train: F-Train. Difference: 3 mph.
Percents One Daily Drills Worksheet Empire State Math Prep
Week 3: Percent Power
3 Daily Drills
Name: __________________________________
MON
Percent of a Number
What is 15% of $80?
What is 200% of 45?
TUE
Sales Tax & Tip
A pizza in Brooklyn costs $24.00. Sales tax is 8.875%. Calculate the tax amount (round to the nearest cent).
Tax: $___________
WED
Discounts
A pair of shoes originally costs $120. They are on sale for 30% off. What is the sale price?
Method 1: Subtract discount from total.
Method 2: Multiply by remaining percent (70%).
Sale Price: $___________
THU
Commissions
A real estate agent earns a 3% commission on a $500,000 apartment sale. How much commission do they earn?
FRI
The "Whole" Challenge
If 40% of a number is 24, what is the number?
Answer: ___________
Percents One Power Practice Worksheet 3
Power Practice
Percents & Applications Review
Standard 7.RP.3
Date: _________________
Part 1: Shopping & Retail
1. A store manager buys a jacket for $45.00. He marks up the price by 60% before selling it. What is the retail price?
Calculation Area
Retail Price: $_________
2. A customer uses a 15% off coupon on a $120.00 purchase. After the discount, an 8% sales tax is added. What is the final total?
1. Discount
2. Sales Tax
Final Total: $___________
Part 2: Multi-Step Word Problems
3. Dinner at a Manhattan Diner
The bill was $85.00. They left a 20% tip based on the $85.00 subtotal. Sales tax is 8.875% of the $85.00. What is the total paid?
Subtotal
$85.00
Tip (20%)
$_________
Tax (8.875%)
$_________
Show final sum logic
Total Paid: $___________
Assessment Mastery Challenge
A sofa costs $800 and is marked down by 20%. Then, an additional 10% off the sale price is applied. What is the final price? Is this the same as a single 30% discount?
Mathematical Explanation Area
Final Price: $___________
Same as 30%?
YES / NO
Visual Logic
Shade approx. 65% of the bar:
If Total = $200, 65% is:
$_________
Percents One Answer Key Answer Key
Week 3: Percents I
Teacher Resource
Daily Drills Solutions
Monday
15% of $80 = \( 0.15 \cdot 80 = \mathbf{\$12} \).
200% of 45 = \( 2.0 \cdot 45 = \mathbf{90} \).
Tuesday
Tax = \( 24.00 \cdot 0.08875 = 2.13 \) (exactly 2.13). Tax: $2.13.
Wednesday
Discount = \( 120 \cdot 0.30 = 36 \). Sale Price = \( 120 - 36 = \mathbf{\$84} \).
Alternative: \( 120 \cdot 0.70 = 84 \).
Thursday
Commission = \( 500,000 \cdot 0.03 = \mathbf{\$15,000} \).
Friday (The "Whole" Challenge)
\( 0.40x = 24 \rightarrow x = 24 / 0.40 = \mathbf{60} \).
Power Practice Solutions
1. Retail Markup
Markup = \( 45 \cdot 0.60 = 27 \). Retail Price = \( 45 + 27 = \mathbf{\$72.00} \).
2. Coupon & Tax
Step 1 (Discount): \( 120 \cdot 0.85 = 102 \). Sale price is $102.
Step 2 (Tax): \( 102 \cdot 1.08 = 110.16 \). Final Total: \$110.16.
3. Diner Bill
Tip: \( 85 \cdot 0.20 = \$17.00 \). Tax: \( 85 \cdot 0.08875 = \$7.54 \) (rounded).
Total: \( 85 + 17 + 7.54 = \mathbf{\$109.54} \).
NYS Assessment Challenge (Sofa)
Step 1 (20% off): \( 800 \cdot 0.80 = 640 \).
Step 2 (10% off of 640): \( 640 \cdot 0.90 = \mathbf{\$576.00} \).
Is it 30%? No. 30% off would be \( 800 \cdot 0.70 = 560 \).
Explanation: The second discount is taken off a smaller amount, not the original $800.
Percents Two Daily Drills Worksheet Empire State Math Prep
Week 4: Percent Progress
4 Daily Drills
Name: __________________________________
MONDAY Percent Change Intro
Original price: $50. New price: $65. Find the percent increase.
Answer: ________ %
Formula: (Change / Original) * 100
TUESDAY Percent Error
A student estimated a table to be 120 cm long. The actual length is 125 cm. What is the percent error?
________ %
WEDNESDAY Simple Interest (I=PRT)
Calculate the simple interest on a $1,000 loan with a 5% annual interest rate for 3 years.
P: $1000
r: 0.05
t: 3
Interest (I): $___________
THURSDAY Percent Decrease
The population of a small town was 4,000 in 2020. In 2024, it is 3,200. What is the percent decrease?
Work Area
FRIDAY Mixed Review
A bank account has $500. After one year, the balance is $525. What was the annual interest rate?
Rate: ________ %
Percents Two Power Practice Worksheet 4
Power Practice
Advanced Percents Review
Standard 7.RP.3
Date: _________________
Part 1: Change and Accuracy
1. Last year, the 7th-grade class had 250 students. This year, there are 285 students. Find the percent increase in the number of students.
Show Work Here
________ %
Percent Increase
2. An architect measured a hallway to be 12.5 meters. The actual hallway was built to be 13.0 meters. What was the percent error of the measurement? (Round to the nearest tenth of a percent).
Percent Error: ________ %
Part 2: Money & Interest
Recall the Formula: \( I = P \cdot r \cdot t \)
3. Sarah deposits $400 into a savings account that pays 2.5% simple interest per year. How much total money will be in the account after 4 years?
Calculate Interest First:
Total Account Balance:
4. Mr. Henderson took out a loan for $2,000. After 2 years, he paid a total of $240 in simple interest. What was the annual interest rate of the loan?
Interest Rate: ________ %
NYS Assessment Mastery
A bike shop sells a mountain bike for $350. During a holiday sale, the price is decreased by 15%. A month later, the sale price is increased by 15%. Is the new price $350? Explain why or why not using calculations to support your answer.
Step 1: Decrease
Step 2: Increase
Written Explanation:
Final Price: $___________
Percents Two Answer Key Answer Key
Week 4: Percents II
Teacher Resource
Daily Drills Solutions
Monday (Percent Increase)
Change = 65 - 50 = 15. Percent = \( (15 / 50) \cdot 100 = \mathbf{30\%} \).
Tuesday (Percent Error)
Error = |120 - 125| = 5. % Error = \( (5 / 125) \cdot 100 = \mathbf{4\%} \).
Wednesday (Simple Interest)
\( I = 1000 \cdot 0.05 \cdot 3 = \mathbf{\$150} \).
Thursday (Percent Decrease)
Change = 4000 - 3200 = 800. % Decrease = \( (800 / 4000) \cdot 100 = \mathbf{20\%} \).
Friday (Finding Rate)
\( I = 25 \). \( 25 = 500 \cdot r \cdot 1 \). \( r = 25 / 500 = 0.05 = \mathbf{5\%} \).
Power Practice Solutions
1. Student Increase
Change = 35. \( (35 / 250) \cdot 100 = \mathbf{14\%} \).
2. Hallway Error
Error = 0.5. \( (0.5 / 13.0) \cdot 100 \approx \mathbf{3.8\%} \).
3. Sarah's Savings
Interest: \( 400 \cdot 0.025 \cdot 4 = \$40 \).
Total Balance: \( 400 + 40 = \mathbf{\$440} \).
4. Loan Rate
\( 240 = 2000 \cdot r \cdot 2 \). \( 240 = 4000r \). \( r = 240 / 4000 = 0.06 = \mathbf{6\%} \).
NYS Mastery (The Bike Problem)
Step 1 (15% decrease): \( 350 \cdot 0.85 = \$297.50 \).
Step 2 (15% increase of \$297.50): \( 297.50 \cdot 1.15 = \mathbf{\$342.13} \).
Explanation: No, the price is not the same. The 15% increase is calculated based on the lower sale price ($297.50), making the increase amount smaller than the original decrease amount.
Expressions Daily Drills Worksheet Empire State Math Prep
Week 5: Expression Experts
5 Daily Drills
Name: __________________________________
MON
Combining Like Terms
7.EE.1
Simplify the expression: \( 4x - 7 + 2x + 15 \)
Result: ___________
TUE
Distributive Property
7.EE.1
Expand and simplify: \( -3(2y - 4) + 5y \)
Result: ___________
WED
Factoring Expressions
7.EE.1
Factor out the GCF: \( 12a - 18 \)
GCF: ________
Answer: ________(________)
THU
Solving 2-Step Equations
7.EE.4a
Solve for \( x \): \( 2x + 10 = 34 \)
x = ________
FRI
Assessment Style Modeling
Write an expression for: "Five less than triple a number \( n \)".
____________________
Expressions Power Practice Worksheet 5
Power Practice
Expressions & Equations Review
Standard 7.EE.1 & 7.EE.4a
Date: _________________
Part 1: Equivalent Expressions
1. Which expression is equivalent to \( 0.5(4x - 10) + 3x \)?
A. \( 2x - 5 + 3x \)
B. \( 5x - 5 \)
C. \( 5x - 10 \)
D. \( 7x - 5 \)
Show steps to justify your answer:
2. Factor the expression \( -4x + 12 \) using a negative factor.
Result: ____________________
Part 2: Multi-Step Equations
3. Solve for \( x \). Show each step of inverse operations.
\( \frac{x}{4} - 7 = -2 \)
x = ________
4. Solve for \( w \): \( 3(w + 5) = 27 \)
Method 1: Distribute first
Method 2: Divide first
Modeling NYC Scenarios
A bike rental shop in Central Park charges a flat fee of $15 plus $8 per hour. If Marcus spent a total of $55, write and solve an equation to find the number of hours (\( h \)) he rented the bike.
The Equation
____________________
The Solution
Marcus rented the bike for ________ hours.
Expressions Answer Key Answer Key
Week 5: Expressions
Teacher Resource
Daily Drills Solutions
Monday
\( 4x + 2x = 6x \). \( -7 + 15 = 8 \). Result: 6x + 8.
Tuesday
\( -6y + 12 + 5y \). Result: -y + 12.
Wednesday
GCF: 6. Answer: 6(2a - 3).
Thursday
\( 2x = 24 \). Result: x = 12.
Friday (Modeling)
Expression: 3n - 5.
Power Practice Solutions
1. Equivalent Expressions
\( 0.5(4x) - 0.5(10) + 3x = 2x - 5 + 3x = 5x - 5 \).
Answer: B.
2. Factoring with Negative Factor
Result: -4(x - 3).
3. Multi-Step Equation (x/4 - 7 = -2)
Step 1: \( \frac{x}{4} = 5 \). Step 2: \( x = 20 \). Result: x = 20.
4. Solving 3(w + 5) = 27
Method 2 (Divide first): \( w + 5 = 9 \). \( w = 4 \). Result: w = 4.
NYC Bike Scenario
Equation: 8h + 15 = 55.
Solution: \( 8h = 40 \). \( h = 5 \). Marcus rented for 5 hours.
Inequalities Daily Drills Worksheet Empire State Math Prep
Week 6: Inequality Investigators
6 Daily Drills
Name: __________________________________
MON
Symbols & Phrases
Translate: "A number \( x \) is at least 15."
\( x < 15 \)
\( x \ge 15 \)
\( x > 15 \)
\( x \le 15 \)
TUE
Solving Inequalities
Solve for \( p \): \( 3p - 5 < 10 \)
\( p < \) _________
WED
The Negative Rule
Solve for \( x \): \( -2x > 10 \). Remember the flipping rule!
\( x \) _________
THU
Graphing Solutions
Graph the solution to \( x \le -2 \) on the number line below.
-4
-3
-2
-1
0
1
2
FRI
Modeling Real-World
You have $50 to spend at a street fair. Admission is $10. Each ride costs $5. How many rides (\( r \)) can you go on?
\( 5r + 10 \le 50 \)
Solution: r \(\le\) _________
Inequalities Power Practice Worksheet 6
Power Practice
Inequalities Final Review
Standard 7.EE.4b
Date: _________________
Part 1: Solutions and Visuals
1. Solve the inequality:
\( -5x + 12 > -3 \)
Show Work Area
Final Solution
x _________
Graph Solution:
-1
0
1
2
3
4
5
2. Solve the inequality:
\( 4(x - 2) \le 12 \)
Show Work Area
Final Solution
x _________
Graph Solution:
1
2
3
4
5
6
7
Part 2: Real-World Scenarios
3. The Theater Trip Fundraising
A drama club is raising money for a Broadway trip. They have $400 already. They sell items for $2.50 each and need more than $1,200. Write and solve an inequality for the minimum items (\( n \)).
Inequality Model
Solution Logic
Minimum items: _________
Empire State Final Challenge
The elevator has a weight limit of 2,500 pounds. A delivery man (190 lbs) is moving boxes (45 lbs each). What is the maximum number of boxes (\( b \)) he can take?
Modeling Workspace
Model Equation
45b + 190 \(\le\) 2500
Max Boxes (b)
b \(\le\) _____
Inequalities Answer Key Answer Key
Week 6: Inequalities
Teacher Resource
Daily Drills Solutions
Monday
Answer: \( x \ge 15 \).
Tuesday
\( 3p < 15 \). Result: \( p < 5 \).
Wednesday
Divide by -2 (flip sign). Result: \( x < -5 \).
Thursday
Graph: Solid circle at -2, shaded to the left.
Friday (Modeling)
\( 5r \le 40 \). Solution: \( r \le 8 \). (Can go on 8 rides).
Power Practice Solutions
1. Solving \( -5x + 12 > -3 \)
\( -5x > -15 \). Divide by -5, flip sign: \( x < 3 \).
Graph: Open circle at 3, shade left.
2. Solving \( 4(x - 2) \le 12 \)
\( x - 2 \le 3 \). \( x \le 5 \).
Graph: Closed circle at 5, shade left.
3. Theater Trip
Inequality: \( 2.5n + 400 > 1200 \). \( 2.5n > 800 \). \( n > 320 \).
Must sell at least 321 items (since it must be "more than" 320).
Empire State Elevator Challenge
\( 45b + 190 \le 2500 \). \( 45b \le 2310 \).
\( b \le 51.333... \).
Conclusion: Max boxes = 51 boxes. (Cannot have 52 because it would exceed weight).
Final Push Daily Drills Worksheet Empire State Math Prep
Week 7: The Final Stretch
7 Daily Drills
Name: __________________________________
Monday
Scale Factors (7.G.1)
A model of the Statue of Liberty is 6 inches tall. The actual statue is 305 feet tall. What is the scale in inches to feet? If a model arm is 0.5 inches long, how long is the actual arm?
Workspace
Scale: 1 in = _________ ft
Actual Arm: _________ ft
Tuesday
Sampling (7.SP.1)
Which sampling method provides the most representative results for a survey of 800 students?
A. Surveying only the basketball team.
B. Surveying every 10th student that enters the building.
C. Surveying students who brought their own lunch.
Wednesday
Inference (7.SP.2)
In a random sample of 50 commuters, 12 were reading. Based on this, how many of the 5,000 daily commuters are likely reading?
Proportion Area
Answer: _________________
Thursday
Probability Basics (7.SP.5)
The probability of rain is 0.85. Describe this probability using a qualitative term (impossible, unlikely, likely, certain).
0 = Impossible
0.5 = Equally Likely
1 = Certain
Term: ________________________________
Friday
Compound Probability (7.SP.8)
Tree Diagram Challenge:
A bagel shop offers Plain, Sesame, or Everything bagels with either Cream Cheese or Butter. Find the total outcomes.
Sample Space Modeling Area
Total Outcomes:
_________________
Final Push Power Practice Worksheet 7
Power Practice
Scale, Stats & Probability Mastery
Standards 7.G.1 & 7.SP.1-8
Date: _________________
Part 1: The Blueprint Challenge
1. A blueprint uses a scale of 2 centimeters = 5 meters. The actual playground is 25 meters long and 15 meters wide. What are the dimensions on the blueprint?
Multi-Step Dimension Calculation Workspace
Blueprint Length
_________ cm
Blueprint Width
_________ cm
Part 2: Data Detectives
2. Subway Delays Inference
A-Line: 12 / 100 delayed
L-Line: 4 / 100 delayed
If the transit system runs 1,500 L-line trains per day, about how many would you expect to be delayed?
Work
Expected: _________
Part 3: Assessment Challenge
Compound Probability Quest
You spin a spinner with 4 equal sections labeled A, B, C, D AND flip a fair coin. What is the probability of spinning a "B" and flipping "Heads"? Show all possible outcomes to justify your answer.
Sample Space Visualization (Tree Diagram or List)
Total Outcomes
_________
P(B, Heads)
_________ / _________
Final Push Answer Key Answer Key
Week 7: The Final Stretch
Teacher Resource
Daily Drills Solutions
Monday
Ratio: 6 in / 305 ft → 1 in ≈ 50.83 ft .
Arm: 0.5 × 50.83 ≈ 25.42 ft .
Tuesday
Answer: Choice B . Systematic random sampling provides representative results.
Wednesday
Rate: 12/50 = 0.24. Total estimate: 0.24 × 5000 = 1,200 commuters .
Thursday
Answer: Likely . 0.85 is significantly closer to 1 than to 0.5.
Friday
Outcomes: {Plain-CC, Plain-B, Sesame-CC, Sesame-B, Everything-CC, Everything-B}. Total = 6 .
Power Practice Solutions
Part 1: Scale Drawings
Scale: 1 cm = 2.5 m. Length: 25 / 2.5 = 10 cm . Width: 15 / 2.5 = 6 cm .
Part 2: Data Detectives
L-Line Rate: 4/100 = 0.04. Expected: 1500 × 0.04 = 60 trains delayed .
Part 3: Compound Probability
Sample Space: {AH, AT, BH, BT, CH, CT, DH, DT}. Total Outcomes = 8 .
Successful Event: {BH}. Final Probability = 1/8 (or 0.125).
Instructional Note
Confirm students use cross-multiplication or unit rates for Scale Factors.
For compound probability, emphasize that sample space shows independence between the spinner and coin.
Remind students that random sampling is the foundation of statistical inference .
