Grade 5 Mathematics
Student Edition
Chapter 1
Grade 5 Mathematics
೦GRADE 5೦
MATHEMATICS
Real-World Problem Solving
Complete Student Edition
GLOBAL SOVEREIGN UNIVERSITY "Building a Bridge to Freedom Through Education
Copyright © 2024 Global Sovereign University Press
All rights reserved.
This textbook is provided FREE to students. No Login. Totally FREE to everyone. Visit this web page to download your free book.
https://www.globalsovereignuniversity.org/mathification
Why This Book Is Different
Global Sovereign University Press Page:1
🏆 NOBEL PRIZE RESEARCH SAYS:
"Students who score 96% on classroom math tests succeed
only 1% of the time in real life."
— Banerjee & Duflo,Nature, February 2025
The Research That Proves Traditional Math Education Fails
In February 2025, Nobel Prize-winning economists published a groundbreaking study in Nature, the world's most respected scientific journal. They tested over 1,400 children in India and discovered something shocking:
Children who ace classroom math CANNOT use it in the real world.
Studentswhoscored96%onstandardschoolmathproblemscouldsolvesimplereal-world market calculations only 1% of the time. Meanwhile, children who worked in markets—without formal education—solved the same problems with 96% accuracy.
The researchers' conclusion was clear:
"Schools need to build a bridge between math learned in the classroom and math encountered in real-life situations."
The Problem: Abstract Doesn't Transfer to Applied
TheNobellaureatesfoundthatschoolchildrenlearnedproceduresbutnotunderstanding. Theycouldsolve"24×8"onaworksheetbyadding24eighttimes.Butgivethemareal problem—"How much do 8 items cost at $24 each?"—and they froze.
Market children used efficient mental strategies: breaking 11 × 43 into (10 × 43) + 43, rounding for easier calculation, and working with meaningful quantities. Schoolchildren followed rigid, slow methods that worked for tests but failed in life.
It'snotthatschoolkidswerelessintelligent.It'sthattheireducationneverconnected the math to reality.
The GSU Solution: Real-World Math
Page2: Dr. Gene A Constant - Author
Grade 5 Mathematics
This textbook does exactly what the Nobel laureates recommend. Instead of abstract problems,
every calculation has a professional context:
Traditional Math GSU Real-World Math
"Multiply 3.45 × 6.8" "You're the Restaurant Manager. Your order is 6.8 pounds at $3.45/lb. What's
the cost?"
"Find 15% of 80" "A customer's bill is $80. Calculate the 15% tip."
"Add 2/3 + 3/4" "Your recipe needs 2/3 cup butter and 3/4 cup oil. Total fat?"
Same math. Completely different learning.
The Bottom Line
Nobel Prize-winning researchers proved that traditional education fails to prepare students
for real-world math. The gap between classroom success and life success is catastrophic:
96% to 1%.
This textbook closes that gap.
Every problem. Every skill. Every chapter. Connected to reality.
“Because math isn't an academic exercise. It's a survival skill.”
Dr. Gene A Constant
Global Sovereign University is a 501(c)(3) educational foundation. This textbook is provided
FREE because learning should never be limited by economics.
Research Citation:
Banerjee, A., Duflo, E., et al. (2025). Children's arithmetic skills do not transfer between applied and academic mathematics.Nature.https://doi.org/10.1038/s41586-024-08502-w
The lead authors received the 2019 Nobel Prize in Economics "for their experimental
approach to alleviating global poverty."
ty
Global Sovereign University Press Page:3
Table of Contents
Chapter 1:The Restaurant Manager Decimals to thousandths, percentages, tips, pricing
Chapter 2:The Warehouse Supervisor Volume, cubic units, shipping, inventory
Chapter 3:The Video Game Designer Coordinate plane, ordered pairs, graphing, transformations
Chapter 4:The Catering Chef Fractions with unlike denominators, multiplying fractions
Chapter 5:The Landscaping Contractor Area of complex shapes, measurement conversions
Chapter 6:The Sports Analyst Advanced statistics, mean/median/mode, data display
Chapter 7:The Travel Agent Time zones, large numbers, multi-step problems
Chapter 8:The Small Business Owner Profit/loss, percentages, financial projections
Chapter 9:The Science Lab Technician
Order of operations, formulas, scientific notation
Chapter 10:The Startup Founder
Capstone project applying ALL skills
Page4: Dr. Gene A Constant - Author
Grade 5 Mathematics
The GSU Difference
Traditional Math Education
• Learn abstract rules • Practice disconnected problems • Take a test • Forget everything • Graduate unable to balance a checkbook
GSU Real-World Math
• You ARE the restaurant manager calculating tips • You ARE the warehouse supervisor measuring volume • You ARE the business owner tracking profit • You solve problems you will actually face • You build skills that earn money
The difference is not just how you learn.
It is whether you can USE what you learn.
Nobel Prize winners proved that traditional education fails. We built the alternative.
Real-World Review Problems
Additional mixed practice from all chapters
Global Sovereign University Press Page:5
Mixed Review Set 1: Restaurant & Retail
1.Food order: 12.5 lbs chicken at $4.89/lb + 8.75 lbs beef at $7.25/lb. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Bill is $86.50. Customer pays with $100. Calculate 8% tax, then change from $100. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Tableof6wantstosplit$234.60billevenlyplus20%tip.Eachpersonpays? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Buy wholesale at $24, markup 85%. Selling price? Then offer 25% off sale. Sale price? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
5.Daily sales: Mon $1,245, Tue $1,567, Wed $1,389, Thu $1,678, Fri $2,134. Mean? Range? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
6.If Saturday sales grow 15% from Friday, projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Mixed Review Set 2: Shipping & Construction
1.Warehouse: 50 × 40 × 15 ft. Volume? How many 8 ft³ boxes fit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Package: 24 × 18 × 16 in. Dim weight (÷139)? Ship at $0.58/lb? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.L-shaped floor: main 60×45 ft + extension 30×25 ft. Total area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page6: Dr. Gene A Constant - Author
Grade 5 Mathematics
4.Same L-shape. Carpet costs $4.50/sq ft. Total carpet cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Rectangle 75×50 ft with 15×10 pool cutout. Deck area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Fence the deck with two 4 ft gates. Fence needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Mixed Review Set 3: Time, Travel & Data
1.Flight departs Seattle (PT) 7:45 AM, flies 5 hr 15 min to Miami (ET). Arrival local? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Meeting in Tokyo (14 hrs ahead of PT) at 9 AM Tokyo time. PT time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Trip costs: Air $2,850, Hotel $1,995, Food $840, Activities $675, Transport $340. Total? Split 5 ways?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Player stats: 22, 18, 31, 25, 19, 28, 24, 17. Mean? Median? Range? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Same player: Identify any outlier. Recalculate mean without it. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Player averages 23 pts. Win bonus $50/point above 20. Bonus for 82-game season? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
Global Sovereign University Press Page:7
Mixed Review Set 4: Fractions & Formulas
1.Recipe needs: 2 1/3 cups flour + 1 3/4 cups sugar + 2/3 cup butter. Total ingredients? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
2.Scale the recipe ×3. New flour amount? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Had 5 lbs butter, used 2 5/8 lbs. Remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Calculate: 5 × (8 - 3)² + 15 ÷ 3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Calculate: 2⁴ + 3³ - 5 × 6 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Density = Mass ÷ Volume. M = 350g, V = 25 cm³. Density? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Mixed Review Set 5: Business Planning
1.Startup costs: Equipment $8,450, Software $2,375, Legal $1,850, Marketing $3,200. Total? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
2.Sell product at $45, cost $18. Profit per item? Profit margin %? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Fixed costs $2,400/month. Profit $27/item. Break-even quantity? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page8: Dr. Gene A Constant - Author
Grade 5 Mathematics
4.Month 1: $12,000 sales. Growing 20%/month. Month 4 projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Annual revenue $156,000. Total costs $98,000. Net profit? Profit margin? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Reinvest 35% of profit. Reinvestment amount? Remaining for owners? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Welcome, Fifth Grade Mathematician!
Fifth grade mathematics opens doors to careers you can start building TODAY. This year, you'll take on professional roles that use mathematics every single day.
Your Roles This Year: • Restaurant Manager:Calculate food costs, tips, and pricing • Warehouse Supervisor:Measure volume and manage shipping • Video Game Designer:Plot coordinates and create game worlds • Catering Chef:Scale recipes for any size event • Landscaping Contractor:Calculate areas and order materials • Sports Analyst:Crunch statistics for teams • Travel Agent:Plan trips across time zones • Small Business Owner:Track profit, loss, and growth • Science Lab Technician:Follow precise formulas and procedures • Startup Founder:Launch your own business!
These aren't pretend jobs. These are skills you can use THIS WEEK to help your family, earn
money, or solve real problems.
Global Sovereign University Press Page:9
CHAPTER 1 The Restaurant Manager
Chapter Goal: Master decimals, percentages, and money calculations to run a successful
restaurant.
Congratulations! You've just been promoted to Restaurant Manager at the family diner. Every day, you'll calculate food costs to three decimal places, figure out tips and taxes, set menu prices, and track daily revenue. One decimal point in the wrong place can cost hundreds of dollars!
Section 1: Reading the Receipts — Decimals to Thousandths
೦೦The Scenario
Your food supplier sends invoices with prices to the thousandth of a dollar. Coffee beans cost $7.425 per pound. Cooking oil costs $3.875 per gallon. Understanding these precise decimals helps you track costs and spot errors.
೦೦The Skill: Decimal Place Value
Decimals extend place value to the right of the decimal point:
• Tenths (0.1) — one decimal place • Hundredths (0.01) — two decimal places (pennies!) • Thousandths (0.001) — three decimal places (mills)
✎ Worked Example: Understanding $7.425
7 is in the ones place = $7.00 4 is in the tenths place = $0.40 (40 cents) 2 is in the hundredths place = $0.02 (2 cents) 5 is in the thousandths place = $0.005 (half a cent) Total:$7.00 + $0.40 + $0.02 + $0.005 = $7.425
When you buy 100 pounds, that half-cent becomes 50 cents!
✎ Worked Example: Comparing $3.875 and $3.85
Line up decimal points and compare left to right:
Ones: Both have 3 Tenths: Both have 8
Hundredths: 7 vs 5 → 7 > 5 Answer:$3.875 > $3.85 (Supplier A is more expensive)
✎ Worked Example: Rounding $4.627 to the Nearest CentThe nearest cent = nearest hundredth
Look at thousandths digit: 7 Is it 5 or more? YES → Round up Answer:$4.627 rounds to $4.63
Page10: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Writing Decimals in Expanded Form $12.345 =
10 + 2 + 0.3 + 0.04 + 0.005 Or: (1×10) + (2×1) + (3×0.1) + (4×0.01) + (5×0.001)
೦೦Practice: Decimal Place Value
1.What is the value of the 6 in $45.678?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Write $23.456 in expanded form. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Round $7.834 to the nearest cent (hundredth). Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Compare using <, >, or =: 5.67 ___ 5.670 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.What digit is in the thousandths place of 12.345? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Round $9.999 to the nearest cent. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Order from least to greatest: 4.52, 4.502, 4.520, 4.052 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Write in standard form: 8 + 0.3 + 0.05 + 0.007 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:11
9.Compare: 6.125 ___ 6.15 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Round $12.5849 to the nearest cent. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.What is the value of the 9 in 34.789? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Order from greatest to least: 7.08, 7.008, 7.8, 7.080 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Write $156.025 in expanded form. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Round $0.9995 to the nearest cent. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Compare: 0.305 ___ 0.350
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Coffee costs $8.457/lb, tea costs $8.475/lb. Which costs less? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
17.What digit is in the hundredths place of 67.891? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page12: Dr. Gene A Constant - Author
Grade 5 Mathematics
18.Round $45.6789 to the nearest tenth. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Daily Totals — Adding and Subtracting Decimals
೦೦The Scenario
At closing time, you total the day's receipts. The lunch shift earned $1,234.56 and the dinner shift earned $2,456.78. You also need to subtract expenses: $345.67 for food delivery, $123.45 for supplies.
✎ Worked Example: Adding: $1,234.56 + $2,456.78
Step 1: Line up decimal points Step 2: Add column by column from right to left
1,234.56 + 2,456.78 ---------- Answer:$3,691.34
✎ Worked Example: Adding with Different Decimal Places: $45.6 + $23.45 +
$8.125
Add zeros to align: $45.600 + $23.450 + $8.125
45.600 23.450 + 8.125 --------- Answer:$77.175 (or $77.18 rounded)
✎ Worked Example: Subtracting: $500.00 - $123.45
500.00 - 123.45 --------- Answer:$376.55
✎ Worked Example: Calculating Net Revenue
Revenue: $3,691.34 Expenses: $345.67 + $123.45 = $469.12
Net: $3,691.34 - $469.12 = $3,222.22 Answer:$3,222.22 net revenue for the day
Global Sovereign University Press Page:13
೦೦Practice: Adding and Subtracting Decimals
1.Add: 45.67 + 23.456 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Add: 123.4 + 56.78 + 9.012 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Subtract: 500.00 - 234.56 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Lunch sales: $1,567.89. Dinner: $2,345.67. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Add: 7.8 + 12.34 + 0.567 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Subtract: 1,000 - 456.789 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Food cost: $234.56 + $178.90 + $345.67. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Revenue $3,456.78. Expenses $1,234.56. Net? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Add: 0.125 + 0.875 + 0.5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page14: Dr. Gene A Constant - Author
Grade 5 Mathematics
10.Subtract: 250.00 - 67.89 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Three orders: $12.45, $8.90, $15.67. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Budget $2,500. Spent $1,678.45. Remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Add: 99.99 + 88.88 + 77.77 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Subtract: 1,234.567 - 890.123 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
y
15.Monday $1,234.56, Tuesday $1,456.78, Wednesday $1,345.67. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Had $5,000. Expenses: $456.78, $234.56, $789.12. Remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
17.Add: 6.7 + 8.91 + 2.345 + 0.6789 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
18.Subtract: 10,000 - 4,567.89 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:15
Section 3: Bulk Orders — Multiplying Decimals
೦೦The Scenario
You order 24.5 pounds of chicken at $4.25 per pound. How much will it cost? Multiplying decimals
precisely is essential for accurate ordering.
✎ Worked Example: Multiplying: 24.5 × $4.25
Step 1: Multiply as whole numbers: 245 × 425 = 104,125 Step 2: Count decimal places: 1 (in 24.5) + 2 (in 4.25) = 3 Step 3: Place decimal 3 places from right: 104.125 Answer:$104.125 (or $104.13 rounded)
✎ Worked Example: Multiplying Decimal by Whole Number: 15 × $6.75
15 × 6.75 = 15 × 675 = 10,125 Two decimal places → 101.25 Answer:$101.25
✎ Worked Example: Multiplying Two Decimals: 2.5 × 3.425 × 34 = 850
1 + 1 = 2 decimal places → 8.50 Answer:8.5
✎ Worked Example: Real Application: Weekly Order
Order 45.5 pounds of beef at $5.85/lb 45.5 × 5.85 = 455 × 585 = 266,175
1 + 2 = 3 decimal places → 266.175 Cost:$266.18 (rounded)
೦೦Practice: Multiplying Decimals
1.Multiply: 3.4 × 5.6 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Multiply: 12.5 × 4 Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
3.24 pounds × $3.75/lb. Total cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page16: Dr. Gene A Constant - Author
Grade 5 Mathematics
4.Multiply: 0.25 × 0.4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Multiply: 15.5 × 2.5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Order 36 gallons at $2.45/gallon. Cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Multiply: 8.125 × 8 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Multiply: 4.5 × 4.5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.45.5 pounds × $5.85/lb. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Multiply: 0.6 × 0.7 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Multiply: 125 × 0.08 (8% tax) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Order: 18.5 lbs chicken × $4.25/lb. Cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:17
13.Multiply: 6.25 × 3.2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Multiply: 100 × 0.065 (6.5% tax) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.28.5 hours × $12.50/hour. Earnings? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Multiply: 2.5 × 2.5 × 2.5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
17.Order: 55 gallons × $3.875/gallon. Cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
18.Multiply: 0.125 × 80 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 4: Tips and Taxes — Understanding Percentages
೦೦The Scenario
A customer's bill is $85.00. They want to leave a 20% tip. The sales tax is 8%. You need to calculate the tip, the tax, and the total. Understanding percentages is essential!
೦೦The Skill: Converting Percentages
'Percent' means 'per hundred.' To convert:
• Percent to decimal: Divide by 100 (move decimal 2 places left) • 20% = 0.20, 8% = 0.08, 15% = 0.15
✎ Worked Example: Calculating a 20% Tip on $85.00
Step 1: Convert 20% to decimal: 20% = 0.20 Step 2: Multiply: $85.00 × 0.20 = $17.00 Tip:$17.00
Page18: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Calculating 8% Tax on $85.00
Step 1: Convert 8% to decimal: 8% = 0.08 Step 2: Multiply: $85.00 × 0.08 = $6.80 Tax:$6.80
✎ Worked Example: Total Bill with Tip and Tax
Food: $85.00 Tax (8%): $6.80 Subtotal: $91.80 Tip (20% of food): $17.00 Total:$108.80
✎ Worked Example: Quick Tip Calculation: 15% ShortcutTo find 15%:
10% of $60 = $6.00 (move decimal one place left) 5% = half of 10% = $3.00
15% = 10% + 5% = $6.00 + $3.00 = $9.00
೦೦Practice: Percentages and Tips
1.Convert to decimal: 25% Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Convert to decimal: 7.5% Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Calculate 20% of $45.00 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Calculate 15% tip on $80.00 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Calculate 8% tax on $125.00 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:19
6.Bill is $65. Find 18% tip. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Convert to decimal: 6.25% Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Calculate 10% of $234.50 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Bill $95.00, tax 8%, tip 20%. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Calculate 25% of $180.00 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Food cost $120. Tax 7%. Total with tax? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Calculate 15% of $55.00 using the shortcut method. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Bill $78.50. Calculate 20% tip. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Convert to decimal: 0.5% (half percent) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Meal $42.00, tax 8.5%, tip 18%. Grand total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page20: Dr. Gene A Constant - Author
Grade 5 Mathematics
16.Server earned $156 in tips on $780 in sales. Tip percentage? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
17.Calculate 6% tax on $450.00 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
18.Bill $200. Tax 9%, tip 22%. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 1 Action Report: Restaurant Daily SummaryComplete
this manager's end-of-day report using ALL your Chapter 1 skills!
Revenue Report
1.Breakfast: $567.89, Lunch: $1,234.56, Dinner: $2,345.67. Total daily revenue? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Round the total revenue to the nearest dollar. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Compare yesterday ($4,102.50) to today. Which day earned more? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Food Cost Report
4.Ordered: 35.5 lbs beef at $6.75/lb. Total cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:21
5.Ordered: 28 lbs chicken at $4.125/lb. Total cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Produce delivery: $234.56 + $178.90 + $145.67. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Tax and Tip Analysis
7.Table 5 bill: $145.00. Calculate 8% tax. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Same table left 22% tip on food (before tax). Tip amount? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Total collected from Table 5 (food + tax + tip)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.All tips today: $567.45. If 15% average, what were total food sales? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Profit Analysis
11.Total revenue: $4,148.12. Total expenses: $1,567.89. Net profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Net profit as percentage of revenue? (Round to nearest whole percent) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page22: Dr. Gene A Constant - Author
Grade 5 Mathematics
CHAPTER 2 The Warehouse Supervisor
Chapter Goal: Master volume calculations to manage shipping and storage efficiently.
You're now the Warehouse Supervisor at a major distribution center. Every day, boxes arrive and ship out. You need to know how much space they take up, how many fit in a truck, and whether packages meet shipping size limits. Volume is your key skill!
Section 1: Filling the Warehouse — Understanding Volume
೦೦The Scenario
A shipment of boxes arrives. Each box is 2 feet long, 3 feet wide, and 4 feet tall. How much space does one box take up? How many can you fit in a storage bay?
೦೦The Skill: Volume of Rectangular Prisms
Volume = Length × Width × Height Volume measures the space inside a 3D shape in cubic units (cubic feet, cubic inches, cubic
meters).
✎ Worked Example: Finding Volume of a Box
Box dimensions: 2 ft × 3 ft × 4 ft Volume = Length × Width × Height Volume = 2 × 3 × 4 = 24 cubic feet Answer:24 cubic feet (also written as 24 ft³)
✎ Worked Example: Using Volume to Count Boxes
Storage bay: 12 ft × 10 ft × 8 ft = 960 cubic feet
Each box: 24 cubic feet Maximum boxes = 960 ÷ 24 = 40 boxes Answer:40 boxes fit in the storage bay
✎ Worked Example: Converting Cubic Inches to Cubic Feet1 foot =
12 inches 1 cubic foot = 12 × 12 × 12 = 1,728 cubic inches Box: 3,456 cubic inches ÷ 1,728 = 2 cubic feet Answer:3,456 in³ = 2 ft³
Global Sovereign University Press Page:23
೦೦Practice: Volume Calculations
1.Find volume: 5 ft × 4 ft × 3 ft Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Find volume: 8 in × 6 in × 10 in Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Box is 2 ft × 2 ft × 2 ft. Volume in cubic feet? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Shipping container: 40 ft × 8 ft × 8 ft. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Find volume: 15 cm × 10 cm × 8 cm Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Storage unit: 10 ft × 10 ft × 10 ft. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Box: 18 in × 12 in × 6 in. Volume in cubic inches? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Truck bed: 20 ft × 8 ft × 6 ft. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Find volume: 3.5 ft × 2 ft × 4 ft Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page24: Dr. Gene A Constant - Author
Grade 5 Mathematics
10.Crate: 4 ft × 3 ft × 2 ft. How many fit in 240 ft³ space? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Find volume: 2.5 m × 2 m × 3 m Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Package: 12 in × 8 in × 4 in. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Bay is 1,000 ft³. Boxes are 25 ft³ each. How many fit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Find volume: 6 ft × 4.5 ft × 3 ft Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Convert 5,184 cubic inches to cubic feet. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Pallet: 4 ft × 4 ft × 5 ft. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Shipping Costs — Volume-Based Pricing೦೦The
Scenario
Shipping companies charge by weight OR by 'dimensional weight' (volume), whichever is greater. A
lightweight but bulky package might cost more to ship than a heavy small one!
✎ Worked Example: Dimensional Weight Formula
Dimensional Weight (lbs) = (L × W × H in inches) ÷ 139 Package: 24 in × 18 in × 12 in Volume: 24 × 18 × 12 = 5,184 cubic inches
Dimensional Weight: 5,184 ÷ 139 = 37.3 lbs Answer:Ship uses 37 lbs dimensional weight if actualweight is less
Global Sovereign University Press Page:25
✎ Worked Example: Comparing Actual vs Dimensional Weight
Package weighs 25 lbs, dimensional weight is 37 lbs Shipping rate: $0.45 per pound
Use the GREATER weight: 37 lbs Cost: 37 × $0.45 = $16.65 Shipping cost:$16.65
✎ Worked Example: Calculating Shipping for Multiple Boxes5 boxes, each 12×12×12 inches, actual weight 15 lbs each
Each box volume: 1,728 in³; Dim weight: 1,728 ÷ 139 = 12.4 lbs Actual (15 lbs) > Dimensional (12.4 lbs), so use 15 lbs Total: 5 × 15 × $0.50 = $37.50 Shipping cost:$37.50 for all 5 boxes
೦೦Practice: Shipping Calculations
1.Package: 20×16×10 in. Calculate dimensional weight (÷139). Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Box weighs 18 lbs. Dim weight is 24 lbs. Which is used for shipping? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Dim weight 30 lbs, rate $0.55/lb. Shipping cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Package: 30×20×15 in. Actual weight 45 lbs. Dim weight? Which is used? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Calculate dim weight: 36×24×18 inches Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.8 packages, dim weight 15 lbs each, $0.48/lb. Total shipping? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page26: Dr. Gene A Constant - Author
Grade 5 Mathematics
7.Package: 14×14×14 in. Dim weight? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Box: actual 22 lbs, dim weight 28 lbs, rate $0.52/lb. Cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Calculate dim weight: 48×32×24 inches Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Which costs more to ship? A: 40 lbs actual, or B: 20×20×30 in (use dim)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.12 boxes × dim weight 20 lbs × $0.45/lb. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Package: 16×12×8 in, weighs 12 lbs. Dim weight? Cost at $0.50/lb? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 3: Packing the Truck — Maximizing Space
೦೦The Scenario
A delivery truck has limited space. Your job: fit as many boxes as possible without wasting space. This requires dividing the truck's volume strategically.
✎ Worked Example: How Many Boxes Fit?
Truck interior: 16 ft × 8 ft × 7 ft = 896 cubic feet
Each box: 2 ft × 2 ft × 2 ft = 8 cubic feet Maximum: 896 ÷ 8 = 112 boxes Answer:112 boxes (if perfectly packed)
Global Sovereign University Press Page:27
✎ Worked Example: Layered Packing
Truck floor: 16 ft × 8 ft. Box base: 2 ft × 2 ft
Boxes per row: 16 ÷ 2 = 8 Rows: 8 ÷ 2 = 4 Boxes per layer: 8 × 4 = 32 Layers: 7 ÷ 2 = 3 (can't stack partial boxes) Total: 32 × 3 = 96 boxes
Note:Actual fit (96) is less than theoretical max(112) due to height waste
✎ Worked Example: Mixed Box Sizes
Space: 100 cubic feet. Large boxes: 10 ft³. Small boxes: 2 ft³.
Need to ship 5 large boxes = 50 ft³ Remaining: 100 - 50 = 50 ft³ Small boxes that fit: 50 ÷ 2 = 25 small boxes Answer:5 large + 25 small boxes
೦೦Practice: Packing Efficiency
1.Truck: 20×8×8 ft. Box: 4×4×4 ft. How many fit (theoretical max)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Container: 1,000 ft³. Each crate: 25 ft³. How many crates? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Truck floor: 20×8 ft. Box base: 2×2 ft. Boxes per layer? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Truck height: 8 ft. Box height: 3 ft. Complete layers possible? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Van: 12×6×6 ft. Boxes: 2×2×2 ft. Maximum boxes? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Space: 500 ft³. Large: 20 ft³ (need 10). Small: 5 ft³. How many small fit after large? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page28: Dr. Gene A Constant - Author
Grade 5 Mathematics
7.Truck: 24×8×8 ft. Calculate total volume. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Same truck, boxes: 4×2×2 ft each. How many fit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Pallet: 4×4×4 ft = 64 ft³. Container: 2,560 ft³. How many pallets? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Floor: 16×8 ft. Box base: 4×2 ft. Boxes per layer? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Truck 1,536 ft³ holds 64 boxes. Volume per box? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Must ship 100 boxes at 8 ft³ each. Truck is 960 ft³. How many trucks needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 2 Action Report: Warehouse Daily OperationsComplete
this supervisor's shipping report!
Volume Calculations
1.New shipment: 50 boxes, each 3×2×2 ft. Total volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Storage bay: 30×20×12 ft. Total capacity?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:29
3.What percentage of the bay will the shipment use? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Shipping Analysis
4.Package: 24×18×12 in, weighs 20 lbs. Dim weight? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Using dim weight, shipping at $0.48/lb costs? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.25 packages same size. Total shipping cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Truck Loading
7.Truck: 24×8×9 ft. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Boxes: 3×2×3 ft. How many fit (theoretical)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Actually loaded 90 boxes. Capacity used? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Remaining space in cubic feet? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
CHAPTER 3 The Video Game Designer
Chapter Goal: Master the coordinate plane to design game worlds and character movement.
Welcome to the game studio! As a Video Game Designer, you use coordinates to place characters,
Page30: Dr. Gene A Constant - Author
Grade 5 Mathematics
objects, and obstacles. Every sprite has a position. Every movement is a coordinate change. Math is the language of game design!
Section 1: The Game Grid — Understanding Coordinates
೦೦The Scenario
Your game world is a coordinate grid. The center is (0, 0). The player starts there. Every treasure, enemy, and power-up has a location given as (x, y).
೦೦The Skill: Reading Coordinates
(x, y) = (horizontal position, vertical position)
• Positive x = right, Negative x = left • Positive y = up, Negative y = down • Origin (0, 0) = center of the grid
✎ Worked Example: Plotting a Point
Place the treasure at (4, 3) Step 1: Start at origin (0, 0) Step 2: Move 4 units RIGHT (positive x) Step 3: Move 3 units UP (positive y)
Location:4 right, 3 up from center
✎ Worked Example: Reading a Point
An enemy is 5 units left and 2 units down from origin
Left = negative x → x = -5 Down = negative y → y = -2 Coordinates:(-5, -2)
✎ Worked Example: The Four Quadrants
Quadrant I: (+, +) — upper right Quadrant II: (-, +) — upper left Quadrant III: (-, -) — lower left Quadrant IV: (+, -) — lower right
Example:(3, -4) is in Quadrant IV
೦೦Practice: Reading and Plotting Coordinates
1.Plot and name the quadrant: (5, 3) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Plot and name the quadrant: (-4, 2) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:31
3.Plot and name the quadrant: (-3, -5) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Plot and name the quadrant: (6, -2) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Write coordinates: 7 right, 4 up from origin Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Write coordinates: 3 left, 6 down from origin Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Which quadrant contains (-8, -1)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Write coordinates: 5 left, 2 up from origin Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.What are the coordinates of the origin? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Plot: (0, 5). What axis is this point on? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Plot: (-4, 0). What axis is this point on? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Write coordinates: 9 right, 7 down from origin Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page32: Dr. Gene A Constant - Author
Grade 5 Mathematics
13.Which quadrant contains (100, 50)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Player at (-2, 4). Describe position in words. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Enemy at (0, -6). Describe position in words. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Power-up is 8 left, 3 up. Write coordinates. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Character Movement — Coordinate Changes
೦೦️The Scenario
Your character moves across the screen. Each arrow key changes the coordinates. Right adds to x.
Up adds to y. Track where the player ends up!
✎ Worked Example: Moving a Character
Player starts at (2, 3) Moves: Right 4, Up 2 New x: 2 + 4 = 6 New y: 3 + 2 = 5 New position:(6, 5)
✎ Worked Example: Negative Movement
Player at (5, 4). Moves: Left 7, Down 6 Left = subtract from x: 5 - 7 = -2 Down = subtract from y: 4 - 6 = -2 New position:(-2, -2)
✎ Worked Example: Finding the Movement
Character went from (1, 2) to (7, 5)
Horizontal change: 7 - 1 = 6 (moved 6 right) Vertical change: 5 - 2 = 3 (moved 3 up)
Movement:Right 6, Up 3
Global Sovereign University Press Page:33
✎ Worked Example: Distance Between Points (Horizontal/Vertical)Treasure at (8, 3), Player at (2, 3) Same y-coordinate → horizontal distance
Distance: |8 - 2| = 6 units Distance:6 units apart
೦೦Practice: Movement Calculations
1.Start (3, 2). Move right 5, up 4. New position? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Start (0, 0). Move left 3, down 7. New position? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Start (-4, 5). Move right 10, down 8. New position? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Start (6, -2). Move left 4, up 6. New position? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Went from (2, 1) to (8, 1). Describe the movement. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Went from (5, 7) to (5, 2). Describe the movement. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Went from (-3, 4) to (4, -2). Horizontal change? Vertical change? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Distance between (0, 0) and (0, 9)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page34: Dr. Gene A Constant - Author
Grade 5 Mathematics
9.Distance between (4, 5) and (10, 5)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Start (8, 8). Move left 12, down 12. New position? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Player needs to reach (7, 3) from (2, 8). What moves? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Went from (10, 10) to (3, 4). Total horizontal + vertical change? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Start (-5, -5). Move right 5, up 5. New position? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Distance between (-3, 0) and (6, 0)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Start (0, 4). After moving, now at (-6, -3). What was the movement? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Character makes 4 moves: Right 3, Up 2, Left 5, Down 4. Starting from origin, final position? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
Section 3: Game Objects — Shapes and Boundaries
೦೦The Scenario
Game objects have boundaries. A power-up zone might be a rectangle from (2, 1) to (6, 4). You need to know if the player is inside the zone!
Global Sovereign University Press Page:35
✎ Worked Example: Drawing a Rectangle
Rectangle with corners at (1, 1), (5, 1), (5, 4), (1, 4) Width: 5 - 1 = 4 units
Height: 4 - 1 = 3 units Dimensions:4 units wide × 3 units tall
✎ Worked Example: Is the Player in the Zone?
Safe zone: x from 2 to 8, y from 1 to 5
Player at (6, 3) Is 2 ≤ 6 ≤ 8? Yes Is 1 ≤ 3 ≤ 5? Yes Answer:Player IS in the safe zone
✎ Worked Example: Perimeter of Game Boundary
Boundary corners: (0, 0), (10, 0), (10, 8), (0, 8) Width: 10 units, Height: 8 units
Perimeter: 2(10) + 2(8) = 36 units Boundary perimeter:36 units
೦೦Practice: Shapes and Boundaries
1.Rectangle corners: (2, 3), (7, 3), (7, 6), (2, 6). Width? Height? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Square corners: (0, 0), (5, 0), (5, 5), (0, 5). Side length? Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Zone: x from 3 to 9, y from 2 to 7. Is (5, 4) inside? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Zone: x from -4 to 4, y from -3 to 3. Is (5, 2) inside? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page36: Dr. Gene A Constant - Author
Grade 5 Mathematics
5.Rectangle corners at (1, 1), (8, 1), (8, 5), (1, 5). Area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Draw rectangle with width 6 starting at (2, 3) going right and up 4. List all 4 corners. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Danger zone: x from -10 to -2, y from 0 to 6. Is (-5, 3) in danger? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Safe zone: x from 0 to 20, y from 0 to 15. Area of safe zone? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Rectangle: (3, 2) to (9, 8). Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Player must stay in x: 5 to 15, y: 10 to 20. Player at (12, 22). Safe? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Enemy patrol area: corners (0, 0), (6, 0), (6, 4), (0, 4). Area?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Two zones: Zone A (0,0) to (5,5), Zone B (4,4) to (9,9). Do they overlap? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:37
Chapter 3 Action Report: Game Level Design
Design a complete game level using coordinates!
Place Game Objects
1.Player spawn point: 3 right, 2 up from origin. Coordinates? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Enemy 1 at (-5, 4). Enemy 2 at (5, 4). Distance between them? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Treasure in Quadrant III, 6 left and 3 down. Coordinates? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Movement Sequences
4.Player starts (0, 0). Moves: Right 4, Up 3, Left 2, Up 2. Final position? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.To reach treasure at (8, 7) from current (3, 2), what moves needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Player at (-4, -4) needs to reach origin. Shortest moves? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Level Boundaries
7.Play area: corners at (-10, -8), (10, -8), (10, 8), (-10, 8). Width? Height? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Same play area. Total area in square units? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page38: Dr. Gene A Constant - Author
Grade 5 Mathematics
9.Safe zone: x from -5 to 5, y from -4 to 4. Is player at (6, 3) safe? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Boss arena: rectangle from (15, 10) to (25, 18). Area of arena? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
CHAPTER 4 The Catering Chef
Chapter Goal: Master fraction operations to scale recipes for events of any size.
You're the head chef for a catering company. Today's challenge: a wedding with 150 guests, a corporate lunch for 45, and a birthday party for 20. Your base recipes serve 8. Time to scale up and down using fractions!
Section 1: Combining Ingredients — Unlike Denominators
೦೦The Scenario
Your cake recipe needs 2/3 cup of butter and 3/4 cup of oil. How much total fat? The denominators are different, so you can't just add the numerators. You need a common denominator!
✎ Worked Example: Finding the LCD
Add: 2/3 + 3/4 Step 1: Find Least Common Denominator (LCD)
Multiples of 3: 3, 6, 9, 12, 15... Multiples of 4: 4, 8, 12, 16... LCD = 12 Result:Use 12 as common denominator
✎ Worked Example: Converting and Adding
2/3 + 3/4 = ?/12 + ?/12 2/3 = 8/12 (multiply top and bottom by 4) 3/4 = 9/12 (multiply top and bottom by 3) 8/12 + 9/12 = 17/12 = 1 5/12 Answer:1 5/12 cups of fat total
Global Sovereign University Press Page:39
✎ Worked Example: Adding Three Fractions
1/2 + 1/3 + 1/4 = ? LCD of 2, 3, 4 = 12 1/2 = 6/12, 1/3 = 4/12, 1/4 = 3/12 6/12 + 4/12 + 3/12 = 13/12 = 1 1/12 Answer:1 1/12
✎ Worked Example: Adding Mixed Numbers with Unlike Denominators2 1/3 + 1 3/4 = ? Add whole numbers: 2 + 1 = 3 Add fractions: 1/3 + 3/4 = 4/12 + 9/12 = 13/12 = 1 1/12 Combine: 3 + 1 1/12 = 4 1/12 Answer:4 1/12
೦೦Practice: Adding Fractions with Unlike Denominators
1.Add: 1/2 + 1/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Add: 2/3 + 1/4
Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
3.Add: 3/4 + 2/5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Add: 1/6 + 1/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Add: 2/5 + 1/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Add: 3/8 + 1/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page40: Dr. Gene A Constant - Author
Grade 5 Mathematics
7.Add: 1/2 + 1/4 + 1/8 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Add: 2/3 + 1/6 + 1/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Add: 1 1/2 + 2 1/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Add: 2 2/3 + 1 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Recipe: 1/2 cup butter + 2/3 cup oil. Total fat? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Add: 3/5 + 2/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Add: 4/5 + 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Add: 2 1/4 + 3 2/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Add: 1/3 + 1/4 + 1/6 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:41
16.Ingredients: 3/4 cup + 2/3 cup + 1/2 cup. Total?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Adjusting Portions — Subtracting Fractions
➖The Scenario
You have 2 1/2 cups of flour but the recipe only needs 1 3/4 cups. How much will be left over? Subtracting fractions requires the same common denominator technique.
✎ Worked Example: Subtracting Unlike Denominators
3/4 - 1/3 = ?
LCD = 12 3/4 = 9/12, 1/3 = 4/12 9/12 - 4/12 = 5/12 Answer:5/12
✎ Worked Example: Subtracting Mixed Numbers
2 1/2 - 1 3/4 = ? Convert to LCD (4): 2 2/4 - 1 3/4
Need to borrow: 2 2/4 = 1 6/4 1 6/4 - 1 3/4 = 3/4 Answer:3/4 cup left over
✎ Worked Example: Subtracting from a Whole Number3 - 2/5 = ? 3 = 2 5/5 2 5/5 - 2/5 = 2 3/5 Answer:2 3/5
೦೦Practice: Subtracting Fractions
1.Subtract: 3/4 - 1/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Subtract: 5/6 - 1/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page42: Dr. Gene A Constant - Author
Grade 5 Mathematics
3.Subtract: 2/3 - 1/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Subtract: 7/8 - 1/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Subtract: 4/5 - 2/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Subtract: 2 - 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Subtract: 3 - 1 1/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Subtract: 2 1/2 - 1 2/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Subtract: 4 1/4 - 2 1/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Subtract: 5 1/3 - 2 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Have 3 cups flour, need 2 1/3 cups. Remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:43
12.Subtract: 7/10 - 2/5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Subtract: 5/6 - 3/8 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Subtract: 6 - 2 2/5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Subtract: 3 1/6 - 1 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Had 4 1/2 lbs meat, used 2 5/8 lbs. Remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 3: Scaling Recipes — Multiplying Fractions
✖️The Scenario
Your recipe serves 8, but you need to serve 20. That's 20/8 = 2 1/2 times the recipe. If the original calls for 2/3 cup sugar, how much do you need now?
✎ Worked Example: Multiplying Fractions
2/3 × 2 1/2 = ? Convert mixed to improper: 2 1/2 = 5/2
Multiply: 2/3 × 5/2 = 10/6 = 5/3 = 1 2/3 Answer:1 2/3 cups sugar needed
✎ Worked Example: Multiplying a Whole Number by a Fraction
Triple the recipe: 3 × 3/4 cup = ? 3/1 × 3/4 = 9/4 = 2 1/4 Answer:2 1/4 cups
Page44: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Finding a Fraction of a Fraction
Use 1/2 of the 2/3 cup you have 1/2 × 2/3 = 2/6 = 1/3 Answer:1/3 cup
✎ Worked Example: Scaling Down
Recipe serves 8, need to serve 4. Scale factor: 4/8 = 1/2 Original: 2 cups flour. New: 2 × 1/2 = 1 cup Answer:Use 1 cup flour for half recipe
೦೦Practice: Multiplying Fractions
1.Multiply: 1/2 × 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Multiply: 2/3 × 3/5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Multiply: 4 × 2/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Multiply: 1/4 × 2/5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Multiply: 5/6 × 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Triple: 2/3 cup × 3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Multiply: 2 1/2 × 1/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:45
8.Multiply: 1 3/4 × 2/5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Scale recipe ×1.5: 2/3 cup × 3/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Half recipe: 3/4 cup × 1/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Recipe ×4: 1 1/2 cups × 4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Multiply: 3/8 × 2/3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Multiply: 5 × 3/10 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Multiply: 2 2/3 × 3/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Quarter recipe: 2 cups × 1/4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Scale ×2.5: 3/4 cup × 5/2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page46: Dr. Gene A Constant - Author
Grade 5 Mathematics
Chapter 4 Action Report: Wedding Catering
Plan the food for a 150-person wedding!
Recipe Scaling
1.Base recipe serves 8. Wedding has 150 guests. Scale factor as a fraction? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Simplify: 150/8 as a mixed number Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Recipe needs 2/3 cup butter. Scaled amount needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Ingredient Totals
4.Appetizers: 1/4 lb cheese per person. Total cheese for 150? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Main course needs: 2 1/3 cups sauce base, 1 3/4 cups cream. Total liquid? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Dessert: 3/4 cup sugar + 2/3 cup flour + 1/2 cup butter. Total dry + wet? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Leftover Calculations
7.Bought 40 lbs flour, used 37 2/3 lbs. Remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Had 25 gallons milk, used 22 5/8 gallons. Left over? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:47
9.Ordered 50 lbs of beef. Used 3/4 of it. Pounds used? Pounds remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Budget was $2,500. Spent 7/8 of budget. Amount spent? Amount remaining? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
CHAPTER 5 The Landscaping Contractor
Chapter Goal: Calculate areas of complex shapes and convert measurements for
professional landscaping projects.
Yourunalandscapingcompany.Today'sproject:designandinstallabackyardmakeoverincluding apatio,gardenbeds,lawnarea,andwalkways.Accuratemeasurementsmeanaccuratebids—and profit!
Section 1: Irregular Yards — Breaking Down Complex Shapes
೦೦The Scenario
Most yards aren't simple rectangles. An L-shaped lawn, a patio with a cutout for a tree, gardens with curved edges approximated as shapes—you need to break these into simpler pieces.
✎ Worked Example: L-Shaped Lawn
Yard is L-shaped: Main section 40×30 ft, extension 20×15 ft Area = Rectangle 1 + Rectangle 2 = (40 × 30) + (20 × 15) = 1,200 + 300 = 1,500 sq ft Answer:1,500 square feet of lawn
✎ Worked Example: Patio with Cutout
Patio: 20×15 ft with 4×4 ft tree cutout Full rectangle: 20 × 15 = 300 sq ft Cutout: 4 × 4 = 16 sq ft Actual patio: 300 - 16 = 284 sq ft Answer:284 square feet of patio
✎ Worked Example: Multiple Garden Beds
Three rectangular beds: 8×4, 10×3, 6×5 ft
Bed 1: 8 × 4 = 32 sq ft Bed 2: 10 × 3 = 30 sq ft Bed 3: 6 × 5 = 30 sq ft Total: 32 + 30 + 30 = 92 sq ft Answer:92 square feet of garden beds
Page48: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Finding Remaining Lawn Area
Total yard: 50×40 = 2,000 sq ft
Patio: 284 sq ft, Gardens: 92 sq ft, Walkway: 45 sq ft Features total: 284 + 92 + 45 = 421 sq ft Lawn: 2,000 - 421 = 1,579 sq ft Answer:1,579 square feet of lawn
೦೦Practice: Complex Area Calculations
1.L-shaped: 30×20 ft main + 15×10 ft extension. Total area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Rectangle 25×18 ft with 5×5 ft cutout. Area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Three beds: 12×4, 8×6, 10×5 ft. Total area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Yard 60×45 ft. Patio 15×12 ft. Remaining lawn? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.U-shaped patio: main 20×10, two extensions each 8×10. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Pool area: 30×20 ft rectangle minus 15×10 ft pool. Deck area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Two L-shapes combined: each is 20×15 + 10×8. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:49
8.Yard: 2,500 sq ft. Subtract: patio 200, gardens 150, shed 80. Lawn? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.T-shaped walkway: stem 15×3 ft, top 12×3 ft. Total area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Rectangle 40×25 with two cutouts: 6×6 and 8×4. Remaining area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Border: outer 50×40, inner 46×36. Border area only? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Four identical flower beds, each 6×4 ft. Total bed area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Borders and Fences — Perimeter Calculations
೦೦The Scenario
Edging around garden beds, fencing around yards, borders around patios—all require perimeter calculations. And complex shapes have longer perimeters than you might expect!
✎ Worked Example: Perimeter of L-Shaped Garden
L-shape: 20 ft, turns left 10 ft, goes 12 ft, turns left 8 ft, connects back Add all outer edges: 20 + 10 + 12 + 8 + 8 + 18 = 76 ft
(Draw it out to find all sides!) Answer:76 feet of edging needed
✎ Worked Example: Fencing with a Gate Opening
Rectangular yard: 80×60 ft. Gate is 4 ft wide. Full perimeter: 2(80) + 2(60) = 280 ft Minus gate: 280 - 4 = 276 ft Answer:276 feet of fencing needed
Page50: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Multiple Beds, Multiple Borders
Three beds: 8×4, 10×3, 6×5 ft
Bed 1 perimeter: 2(8) + 2(4) = 24 ft Bed 2 perimeter: 2(10) + 2(3) = 26 ft Bed 3 perimeter: 2(6) + 2(5) = 22 ft Total edging: 24 + 26 + 22 = 72 ft Answer:72 feet of edging for all beds
೦೦Practice: Perimeter Calculations
1.Rectangle 45×30 ft. Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Square garden, side 12 ft. Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Fence 60×40 yard with 3 ft gate. Fence needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Four beds: 10×4, 8×5, 12×3, 6×6. Total edging? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.L-shaped bed: 15 ft, 8 ft, 9 ft, 4 ft, 6 ft, 12 ft. Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Circular approximation: 8-sided shape, each side 4 ft. Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Border around 20×15 pool, border is 3 ft wide. Outer perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:51
8.Three identical square beds, side 5 ft each. Total edging? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Yard 100×75 ft. Two gates, each 4 ft. Fence needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Patio 18×14 ft with decorative border. Linear feet of border? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Rectangle 50×35 ft minus 10×10 cutout. Perimeter of remaining shape? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.U-shaped garden: outer dims 24×16 ft, inner cutout 12×8 ft. Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 3: Ordering Materials — Area to Quantity
೦೦The Scenario
You know the area. Now you need to order materials: sod by the pallet, mulch by the cubic yard,
pavers by the square foot. Converting area to material quantity is where profit is made or lost!
✎ Worked Example: Sod Coverage
Lawn area: 1,500 sq ft. Sod pallets cover 450 sq ft each. Pallets needed: 1,500 ÷ 450 = 3.33 Round UP (can't buy partial pallets): 4 pallets Cost at $180/pallet: 4 × $180 = $720 Order:4 pallets, $720
✎ Worked Example: Mulch by Cubic Yard
Garden beds: 92 sq ft. Mulch depth: 3 inches = 0.25 ft Volume: 92 × 0.25 = 23 cubic feet Convert: 23 ÷ 27 = 0.85 cubic yards (27 cu ft per cu yd)
Round up: 1 cubic yard Order:1 cubic yard of mulch
Page52: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Pavers with Waste Factor
Patio: 284 sq ft. Add 10% for cuts/waste. 284 × 1.10 = 312.4 sq ft
Pavers: 4 sq ft each. Quantity: 312.4 ÷ 4 = 78.1 Round up: 79 pavers Order:79 pavers
೦೦Practice: Material Calculations
1.Lawn 2,000 sq ft. Sod pallets cover 500 sq ft. How many pallets? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Same lawn. Pallets cost $200 each. Total cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Garden 150 sq ft, mulch 4 in deep. Volume in cubic feet? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Convert 54 cubic feet to cubic yards. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Patio 320 sq ft + 10% waste. Pavers are 2 sq ft each. How many? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Edging 72 ft. Pieces are 8 ft long. How many pieces? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Gravel path: 45 sq ft × 2 in deep. Volume in cubic feet? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:53
8.Fence 276 ft. Panels are 8 ft wide. How many panels? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Seed covers 1,000 sq ft per bag. Lawn is 3,500 sq ft. Bags needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Mulch: $45 per cubic yard. Need 3.5 cu yd (round up). Cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Pavers: $3.50 each. Need 79 pavers. Material cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Total project: sod $720, mulch $180, pavers $277. Grand total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 5 Action Report: Backyard Makeover BidCreate a
complete materials bid for a backyard project!
Area Calculations
1.Yard: 60×45 ft. Total area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Patio: 18×15 ft with 3×3 tree cutout. Patio area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Three garden beds: 10×4, 8×6, 12×5 ft. Total bed area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Remaining lawn area after patio and beds? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page54: Dr. Gene A Constant - Author
Grade 5 Mathematics
Perimeter Calculations
5.Fence entire yard with one 4 ft gate. Fence length? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Edging around all three garden beds. Total edging? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Patio border (outer edge only). Length? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Material Order
8.Sod for lawn. Pallets cover 400 sq ft. Pallets needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Mulch for beds, 3 in deep. Cubic yards needed? (Round up) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Pavers for patio + 10% waste. Each paver is 1 sq ft. Quantity? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:55
CHAPTER 6 The Sports Analyst
Chapter Goal: Master advanced statistics to analyze team performance and make
predictions.
You've been hired as the data analyst for a professional sports team. The coach wants to know: Who's the most consistent player? Is our scoring improving? What should we expect next game? Statistics tell the story!
Section 1: Player Performance — Mean, Median, Mode
೦೦The Scenario
A player scored these points in 7 games: 12, 18, 15, 22, 15, 28, and 15. What's their average? What score appears most? What's the middle value? Each measure tells you something different.
✎ Worked Example: Finding the Mean (Average)
Scores: 12, 18, 15, 22, 15, 28, 15 Step 1: Add all values: 12+18+15+22+15+28+15 = 125 Step 2: Count values: 7 games Step 3: Divide: 125 ÷ 7 = 17.86
Mean:17.86 points per game (round to 17.9)
✎ Worked Example: Finding the Median (Middle Value)First,
order the data: 12, 15, 15, 15, 18, 22, 28 Count: 7 values (odd number)
Middle position: (7+1) ÷ 2 = 4th value The 4th value is 15.
Median:15 points
✎ Worked Example: Finding the Mode (Most Frequent)Scores: 12, 15, 15, 15, 18, 22, 28 Count each: 12(1), 15(3), 18(1), 22(1), 28(1)
15 appears most often (3 times) Mode:15 points
✎ Worked Example: Median with Even Number of ValuesScores: 10, 14, 18, 22, 26, 30 (6 values)
Middle positions: 3rd and 4th values Values: 18 and 22
Median = (18 + 22) ÷ 2 = 20 Median:20
Page56: Dr. Gene A Constant - Author
Grade 5 Mathematics
೦೦Practice: Mean, Median, Mode
1.Find mean: 8, 12, 15, 9, 11 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Find median: 23, 45, 67, 34, 56 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Find mode: 5, 8, 5, 9, 5, 8, 7 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Scores: 14, 18, 22, 16, 20. Find mean. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Scores: 88, 92, 75, 84, 96, 88. Find median. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Find all three (mean, median, mode): 10, 15, 10, 20, 10, 25 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Points: 24, 18, 30, 22, 26. Mean? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Rebounds: 8, 12, 8, 10, 8, 14, 8. Mode? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Assists: 5, 7, 9, 11, 13. Median? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:57
10.Scores: 100, 85, 92, 88, 95, 90, 85. Find mean and mode. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Six games: 15, 18, 21, 24, 27, 30. Median? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Data: 45, 50, 55, 50, 45, 50. Find mode. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
13.Team scores: 78, 82, 75, 90, 85. Mean? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Eight values: 3, 5, 7, 9, 11, 13, 15, 17. Median? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Goals: 2, 0, 3, 1, 2, 4, 2, 1. Find mean and mode. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.If mean of 5 numbers is 20, what's the sum of all 5? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Consistency Check — Range and Outliers
೦೦The Scenario
Two players both average 20 points. But Player A scores between 18-22 every game, while Player
B swings from 8 to 35. Who's more consistent? Range tells you!
✎ Worked Example: Finding the Range
Player A scores: 18, 20, 22, 19, 21 Range = Highest - Lowest = 22 - 18 = 4 Range:4 points (very consistent)
Page58: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Comparing Consistency
Player A: Range = 4 (scores 18-22) Player B scores: 8, 15, 25, 35, 17. Range = 35 - 8 = 27 Player A has smaller range = more consistent Analysis:Player A is more reliable
✎ Worked Example: Identifying Outliers
Team scores: 72, 75, 78, 74, 45, 76, 73
Most scores cluster around 72-78 45 is much lower than the rest—it's an outlier Without outlier, mean = 74.7. With outlier, mean = 70.4
Impact:One bad game dropped average by 4.3 points
೦೦Practice: Range and Data Analysis
1.Find range: 45, 52, 48, 67, 51 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Find range: 88, 92, 85, 90, 87 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Scores: 12, 15, 18, 45, 14, 16. Identify the outlier. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Player A range: 8. Player B range: 22. Who's more consistent? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Find range: 100, 95, 102, 98, 97, 103 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Data: 25, 28, 26, 27, 5, 29. Find range with and without outlier. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:59
7.Rebounds: 8, 10, 9, 11, 8, 35. Outlier? Range without it? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Which set is more consistent? A: 50,52,48,51 or B: 30,70,45,55 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Find range: 3.5, 4.2, 3.8, 4.0, 3.9 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Scores: 78, 82, 80, 15, 79, 81. Mean with outlier? Without? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Assists: 5, 7, 6, 8, 5, 7, 6. Range? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Game times (min): 45, 48, 52, 47, 90, 46. Outlier? Adjusted range? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 3: Future Performance — Using Data to Predict
೦೦The Scenario
Based on past performance, what should we expect in future games? If a player averages 18 points, we can predict they'll score around 18 next game. Projections help with planning!
✎ Worked Example: Predicting Season Totals
Player averaged 22 points in first 10 games Season has 82 games
Predicted total: 22 × 82 = 1,804 points Projection:1,804 points for the season
✎ Worked Example: Predicting Team Wins
Team won 12 of first 20 games = 60% win rate Season has 82 games
Predicted wins: 0.60 × 82 = 49.2 ≈ 49 wins Projection:About 49 wins this season
Page60: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: What Score is Needed?
Player wants 20-point average after 5 games Current scores: 18, 22, 16, 24. Sum = 80
Need: 20 × 5 = 100 total points Must score: 100 - 80 = 20 points in game 5 Target:20 points needed
೦೦Practice: Predictions and Projections
1.Player averages 15 points. Predict total for 50-game season. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Team wins 70% of games. In 80-game season, predicted wins?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Scores: 22, 18, 24. What's needed in game 4 for 22 average? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Player averages 8 rebounds in 15 games. Season projection for 82 games? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Team scored 450 points in 5 games. Average? 20-game projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Win rate 55%. Predict wins out of next 40 games. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Current average: 12 assists. Need 15 average after 4 games. Game 4 target? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:61
8.First 10 games: 180 points total. Next 10 games predict? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Scores: 25, 30, 20, 15. Need 24 average after 5 games. Game 5 need? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Team averages 95 points/game. Predict 82-game season total. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Player shoots 80% free throws. Predict makes out of next 50 attempts. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.First half average: 18 pts. Second half goal: 22 average. What total needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 6 Action Report: Season Analysis
Analyze this player's performance data!
Games 1-8 scores: 22, 18, 25, 15, 28, 20, 22, 30
Statistical Analysis
1.Calculate the mean score. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Find the median score. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Find the mode (if any). Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page62: Dr. Gene A Constant - Author
Grade 5 Mathematics
4.Calculate the range. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Consistency and Outliers
5.Is the player consistent? Explain using range. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Are there any outliers? If yes, which? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Recalculate mean without the lowest score. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Projections
8.Based on current average, predict 82-game season total. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Player wants 25 average. What must they score in game 9? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.If scoring continues at this rate, will player reach 2,000 season points? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:63
CHAPTER 7 The Travel Agent
Chapter Goal: Master time zones, elapsed time, and large number calculations for global
travel planning.
Welcome to the travel agency! Clients want trips across the country and around the world. You'll calculate flight times across time zones, figure out arrival times, and work with prices in the thousands and tens of thousands. Let's plan some trips!
Section 1: Around the World — Time Zone Calculations
೦೦The Scenario
A client in New York wants to call their hotel in Los Angeles. NY is Eastern Time, LA is Pacific Time —3 hours behind. If it's 2:00 PM in NY, what time is it in LA?
೦೦Key Time Zones (US)
Eastern (ET) → Central (CT): subtract 1 hour Central (CT) → Mountain (MT): subtract 1 hour Mountain (MT) → Pacific (PT): subtract 1 hour Eastern to Pacific: subtract 3 hours
✎ Worked Example: Converting Eastern to Pacific
It's 2:00 PM Eastern Time Pacific is 3 hours behind Eastern 2:00 PM - 3 hours = 11:00 AM Answer:11:00 AM Pacific Time
✎ Worked Example: Converting Pacific to Eastern
Flight departs LA at 8:00 AM Pacific Eastern is 3 hours ahead of Pacific 8:00 AM + 3 hours = 11:00 AM Answer:11:00 AM Eastern Time when flight departs
✎ Worked Example: International: London to New YorkLondon
(GMT) is 5 hours ahead of New York (ET) Meeting in London at 3:00 PM GMT New York time: 3:00 PM - 5 hours = 10:00 AM ET Answer:10:00 AM Eastern Time
Page64: Dr. Gene A Constant - Author
Grade 5 Mathematics
೦೦Practice: Time Zone Conversions
1.3:00 PM Eastern. What time is it Pacific? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.9:00 AM Pacific. What time is it Eastern? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Noon Central. What time is it Mountain? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.5:00 PM Mountain. What time is it Eastern? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Call scheduled for 2:00 PM Pacific. What time in Central? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Flight departs NY (ET) at 6:00 AM. What time is that in LA (PT)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Meeting in Chicago (CT) at 10:00 AM. Time in Denver (MT)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.London is 5 hours ahead of NY. If NY is 8:00 PM, London time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Tokyo is 14 hours ahead of LA. LA is 3:00 PM. Tokyo time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:65
10.Paris is 6 hours ahead of Eastern. Paris is 8:00 PM. Eastern time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Hawaii is 5 hours behind Eastern. NY is 4:00 PM. Hawaii time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Conference call: 9 AM Pacific. Times for CT, ET, and London (8 hrs ahead of PT)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Flight Planning — Elapsed Time with Time Zones
✈️The Scenario
A flight leaves New York at 8:00 AM Eastern and flies 5 hours to Los Angeles. What time does it arrive in LA local time? You must account for both the flight duration AND the time zone change!
✎ Worked Example: Cross-Country Flight
Depart NY: 8:00 AM Eastern Flight time: 5 hours Step 1: Add flight time: 8:00 AM + 5 hours = 1:00 PM Eastern Step 2: Convert to Pacific: 1:00 PM - 3 hours = 10:00 AM Pacific Arrival:10:00 AM Pacific Time
✎ Worked Example: Eastbound Flight (Gaining Time)
Depart LA: 11:00 AM Pacific Flight time: 5 hours
Step 1: Add flight time: 11:00 AM + 5 hours = 4:00 PM Pacific Step 2: Convert to Eastern: 4:00 PM + 3 hours = 7:00 PM Eastern Arrival:7:00 PM Eastern Time
✎ Worked Example: Overnight International Flight
Depart NY: 7:00 PM Eastern (Thursday) Flight to London: 7 hours, London is 5 hours ahead Step 1: 7:00 PM + 7 hours = 2:00 AM Eastern (Friday) Step 2: Convert: 2:00 AM + 5 hours = 7:00 AM London time (Friday) Arrival:7:00 AM Friday, London time
Page66: Dr. Gene A Constant - Author
Grade 5 Mathematics
೦೦Practice: Flight Time Calculations
1.DepartChicago(CT)9:00AM,fly4hourstoDenver(MT).Arrivallocaltime? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Depart LA 6:00 AM PT, fly 5.5 hours to NY. Arrival ET? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Depart NY 3:00 PM ET, fly 6 hours to London (5 hrs ahead). Arrival? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Depart Denver 2:00 PM MT, fly 3 hours to Chicago. Arrival CT? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Flight is 4 hours. Depart Seattle (PT) 8:00 AM, arrive Dallas (CT). Arrival? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Depart Miami (ET) 11:00 PM, fly 5 hours to LA. Arrival PT? What day? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Depart London 10:00 AM, fly 8 hours to NY (5 hrs behind). Arrival ET? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Round trip: NY to LA (5 hrs) and back (5 hrs). Depart NY 6 AM ET. Return ET? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Layover: Arrive Chicago 2:00 PM CT. Depart 5:30 PM CT. Layover time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:67
10.DepartTokyo1:00PM(14hrsaheadofPT),fly11hourstoLA.ArrivalPT? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Depart Phoenix (MT) 7:30 AM, fly 2 hr 45 min to Dallas (CT). Arrival? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Depart NY noon ET, arrive Paris 7:00 AM next day (6 hrs ahead). Flight time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 3: Trip Budgeting — Large Number Calculations
೦೦The Scenario
A family of 4 wants a 7-day trip. Airfare is $450 per person, hotel is $189 per night, and activities
budget is $200 per day. Calculate the total trip cost and compare packages!
✎ Worked Example: Calculating Total Trip Cost
Airfare: 4 people × $450 = $1,800
Hotel: 7 nights × $189 = $1,323 Activities: 7 days × $200 = $1,400
Food: 7 days × $150 = $1,050 Total: $1,800 + $1,323 + $1,400 + $1,050 = $5,573 Trip cost:$5,573
✎ Worked Example: Comparing Packages
Package A: $1,200/person all-inclusive × 4 = $4,800 Package B: Separate booking = $5,573 (from above) Savings: $5,573 - $4,800 = $773
Better deal:Package A saves $773
✎ Worked Example: Per-Person Cost
Total trip: $5,573 for 4 people
Per person: $5,573 ÷ 4 = $1,393.25 Cost per person:$1,393.25
೦೦Practice: Travel Cost Calculations
1.Airfare $385/person × 6 people. Total airfare? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page68: Dr. Gene A Constant - Author
Grade 5 Mathematics
2.Hotel $225/night × 5 nights. Total hotel cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Family of 5, all-inclusive $950/person. Total cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Trip costs: Air $2,400, Hotel $1,575, Food $840, Activities $650. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Total trip $6,240 for 4 people. Cost per person? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Package A: $4,500 total. Package B items total $5,125. Savings with A? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Budget $8,000. Costs total $7,450. Under budget by how much? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Rental car: $89/day × 10 days + $45 insurance. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Cruise: $1,299/person × 4 + $400 port fees + $600 excursions. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Hotel upgrade: $189/night vs $249/night for 7 nights. Difference? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:69
11.6 people split $5,400 trip equally. Each pays? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Flight $525, hotel $1,400, food $500, activities $375, transport $200. Grand total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 7 Action Report: Family Vacation PlanningPlan a
complete cross-country vacation!
Flight Schedule
1.Flight departs Boston (ET) 7:30 AM, arrives San Francisco (PT) after 6 hours. Arrival local? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
2.Return flight departs SF 4:00 PM PT, 5.5 hour flight. Arrival in Boston ET? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Total travel time (both flights)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Time Zone Coordination
4.Family in Boston wants to video call family at hotel in SF at 8 PM Pacific. Boston time? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
5.Dinner reservation in SF at 7:00 PM. Reminder set for Boston time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page70: Dr. Gene A Constant - Author
Grade 5 Mathematics
6.Flight confirmation says departure 7:30 AM ET. Convert to Pacific and Central.
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Budget
7.Airfare: $475/person × 4. Hotel: $199/night × 6 nights. Total air + hotel? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Food budget $175/day × 7 days. Activities $125/day × 5 days. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Car rental $79/day × 7 days + $55 insurance. Total transport? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Grand total for entire trip? Per person cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:71
CHAPTER 8 The Small Business Owner
Chapter Goal: Master profit/loss calculations and financial projections to run a successful
business.
Congratulations—you're opening your own business! Every decision affects your profit: pricing, costs, expenses, growth. Understanding the numbers is the difference between success and failure.
Section 1: The Bottom Line — Revenue, Cost, Profit
೦೦The Scenario
You sell handmade candles. Each candle costs $4 to make and sells for $12. You sold 150 candles this month. What's your profit?
೦೦Key Formulas
Revenue = Price × Quantity Sold Cost = Cost per item × Quantity Profit = Revenue - Total Costs
✎ Worked Example: Calculating Profit
Selling price: $12/candle. Cost: $4/candle. Sold: 150
Revenue: $12 × 150 = $1,800 Cost of goods: $4 × 150 = $600
Profit: $1,800 - $600 = $1,200 Profit:$1,200
✎ Worked Example: Including Fixed Costs
Same candle business, but add: Rent $200, Utilities $50, Supplies
$75 Fixed costs: $200 + $50 + $75 = $325
Net profit: $1,200 - $325 = $875 Net profit:$875 after all expenses
✎ Worked Example: Profit Margin Percentage
Revenue: $1,800. Net profit: $875 Profit margin = (Profit ÷ Revenue) × 100 = ($875 ÷ $1,800) × 100 = 48.6%
Profit margin:48.6%
Page72: Dr. Gene A Constant - Author
Grade 5 Mathematics
೦೦Practice: Revenue, Cost, and Profit
1.Sell 200 items at $15 each. Revenue? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Items cost $6 each to make. Cost for 200 items? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Revenue $3,000. Costs $1,200. Profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Sold 85 shirts at $25. Cost per shirt $10. Profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Revenue $5,400. Fixed costs $800. Variable costs $2,700. Net profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Price $18, cost $7, sold 250 units. Profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Revenue $4,500, profit $1,800. What were total costs? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Need $2,000 profit. Price $20, cost $12. How many must sell? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Revenue $12,000. Profit margin 35%. Profit amount? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:73
10.Profit $1,500. Revenue $6,000. Profit margin %? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Sold 500 units, profit $2,500. Profit per unit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Monthly expenses: Rent $450, utilities $125, supplies $225, insurance $100. Total fixed? Work: ________________________________________________________________________ _____________________________________________________________________________Answer: _______________________
Section 2: Setting Prices — Markup and Discounts
೦೦️The Scenario
You buy wholesale items for $20 each. You want a 75% markup. What's your selling price? Later, you offer a 20% sale. What's the sale price?
✎ Worked Example: Calculating Markup
Cost: $20. Markup: 75%
Markup amount: $20 × 0.75 = $15 Selling price: $20 + $15 = $35
Price:$35 (or: $20 × 1.75 = $35)
✎ Worked Example: Calculating Discount
Regular price: $35. Discount: 20% Discount amount: $35 × 0.20 = $7 Sale price: $35 - $7 = $28
Sale price:$28 (or: $35 × 0.80 = $28)
✎ Worked Example: Profit After Discount
Cost: $20. Sale price: $28
Profit per item: $28 - $20 = $8 Original profit was: $35 - $20 = $15
Profit decrease: $15 - $8 = $7 (or 47% less profit) Note:20% off price = 47% less profit!
Page74: Dr. Gene A Constant - Author
Grade 5 Mathematics
೦೦Practice: Markup and Discounts
1.Cost $40. Markup 50%. Selling price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Cost $25. Markup 100% (double). Selling price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Price $80. Discount 25%. Sale price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Cost $15, selling $36. Markup percentage? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Regular $50, sale $35. Discount percentage? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Cost $30, markup 60%. Then 15% discount. Final price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Buy wholesale $12, sell $30. Markup % ? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Price $45, 30% off sale. Cost was $20. Profit per item at sale price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Cost $8, want 125% markup. Selling price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:75
10.Original $120, now $84. Discount %? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.After 40% markup, price is $56. Original cost? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Cost $25, sell $50, offer 20% discount. Still profitable? By how much? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 3: Looking Ahead — Financial Projections
೦೦The Scenario
Your business sold $3,000 in January, $3,600 in February, $4,320 in March. You're growing 20% each month! Project future sales and plan for growth.
✎ Worked Example: Projecting with Percentage GrowthMarch
sales: $4,320. Growth rate: 20% April projection: $4,320 × 1.20 = $5,184
May projection: $5,184 × 1.20 = $6,220.80 Projections:April $5,184, May $6,221
✎ Worked Example: Break-Even Analysis
Fixed costs: $500/month. Price: $25. Cost per item: $10. Profit per item: $25 - $10 = $15 Break-even: $500 ÷ $15 = 33.3 items Must sell at least 34 items to cover costs Break-even point:34 items
✎ Worked Example: Annual Revenue from Monthly
Average monthly revenue: $4,500 Annual projection: $4,500 × 12 = $54,000 Annual revenue:$54,000
೦೦Practice: Financial Projections
1.Sales $2,000. Grow 10% monthly. Next month projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page76: Dr. Gene A Constant - Author
Grade 5 Mathematics
2.January $5,000, growing 15%/month. April projection? (3 months later) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Fixed costs $750. Profit per item $12. Break-even quantity? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Average monthly sales $8,500. Annual projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.This month: 200 customers. Growing 25%/month. Customers in 2 months? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Fixed costs $1,200. Price $40, cost $22. Break-even? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Q1 total $18,000. If same rate, annual projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Sales: Jan $1,000, Feb $1,500, Mar $2,250. Growth %? April projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Need $36,000 annual revenue. Required monthly average? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Profit margin 40%. Need $800/month profit. Monthly revenue needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Fixed costs $600, profit per unit $8. Sold 100 units. Net profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:77
12.Current: $4,000/month. Goal: $10,000/month. Grow 25%/month. Months to goal? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 8 Action Report: Monthly Business ReviewComplete
this month-end business analysis!
Revenue Analysis
1.Sold 340 items at $18 each. Monthly revenue? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Items cost $7 each to make. Total cost of goods? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Gross profit (revenue - cost of goods)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Expense Tracking
4.Fixed costs: Rent $650, Utilities $180, Insurance $120, Marketing $250. Total? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Net profit (gross profit - fixed costs)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Profit margin percentage? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Pricing Check
7.Your markup % on $7 cost items sold at $18? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page78: Dr. Gene A Constant - Author
Grade 5 Mathematics
8.Planning 25% off sale. Sale price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Profit per item at sale price? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Projections
10.If sales grow 15% next month, projected revenue? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Break-even: How many items needed to cover $1,200 fixed costs at $11 profit/item? Work: ________________________________________________________________________ _____________________________________________________________________________Answer: _______________________
12.Annual revenue projection based on this month? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
CHAPTER 9 The Science Lab Technician
Chapter Goal: Master order of operations and formulas to perform precise scientific
calculations.
Welcome to the laboratory! As a Science Lab Technician, precision is everything. One calculation error can ruin an experiment. You'll use formulas, follow the order of operations exactly, and express very large and small numbers correctly.
Section 1: Following the Rules — Order of Operations
೦೦The Scenario
A formula reads: 3 + 4 × 5 - 2. Is the answer 33, 19, or 21? Without rules, everyone gets different answers. PEMDAS saves the day!
೦೦PEMDAS Rules
P - Parentheses first E - Exponents next MD - Multiplication and Division (left to right) AS - Addition and Subtraction (left to right)
Global Sovereign University Press Page:79
✎ Worked Example: Basic Order of Operations
Calculate: 3 + 4 × 5 - 2 Step 1: Multiplication first: 4 × 5 = 20 Step 2: Left to right: 3 + 20 - 2 = 21 Answer:21
✎ Worked Example: With Parentheses
Calculate: (3 + 4) × 5 - 2 Step 1: Parentheses: (3 + 4) = 7 Step 2: Multiply: 7 × 5 = 35 Step 3: Subtract: 35 - 2 = 33 Answer:33
✎ Worked Example: With Exponents
Calculate: 2 + 3² × 4 Step 1: Exponent: 3² = 9 Step 2: Multiply: 9 × 4 = 36 Step 3: Add: 2 + 36 = 38 Answer:38
✎ Worked Example: Complex Expression
Calculate: 48 ÷ (4 + 4) × 2 - 3 Step 1: Parentheses: (4 + 4) = 8 Step 2: Division (left to right): 48 ÷ 8 = 6 Step 3: Multiply: 6 × 2 = 12 Step 4: Subtract: 12 - 3 = 9 Answer:9
೦೦Practice: Order of Operations
1.Calculate: 8 + 3 × 4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Calculate: 20 - 4 × 3 + 2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Calculate: (6 + 2) × 5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page80: Dr. Gene A Constant - Author
Grade 5 Mathematics
4.Calculate: 36 ÷ 6 + 3 × 2 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Calculate: 5 + 2³ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Calculate: (10 - 4)² ÷ 3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Calculate: 100 - 5 × 10 + 25 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Calculate: 18 ÷ (2 + 4) × 5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Calculate: 4² + 3² - 5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Calculate: 2 × (8 + 4) ÷ 3 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Calculate: 50 - 2 × 3² + 1 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Calculate: (15 - 5) × (8 ÷ 2) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:81
13.Calculate: 24 ÷ 4 + 6 × 3 - 5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Calculate: 3 × (4 + 2)² ÷ 9 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
15.Calculate: 100 ÷ (5 + 5) ÷ 2 + 8 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Calculate: 2³ + 4² - 3 × 5 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 2: Lab Formulas — Substituting Values
⚗️The Scenario
The formula for density is D = M ÷ V (mass divided by volume). If a sample has mass 45 grams and volume 15 cubic centimeters, what's its density?
✎ Worked Example: Using the Density Formula
Formula: D = M ÷ V Given: M = 45 g, V = 15 cm³ Substitute: D = 45 ÷ 15 = 3
Density:3 g/cm³
✎ Worked Example: Temperature Conversion
Formula: F = (9/5 × C) + 32 Convert 25°C to Fahrenheit
F = (9/5 × 25) + 32 F = (1.8 × 25) + 32 = 45 + 32 = 77 Answer:77°F
✎ Worked Example: Speed Formula
Formula: Speed = Distance ÷ Time A car traveled 240 miles in 4 hours Speed = 240 ÷ 4 = 60 mph Speed:60 miles per hour
Page82: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Finding a Missing Value
Speed = 50 mph, Time = 3 hours. Find Distance.
Rearrange: Distance = Speed × Time Distance = 50 × 3 = 150 miles Distance:150 miles
೦೦Practice: Using Formulas
1.D = M ÷ V. M = 80 g, V = 20 cm³. Find D. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.F = 1.8C + 32. Convert 30°C to Fahrenheit. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Speed = Distance ÷ Time. 180 miles in 3 hours. Speed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Distance = Speed × Time. 65 mph for 4 hours. Distance? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Area = Length × Width. L = 12, W = 8. Area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Perimeter = 2L + 2W. L = 15, W = 9. Perimeter? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Volume = L × W × H. 5 × 4 × 3. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Average = Sum ÷ Count. Sum = 450, Count = 6. Average? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:83
9.C = (F - 32) ÷ 1.8. Convert 86°F to Celsius. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Time = Distance ÷ Speed. 300 miles at 60 mph. Time? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Simple Interest = Principal × Rate × Time. $1,000 × 0.05 × 2 years. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Force = Mass × Acceleration. M = 50 kg, A = 3 m/s². Force? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Section 3: Powers and Patterns — Exponents
೦೦The Scenario
Bacteria double every hour. Starting with 1 bacterium: after 1 hour = 2, after 2 hours = 4, after 3 hours = 8. That's 2¹, 2², 2³... Exponents show repeated multiplication!
✎ Worked Example: Understanding Exponents
2⁴ means 2 × 2 × 2 × 2 = 16
Base: 2, Exponent: 4 Read as: '2 to the fourth power' 2⁴ =16
✎ Worked Example: Powers of 10
10¹ = 10 10² = 100 10³ = 1,000 10⁴ = 10,000
Pattern: The exponent tells how many zeros! 10⁶ =1,000,000 (one million)
Page84: Dr. Gene A Constant - Author
Grade 5 Mathematics
✎ Worked Example: Bacteria Growth Problem
Start with 5 bacteria, double every hour After n hours: 5 × 2ⁿ After 6 hours: 5 × 2⁶ = 5 × 64 = 320 bacteria Answer:320 bacteria
೦೦Practice: Exponents
1.Calculate: 3⁴ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Calculate: 5³ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Calculate: 2⁶ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Calculate: 10⁵ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Write 81 as a power of 3. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Write 64 as a power of 2. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Bacteria double hourly. Start 10. After 5 hours? (10 × 2⁵) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Calculate: 4³ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:85
9.Calculate: 2⁵ + 3² Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Population triples yearly. Start 100. After 4 years? (100 × 3⁴) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Write 1,000,000 as a power of 10. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Calculate: 6² × 2³ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 9 Action Report: Lab Calculations
Complete these lab analysis problems!
Order of Operations
1.Calculate: 5 + 3 × 8 - 12 ÷ 4 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Calculate: (24 - 4) ÷ (2 + 3) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Calculate: 2³ × 4 - 6² Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Formula Applications
4.Density: M = 156 g, V = 12 cm³. Find D. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page86: Dr. Gene A Constant - Author
Grade 5 Mathematics
5.Convert 35°C to Fahrenheit. (F = 1.8C + 32) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Speed = 72 mph, Time = 4.5 hours. Distance? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Exponents
7.Calculate: 4⁴ Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Bacteria start at 8, double every hour. Count after 8 hours? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Write 10,000,000 as a power of 10. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Combined Problems
10.Solution A: D = 2.5 g/cm³. Solution B: D = 3.2 g/cm³. Which is denser? By how much? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
11.Experiment runs 2⁴ minutes. How many minutes? How many hours?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.Formula: Result = (A + B)² ÷ C. A = 3, B = 5, C = 4. Result?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:87
CHAPTER 10 The Startup Founder
Chapter Goal: Apply ALL your fifth-grade math skills to launch and run your own business!
This is it—your capstone project! You're launching a tech startup that creates and sells mobile apps. You'll use every skill from this year: decimals, fractions, percentages, coordinates, statistics, time zones, profit calculations, and formulas. Let's build a business!
Part 1: Startup Costs and Funding
You need $25,000 to launch. Calculate your funding sources and expenses.
1.Personal savings: $8,500. Family loan: $6,750. Crowdfunding: $5,425. Bank loan: remainder. Bank loan amount?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Equipment: $7,850.45. Software licenses: $2,345.99. Legal fees: $1,875.50. Office setup: $3,428.06. Total startup expenses?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Money remaining after expenses from $25,000? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.If 35% of startup costs are equipment-related, what's that amount? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Part 2: Product Development Timeline
Plan your development schedule across time zones.
5.Developer in India (10.5 hours ahead of Eastern). Your meeting at 8 AM ET = what time in India? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
6.Development takes 720 hours total. Working 8 hrs/day, 5 days/week, how many weeks? Work: ________________________________________________________________________ _____________________________________________________________________________
Answer: _______________________
Page88: Dr. Gene A Constant - Author
Grade 5 Mathematics
7.Start March 1, need 18 weeks. Completion date? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Team meeting: LA (PT), Chicago (CT), NY (ET), London (5 hrs ahead ET). Meeting at 10 AM ET. Times for each?
Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Part 3: App Store Pricing
Set prices and calculate revenue.
9.App costs $0.85 to distribute. You price at $2.99. Profit per sale? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.App store takes 30% of price. Your net per sale after store fee? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.After store fee AND distribution cost, actual profit per sale? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.First month: 4,250 downloads. Revenue at $2.99 each? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Part 4: User Statistics
Analyze your user data.
13.Daily users (Week 1): 150, 225, 340, 510, 425, 380, 290. Mean? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
14.Same data: Median? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:89
15.Same data: Range? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
16.Users growing 40%/month. Month 1: 1,000 users. Month 4 projection? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Part 5: Office Space
Design your startup office.
17.L-shaped office: main 30×20 ft, extension 15×10 ft. Total area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
18.Rent is $2.25 per square foot. Monthly rent? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
19.Meeting room takes up 1/8 of total space. Meeting room area? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
20.Desk area: 6×4 ft each. How many desks fit in remaining 5/8 of space? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Part 6: Growth Projections
Project your business growth.
21.Month 1 revenue: $12,707.50. Growing 25%/month. Month 3 revenue? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
22.Fixed costs: $4,500/month. Profit per download: $1.24. Break-even downloads? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page90: Dr. Gene A Constant - Author
Grade 5 Mathematics
23.Year 1 projection if monthly average is $18,000? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
24.Investor wants 15% of profits. Year 1 projected profit $85,000. Investor share? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Part 7: Final Business Report
Synthesize everything into a business summary.
25.Total Year 1 revenue projection: $216,000. Total costs: $148,500. Net profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
26.Net profit as percentage of revenue (profit margin)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
27.If you reinvest 40% of profit back into the business, reinvestment amount? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
28.Remaining profit split between 2 founders. Each receives? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
29.Year 2 goal: grow revenue 50%. Year 2 revenue target? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
30.At same profit margin, Year 2 projected profit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:91
About Global Sovereign University
"Building a Bridge to Freedom Through Education—Not Handouts"
Global Sovereign University is a 501(c)(3) educational foundation. We believe every person deserves access to quality education that builds real capabilities.
This textbook is provided FREE because learning should never be limited by economics.
For more free educational resources, visit: www.globalsovereignuniversity.org
Together, we build capability—not dependency.
Extra Practice
Additional problems for each chapter
Chapter 1: Decimals Extra Practice
೦೦Mixed Review
1.Round $456.7891 to nearest cent. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Order: 3.405, 3.45, 3.045, 3.504 (least to greatest) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
3.Add: 234.567 + 89.45 + 12.8 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Subtract: 1,000 - 456.789 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Multiply: 45.6 × 7.8 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page92: Dr. Gene A Constant - Author
Grade 5 Mathematics
6.Calculate 18% tip on $85.50 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Bill $124.50, tax 8.5%. Total with tax? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Add: $1,234.56 + $567.89 + $234.50 Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Convert 6.5% to decimal. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Revenue $2,456.78, expenses $1,234.56. Net? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Multiply: 125 × 0.065 (6.5% tax) Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.25% of $840 = ? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Chapter 2: Volume Extra Practice
೦೦Mixed Review
1.Volume: 8 × 6 × 5 ft Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
2.Container: 40 × 8 × 9 ft. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Global Sovereign University Press Page:93
3.Box: 24 × 18 × 12 in. Dim weight (÷139)? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
4.Truck 1,200 ft³. Boxes 15 ft³ each. How many fit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
5.Convert 6,912 cubic inches to cubic feet. Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
6.Warehouse bay: 25 × 20 × 12 ft. Capacity? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
7.Package weighs 25 lbs, dim weight 32 lbs. Shipping at $0.55/lb? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
8.Pallet: 4 × 4 × 6 ft. Volume? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
9.Truck floor: 24 × 8 ft. Box base: 3 × 2 ft. Boxes per layer? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
10.Space: 800 ft³. Large boxes: 40 ft³ (need 12). Small: 5 ft³. How many small fit? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
11.Two trucks: 960 ft³ and 1,440 ft³. Total capacity? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
12.50 boxes at 16 ft³ each. Total volume needed? Work: ________________________________________________________________________ _____________________________________________________________________________ Answer: _______________________
Page94: Dr. Gene A Constant - Author
Grade 5 Mathematics
Global Sovereign University Press Page:95