4th Grade Math Textbook

Chapter 1

Real-World Problem Solving Complete Student Edition BUILDING A BRIDGE TO FREEDOM GLOBAL SOVEREIGN UNIVERSITY "Building a Bridge to Freedom Through Education Grade 4 Mathematics: Real-World Problem Solving Student Edition Copyright © 2024 Global Sovereign University Press All rights reserved. First Edition. 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 Global Sovereign University Press Page: 1 "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.

Students who scored 96% on standard school math problems could solve simple real-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 The Nobel laureates found that school children learned procedures but not understanding. They could solve "24 x 8" on a worksheet by adding 24 eight times. But give them a real problem—"How much do 8 items cost at $24 each?"—and they froze.

Market children used efficient mental strategies: breaking 11 x 43 into (10 x 43) + 43, rounding for easier calculation, working with meaningful quantities. School children followed rigid, slow methods that worked for tests but failed in life.

It's not that school kids were less intelligent. It's that their education never connected the math to reality.

The GSU Solution: Real-World Math This textbook does exactly what the Nobel laureates recommend. Instead of abstract problems, every calculation has a professional context:

Page: 2 Dr. Gene A Constant - Author Traditional Math GSU Real-World Math "Multiply 3.45 x 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. Your Roles in This Book You won't just learn math in this book. You'll BE someone who uses it: e The Restaurant Manager — Decimals, percentages, tips e The Warehouse Supervisor — Volume and shipping e The Video Game Designer — Coordinates and graphing e The Catering Chef — Fractions and scaling e The Landscaping Contractor — Area and perimeter e The Sports Analyst — Statistics and predictions e The Travel Agent — Time zones and large numbers e The Small Business Owner — Profit and loss e The Science Lab Technician — Formulas and order of operations e The Startup Founder — Everything combined These aren't pretend jobs. These are skills you can use THIS WEEK. 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. 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." Global Sovereign University Press Page: 3 Table of Contents Chapter 1: The Classroom Store Place value, operations, money Chapter 2: The Festival Planner Multiplication, division, geometry Chapter 3: The Pet Shop Owner Fractions Chapter 4: The Recipe Master Mixed numbers, fraction multiplication Chapter 5: The Construction Crew Measurement, area, perimeter Chapter 6: The Sports League Manager Data, statistics, predictions Chapter 7: The Savings Account Decimals Chapter 8: The Delivery Driver Time and schedules Chapter 9: The Garden Designer Patterns, variables, equations Chapter 10: The Business Plan Capstone: all skills Extra Practice Sections

Welcome!

This year, you become a problem solver who uses mathematics in the real world. You'll take on exciting roles: ¢ Store Manager: Track inventory and money ¢ Event Planner: Calculate supplies for festivals ¢ Pet Shop Owner: Use fractions for feeding schedules ¢ Recipe Master: Scale recipes up and down ¢ Construction Worker: Measure and build * Sports Manager: Analyze team statistics ¢ Junior Banker: Manage savings and spending ¢ Delivery Driver: Plan routes and schedules ¢ Garden Designer: Discover patterns and equations ¢ Business Owner: Create your own lemonade stand! How to Use This Book: @@ The Scenario: Step into a real role @@ The Skill: Learn the mathematics ‘~ Worked Examples: See step-by-step solutions @@ Practice Problems: Build mastery @@ Action Reports: Apply everything Remember: Show your work! The process matters as much as the answer. Page: 4 Dr. Gene A Constant - Author How to Show Your Work Every problem includes workspace. Use it! Step 1: Read Carefully » What information is given? What are you finding? Step 2: Plan * What operation(s) will you use? Can you estimate first? Step 3: Calculate + Write each step. Line up numbers neatly. Label your work. Step 4: Check « Does it match your estimate? Does it make sense? Example: Problem: Store sold 1,234 pencils Monday and 2,456 Tuesday. Total? Work: Estimate 1,000 + 2,500 = 3,500 1,234 + 2,456 = 3,690 Answer: 3,690 pencils (matches estimate) V

Global Sovereign University Press Page: 5 CHAPTER 1 The Classroom Store Chapter Goal: Use place value and multi-digit operations to run a school supply business. Congratulations! You've just been hired as the manager of the Classroom Store, a student-run business that sells school supplies to your entire school. Running this store requires careful mathematical thinking every day. You'll track thousands of items, manage money, make ordering decisions, and ensure your customers are happy. Let's open for business! Section 1: Taking Inventory — Understanding Large Numbers @@ The Scenario The school district just delivered your starting inventory: 3,256 pencils, 1,847 erasers, 2,093 notebooks, 4,125 sticker sheets, and 5,678 index cards. You need to record these quantities accurately in your inventory system. One mistake could mean running out of supplies or wasting money on items you don't need! @@ The Skill: Place Value Place value means the position of each digit determines its value. Think about the number 3,256: * The 3 is in the thousands place, so it means 3,000 * The 2 is in the hundreds place, so it means 200 * The 5 is in the tens place, so it means 50 * The 6 is in the ones place, so it means 6 Understanding place value helps you read, write, compare, and round numbers accurately. “Worked Example: Breaking Down 3,256 Standard form: 3,256 Expanded form: 3,000 + 200 + 50 +6 Word form: Three thousand, two hundred fifty-six Each digit has a value based on WHERE it sits. The 3 is worth 3x1,000 = 3,000. ‘“ Worked Example: Comparing 4,256 and 4,265 Compare from left to right, starting with the biggest place value: « Thousands: Both have 4 — keep looking « Hundreds: Both have 2 — keep looking * Tens: 5 vs 6 — 5 is less than 6 Answer: 4,256 < 4,265 The first difference determines which number is larger! *. Worked Example: Rounding 4,783 to the Nearest Hundred Step 1: Find the hundreds place (7) Step 2: Look at the digit to the right (8 in tens place) Step 3: Is it 5 or more? YES! So round UP Answer: 4,783 rounds to 4,800 If the tens digit were 4 or less, we would round DOWN to 4,700. Page: 6 Dr. Gene A Constant - Author ‘“ Worked Example: Rounding 6,549 to the Nearest Thousand Step 1: Find the thousands place (6) Step 2: Look at the hundreds digit (5) Step 3: Is it 5 or more? YES! Round UP Answer: 6,549 rounds to 7,000 @¢@ Practice: Place Value 1. Write 5,384 in expanded form. Answer: 2. What is the value of the digit 7 in 6,742? Answer: 3. Compare using <, >, or =:4,256 4,265 Answer: 4. Write the number: 8 thousands, 3 hundreds, 0 tens, 5 ones. Answer: 5. Order from least to greatest: 3,842; 3,824; 3,482; 3,248 Answer: 6. Write 2,456 in word form. Answer: Global Sovereign University Press Page: 7 7. Round 4,783 to the nearest hundred. Answer: 8. Which is greater: 6,099 or 6,100? Explain your reasoning. Answer: 9. Write the smallest 4-digit number using 7, 2, 9, 4 (use each digit once). Answer: 10. Write the largest 4-digit number using 3, 8, 1, 6 (use each digit once). Answer: 11. A box has 8 thousands + 12 hundreds + 4 tens + 3 ones. Write in standard form. (Hint: Regroup!) Answer: 12. The store sold 3,456 items last month and 3,564 this month. Which month had more sales? Answer: 13. Write 9,007 in expanded form. (Watch out for the zeros!) Answer: 14. Round 6,549 to the nearest thousand. Answer: Page: 8 Dr. Gene A Constant - Author 15. What number is 100 more than 4,967?

Answer: 16. Compare using <, >, or =:7,890__—~7,809

Answer: 17. In the number 45,678, what is the value of the 5?

Answer: 18. Order from greatest to least: 5,678; 5,687; 5,768; 5,867

Answer: 19. Round 3,450 to the nearest hundred. (Hint: What happens when the digit is exactly 5?)

Answer:

20. What number is 1,000 less than 8,234?

Answer: Section 2: Monday Restock — Multi-Digit Addition @@ The Scenario Three deliveries arrived this morning! You had 1,347 pencils in stock. Delivery #1 brought 2,456 pencils. Delivery #2 brought 1,234 more. You need to calculate your new inventory totals. Accurate addition is essential for knowing what you have! @@ The Skill: Addition with Regrouping When a column adds to 10 or more, we 'carry' or 'regroup' to the next place value. Always estimate first to check if your answer makes sense!

Global Sovereign University Press Page: 9 ‘%. Worked Example: Adding 1,347 + 2,456 Step 1 - Estimate: 1,000 + 2,000 = 3,000 (answer should be close) Step 2 - Set up vertically and add column by column from right to left: * Ones: 7 + 6 = 13 — write 3, carry 1 * Tens: 1+ 4+5=10- write 0, carry 1 « Hundreds: 1+ 3+4=8 — write 8 * Thousands: 1 + 2 = 3 — write 3 Answer: 3,803 pencils (close to our estimate of 3,000) V *%. Worked Example: Adding Three Numbers: 1,347 + 2,456 + 1,234 Method 1: Add two at a time 1,347 + 2,456 = 3,803 3,803 + 1,234 = 5,037 Method 2: Stack all three and add each column Answer: 5,037 pencils total ‘ Worked Example: Adding Money: $1,234.56 + $2,789.34 Key rule: Line up the decimal points! Add cents: 56 + 34 = 90 cents Add dollars: 1,234 + 2,789 = 4,023 dollars Answer: $4,023.90 *%. Worked Example: Checking with Estimation Problem: 4,892 + 3,567 Estimate: 5,000 + 4,000 = 9,000 Actual: 4,892 + 3,567 = 8,459 Check: 8,459 is close to 9,000 V @¢@ Practice: Multi-Digit Addition 1. Calculate: 2,456 + 1,378 Answer: 2. Calculate: 3,847 + 2,956 Answer: Page: 10 Dr. Gene A Constant - Author 3. You have 1,245 red pens and receive 2,367 more. What is the total? Answer: 4. Calculate: 456 + 789 + 234 Answer: 5. Store earned $1,456 Monday, $2,378 Tuesday, $1,892 Wednesday. Total earnings? Answer: 6. Calculate: 5,678 + 3,456 Answer: 7. Add three deliveries: 2,456 + 3,789 + 1,234 Answer: 8. Estimate first, then calculate: 4,892 + 3,567 Answer: 9. Had 3,456 notebooks. Received 1,234 more, then 2,567 more. New total? Answer: 10. Calculate: 6,789 + 2,345 + 1,876 Answer: Global Sovereign University Press Page: 11 11. Three busiest days: $4,567 + $5,234 + $3,899. Total sales? Answer:

12. Calculate: 7,654 + 2,789 Answer:

13. Combine inventory from 3 boxes: 2,345 + 1,876 + 3,459 items Answer:

14. Calculate: 8,234 + 567 + 3,491 Answer:

15. Add: $234.56 + $567.89 + $123.45 Answer:

16. Inventory from 4 boxes: 1,250 + 1,340 + 1,125 + 1,285 Answer:

17. Calculate: 9,999 + 1 (What happens?) Answer:

18. Weekly deposits: $456.78 + $523.45 + $398.67 + $612.34 + $445.89 Answer:

Page: 12 Dr. Gene A Constant - Author 19. Calculate: 4,567 + 3,892 + 2,541 Answer: 20. Total of all starting inventory: 3,256 + 1,847 + 2,093 + 4,125 + 5,678 Answer: Section 3: The Big Sale — Multi-Digit Subtraction @@ The Scenario It's the Back-to-School Sale! You started with 5,037 pencils and sold 2,789 by lunchtime. How many pencils remain? Knowing your current inventory helps you avoid disappointing customers who want to buy supplies. @¢@ The Skill: Subtraction with Regrouping When you can't subtract a digit because the top number is smaller, you need to 'borrow' or ‘regroup’ from the next place value. This is like breaking a ten-dollar bill into ten ones. *~ Worked Example: Subtracting 5,037 - 2,789 Step 1 - Estimate: 5,000 - 3,000 = 2,000 Step 2 - Work right to left, borrowing when needed: * Ones: 7 - 9? Can't do it! Borrow from tens. + But tens is 3, and we need to borrow... it becomes complex with the 0. * Borrow through: 5,037 — 5,0(2)(17) — 4,(10)(2)(17) — 4,9,12,17 + Now: 17-9=8, 12-8=4, 9-7=2, 4-2=2 Answer: 2,248 pencils remain / ‘%. Worked Example: Subtracting from Zeros: 6,000 - 3,456 When subtracting from a number with zeros, you must borrow through multiple places: 6,000 > 5,10,0,0 — 5,9,10,0 — 5,9,9,10 Now subtract: 10-6=4, 9-5=4, 9-4=5, 5-3=2 Answer: 2,544 ‘% Worked Example: Making a Reorder Decision Current stock: 2,248 pencils Reorder point: 2,000 pencils (when to order more) 2,248 - 2,000 = 248 pencils above reorder point But the sale continues! If you expect to sell 300+ more today... Decision: YES, place a reorder now to avoid running out! Global Sovereign University Press Page: 13 ‘% Worked Example: Checking Subtraction with Addition Problem: 7,234 - 4,567 = ? Answer: 2,667 Check: 2,667 + 4,567 = 7,234 V If the check doesn't equal the original number, redo the problem! @@ Practice: Multi-Digit Subtraction 1. Calculate: 5,234 - 2,678 Answer: 2. Had 4,567 erasers, sold 1,789. How many remain? Answer: 3. Calculate: 6,000 - 3,456 Answer: 4. Register had $8,456. Gave $3,789 in change. What remains? Answer: 5. Calculate: 7,234 - 4,567 Answer: 6. Started with 5,000 notebooks. Sold 2,347 Monday and 1,456 Tuesday. How many left? Answer: Page: 14 Dr. Gene A Constant - Author 7. Calculate: 9,000 - 4,567 Answer: 8. Reorder point is 1,500. Have 4,234 markers, sold 2,856. Do you need to reorder? Answer: 9. Calculate: 8,234 - 3,789 Answer: 10. Had 6,543 items. Sold 2,345. Got 123 returns. Current inventory? Answer: 11. Calculate: 7,006 - 2,789 Answer: 12. Budget is $10,000. Spent $7,234. How much remains? Answer: 13. Calculate: 5,003 - 1,678 Answer: 14. Last year total: $45,678. This year: $52,345. How much more this year? Answer: Global Sovereign University Press Page: 15 15. Calculate: 8,040 - 3,567 Answer: 16. Subtract: $500.00 - $267.89 Answer: 17. Calculate: 10,000 - 6,543 Answer: 18. Started week with 8,500 items. Daily sales: 1,234; 1,456; 1,789; 1,123; 1,567. Remaining? Answer: 19. Calculate: 9,001 - 5,678 Answer: 20. Had $25,000 budget. Expenses: $8,456 + $7,234 + $5,678. Remaining budget? Answer: Page: 16 Dr. Gene A Constant - Author Section 4: Counting the Register — Money Math @@ The Scenario The store closes at 3:00 PM. Time to count the register! You started with $1,234.56 in the drawer. Customers paid a total of $6,789.34 throughout the day. You gave back $3,456.78 in change. What should the register contain now? @@ The Skill: Decimal Operations with Money Money uses decimals. The digits after the decimal point represent cents. The most important rule: ALWAYS line up the decimal points when adding or subtracting! %. Worked Example: Balancing the Register Starting amount: $1,234.56 + Customer payments: $6,789.34 = Subtotal: $8,023.90 - Change given: $3,456.78 Register should have: $4,567.12 If the actual count doesn't match, there's an error somewhere! ‘ Worked Example: Making Change: Customer Pays $100 for $67.89 Purchase Method 1: Subtract $100.00 - $67.89 = $32.11 Method 2: Count up $67.89 — $67.90 (1¢) — $68.00 (10¢) — $70.00 ($2) — $100.00 ($30) Total: 1¢ + 10¢ + $2 + $30 = $32.11 Change due: $32.11 ‘%. Worked Example: Adding Multiple Transactions Monday: $234.56 Tuesday: $567.89 Wednesday: $345.67 Line up decimals and add: 234.56 567.89 + 345.67 Total: $1,148.12 ‘% Worked Example: Finding How Much More is Needed Goal: Raise $5,000 for new equipment Currently have: $3,678.90 $5,000.00 - $3,678.90 = $1,321.10 still needed Amount needed: $1,321.10 Global Sovereign University Press Page: 17 @¢@ Practice: Money Math 1. Add: $45.67 + $123.89 Work: Answer: 2. Subtract: $234.56 - $78.90 Work Answer: 3. Register has $456.78, receive $234.56 in sales. New total? Work: Answer: 4. Customer pays $100.00 for $67.89 purchase. What change? Work Answer: 5. Add: $45.67 + $89.12 + $34.56 Work: Answer: 6. Register: $1,234.56. Give $567.89 change. What remains? Work: Answer: 7. Calculate: $456.78 + $234.56 + $789.12 Work: Answer: 8. Subtract: $1,000.00 - $678.90 Work: Answer: Page: 18 Dr. Gene A Constant - Author 9. Monday sales: $2,345.67. Tuesday: $3,456.78. Combined total? Answer: 10. Customer total is $89.99. Pays with $100.00. Change due? Answer: 11. Start with $500, earn $2,345.67 in sales, give $1,234.56 change. Register total? Answer: 12. Need $5,000.00. Have $3,678.90. How much more needed? Answer: 13. Calculate: $250.00 + $675.50 - $123.89 Answer: 14. Three purchases: $45.99, $67.50, $123.75. Total? Answer: 15. Had $2,500.00. Spent $456.78, $234.56, and $189.99. Remaining? Answer: 16. Weekly earnings: $1,234.56 + $1,567.89 + $1,345.67 + $1,456.78 + $1,789.34 Answer: Global Sovereign University Press Page: 19 17. Customer pays $50.00 for $23.47 item. Change? Answer: 18. Bank balance: $4,567.89. Deposit $1,234.56. Withdraw $500.00. New balance? Answer: 19. Price is $199.99. Tax is $16.50. Total due? Answer: 20. Had $10,000.00 budget. Expenses: $2,345.67, $3,456.78, $1,234.56. Remaining? Answer: Chapter 1 Action Report: Store Manager's Weekly Summary Complete this manager's report using ALL your Chapter 1 skills! Show your work for each problem. Inventory Report 1. TOTAL INVENTORY: Store has 3,456 pencils, 2,789 pens, 4,123 markers, and 1,892 erasers. What is the total number of writing supplies? Answer: 2. WEEKLY SALES: Sold 1,234 pencils Monday, 987 Tuesday, 1,456 Wednesday, 876 Thursday, 1,547 Friday. Total pencils sold? Answer: Page: 20 Dr. Gene A Constant - Author 3. REMAINING STOCK: Started with 3,456 pencils, sold the total from problem 2. How many pencils remain?

Answer: 4. REORDER CHECK: Reorder point is 1,500 pencils. Based on problem 3, do you need to reorder? By how much are you above or below?

Answer: Financial Report 5. DAILY REGISTER: Started $567.89, received $4,567.34 in payments, gave $2,345.67 change. Ending balance?

Answer: 6. WEEKLY REVENUE: Mon $1,234.56, Tue $987.34, Wed $1,567.89, Thu $876.54, Fri $2,345.67. Total weekly revenue?

Answer: 7. PROFIT CALCULATION: Weekly revenue (from #6) minus weekly expenses of $4,567.00. Weekly profit?

Answer: 8. BUDGET STATUS: Monthly budget is $25,000. Week 1 spent $5,678.90, Week 2 spent $6,234.56. Remaining budget?

Answer: Analysis Questions 9. PLACE VALUE: The store's inventory ID number is 48,052. Write this in expanded form and word form.

Answer:

Global Sovereign University Press Page: 21 10. COMPARISON: Store A sold 4,567 items. Store B sold 4,657 items. Store C sold 4,576 items. Rank from most to least sales.

Answer: 11. ROUNDING: For the monthly report, round total inventory of 12,847 items to the nearest thousand.

Answer: 12. ESTIMATION: Estimate 4,892 + 3,178 by rounding to nearest thousand, then calculate the exact answer. How close was your estimate?

Answer: Page: 22 Dr. Gene A Constant - Author CHAPTER 2 The Festival Planner Chapter Goal: Use multiplication, division, and geometry to plan a community event. Welcome to the Festival Planning Committee! The Fall Festival is your school's biggest event of the year. As lead planner, you'll calculate supplies for hundreds of guests, divide money among charities, and design the festival layout. Mathematics makes it all possible! Section 1: The Inventory — Multi-Digit Multiplication @@ The Scenario You need prizes for carnival games! Super-Bounce Balls come in boxes of 24. Your school has 15 classes with 25 students each. How many students total? Will 18 boxes of balls be enough for one prize per student? @@ The Skill: Multi-Digit Multiplication For larger numbers, we can use the area model (breaking numbers into parts) or the standard algorithm. Always estimate first! *% Worked Example: Area Model: 15 x 25 Break each number into parts: 15 = 10 + 5 and 25 = 20+5 Create a grid and multiply each part: +10 x 20 = 200 *10x5=50 +5 x 20 = 100 °5x5=25 Total: 200 + 50 + 100 + 25 = 375 students *« Worked Example: Standard Algorithm: 34 x 27 Step 1: Multiply by ones digit (7) 34 x 7 = 238 Step 2: Multiply by tens digit (20) 34 x 20 = 680 Step 3: Add partial products Answer: 238 + 680 = 918 ‘“ Worked Example: Checking: Are 18 Boxes Enough? Need: 375 students (one prize each minimum) Have: 18 boxes x 24 balls per box 18 x 24 = 432 balls 432 > 375 Answer: YES! We have 57 extra prizes ‘% Worked Example: Money Multiplication: Ticket Sales Tickets cost $12 each. Sold 145 tickets. 145 x 12 = 145 x 10 + 145 x 2 = 1,450 + 290 = 1,740 Total earned: $1,740 Global Sovereign University Press Page: 23 @¢@ Practice: Multi-Digit Multiplication 1. Calculate: 23 x 14 Work:

Answer: 2. Calculate: 36 x 25 Work:

Answer: 3. 15 tables with 8 chairs each. Total chairs? Work:

Answer: 4. Calculate: 42 x 18 Work:

Answer: 5. 24 boxes with 36 prizes each. Total prizes? Work:

Answer: 6. Calculate: 56 x 34 Work:

Answer: 7. Tickets are $12 each. Sold 145. Total earned? Work:

Answer: 8. Calculate: 67 x 43 Work:

Answer: Page: 24 Dr. Gene A Constant - Author 9. 28 volunteers work 6 hours each. Total volunteer hours? Answer: 10. Calculate: 85 x 52 Answer: 11. 15 classes, 24 students each, need 3 tickets per student. Total tickets needed? Answer: 12. Stage rental: $75 per hour for 8 hours. Total cost? Answer: 13. Calculate: 48 x 37 Answer: 14. 125 guests, each receives 4 raffle tickets. Total tickets needed? Answer: 15. Calculate: 94 x 28 Answer: 16. Parking lot has 35 rows with 18 spaces each. Total capacity? Answer: Global Sovereign University Press Page: 25 17. Calculate: 63 x 45 Answer: 18. Food vendor serves 256 guests, 3 items each. Total items served? Answer: 19. Calculate: 78 x 54 Answer: 20. Festival runs 12 hours. Average 85 visitors per hour. Total visitors? Answer: Section 2: The Ticket Booth — Long Division @@ The Scenario The festival raised $1,452 to donate! You want to split it equally among 4 local charities. How much does each charity receive? What if there's money left over? @¢@ The Skill: Long Division Long division follows a pattern: Divide, Multiply, Subtract, Bring down. Repeat until done! ‘% Worked Example: Long Division: 1,452 + 4 Step by step: °14+4=3 remainder 2 * Bring down 5 —> 25 + 4 = 6 remainder 1 ¢ Bring down 2 > 12 +4 =3 exactly Answer: $363 per charity Check: 363 x 4 = 1,452 V ‘% Worked Example: Handling Remainders: 1,457 + 4 1,457 + 4 = 364 remainder 1 Each charity gets $364, with $1 left over Options for the extra $1: * Give one charity $365 (others get $364) ¢ Buy a thank-you card for all volunteers Real-world decisions go beyond just the math! Page: 26 Dr. Gene A Constant - Author *%. Worked Example: Division for Equal Groups Problem: 936 students need to form teams of 12. 936 + 12 = 78 teams Check: 78 x 12 = 936 W *% Worked Example: Finding How Many Groups Fit Have 1,728 cookies. Each box holds 144 cookies. 1,728 + 144 = 12 boxes needed All cookies fit perfectly with no remainder! @@ Practice: Long Division 1. Calculate: 864 + 4 Answer: 2. Calculate: 1,575 + 5 Answer: 3. Split $2,436 equally among 6 game booths. Each gets? Answer: 4. Calculate: 2,184 + 7 Answer: 5. 945 guests seated at tables of 9. How many tables needed? Answer: 6. Calculate: 3,456 + 8 Answer: Global Sovereign University Press Page: 27 7. 1,250 prizes shared among 5 games equally. Each game gets? Work: Answer: 8. Calculate: 2,709 + 3 Work: Answer: 9. 4,872 tickets sold over 6 hours. Average per hour? Work: Answer: 10. Calculate: 5,432 +4 Work: Answer: 11. $8,645 split among 5 partners. Each gets? Any remainder? Work: Answer: 12. 2,500 flyers for 8 volunteers to distribute. Each takes? Work Answer: 13. Calculate: 7,236 + 9 Work Answer: 14. 936 students form teams of 12. How many teams? Work Answer: Page: 28 Dr. Gene A Constant - Author 15. Calculate: 4,128 + 6 Answer: 16. 1,500 programs split among 8 classrooms. Each gets? Answer: 17. Calculate: 2,345 + 5 Answer: 18. Cookie boxes hold 144 cookies. Have 1,728 cookies. How many boxes? Answer: 19. Calculate: 6,384 + 8 Answer: 20. $9,876 profit shared among 6 committees. Each gets? Answer: Section 3: The Map Design — Geometry @@ The Scenario The festival will be held on a rectangular plot measuring 60 feet by 40 feet. You need to calculate the area for surface covering and the perimeter for fencing. @@ The Skills Area: The space inside a shape. For rectangles: Area = Length x Width Perimeter: The distance around a shape. For rectangles: P = 2 x Length + 2 x Width Global Sovereign University Press Page: 29 *%. Worked Example: Festival Plot Calculations Plot dimensions: 60 ft x 40 ft Area: 60 x 40 = 2,400 square feet Perimeter: 60 + 40 + 60 + 40 = 200 feet of fencing needed The stage takes up 10 x 10 = 100 sq ft, which is 100/2,400 = 4% of total space ‘% Worked Example: Finding a Missing Side A rectangle has perimeter 48 feet and length 14 feet. Find the width. P=2L+2W 48 = 2(14) + 2W 48 = 28+ 2W 20 = 2W Width: 10 feet ‘%. Worked Example: Area with a Cutout (L-Shaped) Large rectangle: 20 x 10 = 200 sq ft Cutout section: 8 x 6 = 48 sq ft Remaining area: 200 - 48 = 152 sq ft ‘~. Worked Example: Border Area Pool: 30 x 20 ft with a 2-ft wide border around it Outer rectangle: 34 x 24 = 816 sq ft Inner (pool): 30 x 20 = 600 sq ft Border area: 816 - 600 = 216 sq ft @@ Practice: Geometry 1. Rectangle 12 ft x 8 ft. Find the area. Answer: 2. Square with sides 15 ft. Find the perimeter. Answer: 3. Booth measures 8 ft x 6 ft. Area of booth space? Answer: Page: 30 Dr. Gene A Constant - Author 4. Need fence around 25 ft x 18 ft area. How much fence? Answer:

5. Stage is 12 ft x 12 ft square. Area? Answer:

6. Walkway: 50 ft long, 4 ft wide. Area? Answer:

7. Festival plot: 80 ft x 50 ft. Total area? Answer:

8. Square has perimeter 36 ft. What is the side length? Answer:

9. Rectangle area is 72 sq ft, length is 9 ft. Width? Answer:

10. Three booths: 6x8, 5x10, 8x8 ft. Combined area? Answer:

11. Plot 100x60 ft. Stage 15x15 ft. Area remaining? Answer:

Global Sovereign University Press Page: 31 12. Rectangle 24 ft x 16 ft. Perimeter? Answer:

13. Two squares: 10x10 and 8x8. Combined area? Answer:

14. Perimeter is 48 ft, length is 14 ft. Width? Answer:

15. L-shaped area: 20x10 with 8x6 cut out. Remaining area? Answer:

16. 2-ft wide border around 30x20 pool. Border area only? Answer:

17. Room is 15x12 ft. Carpet costs $3/sq ft. Total cost? Answer:

18. Square garden area is 144 sq ft. Side length? Answer:

19. Fence costs $12/ft. Rectangle 40x30 ft needs fence. Cost? Answer:

Page: 32 Dr. Gene A Constant - Author 20. Three sections: 25x20, 30x15, 20x20 ft. Total area? Answer: Chapter 2 Action Report: Festival Planning Summary Use ALL Chapter 2 skills to complete this planning report! Supplies & Budget 1. PRIZES NEEDED: 15 classes = 25 students x 3 prizes each. Total prizes? Answer: 2. PRIZE CHECK: Boxes contain 48 prizes. Need total from #1. How many boxes to order? Answer: 3. CHARITY: Raised $2,568 to split among 4 charities. Each receives? Answer: Layout Planning 4. TOTAL AREA: Festival plot is 75 ft x 50 ft. Area? Answer: 5. BOOTH SPACE: 5 booths, each 10 x 12 ft. Combined booth area? Answer: Global Sovereign University Press Page: 33 6. REMAINING: Plot area (#4) minus booth area (#5). Space for activities? Answer: 7. FENCING: Perimeter of 75 x 50 plot for safety fence? Answer: Financial Summary 8. TICKET REVENUE: $8 tickets, goal is $2,400. How many tickets must sell? Answer: 9. VOLUNTEER HOURS: 144 volunteers + 8-person teams. How many teams? Answer: 10. EXPENSE TRACKING: Budget $3,000. Spent $456 + $789 + $234 + $567. Remaining? Answer: Page: 34 Dr. Gene A Constant - Author CHAPTER 3 The Pet Shop Owner Chapter Goal: Master fractions through feeding schedules, tank measurements, and inventory. Welcome to Paws & Fins Pet Shop! As the owner, you'll use fractions every single day. How much food for each animal? What fraction of tanks need cleaning? What portion of your inventory is fish supplies? Let's care for these animals with mathematical precision! Section 1: Understanding Fractions @@ The Scenario Your pet shop is divided into sections: 3/8 for dogs, 2/8 for cats, 1/8 for fish, and 2/8 for small animals. Understanding fractions helps you manage space, food, and supplies. @@ The Skill: Fraction Basics Numerator (top): The number of parts you have Denominator (bottom): The total number of equal parts In 3/8: You have 3 parts out of 8 total equal parts. ‘%. Worked Example: Naming Fractions A cage has 6 equal compartments. 4 have hamsters. Fraction with hamsters: 4/6 Fraction empty: 2/6 Notice: 4/6 + 2/6 = 6/6 = 1 whole cage ‘% Worked Example: Fractions of a Group 12 puppies: 7 are brown, 5 are white Fraction brown: 7/12 Fraction white: 5/12 Check: 7/12 + 5/12 = 12/12 = 1 (all puppies accounted for) ‘%. Worked Example: Fractions and Remainders Bag of food is 3/4 full. What fraction is empty? A full bag = 4/4 Empty portion: 4/4 - 3/4 = 1/4 Answer: 1/4 of the bag is empty @@ Practice: Understanding Fractions 1. Cage has 6 compartments, 4 have hamsters. Fraction with hamsters? Answer: Global Sovereign University Press Page: 35 2. Tank divided into 5 sections, 2 have plants. Fraction with plants? Answer:

3. 12 puppies, 7 are brown. Fraction that are brown? Answer:

4. Bag is 3/4 full. What fraction is empty? Answer:

5. 8 tanks in store, 5 need cleaning. Fraction needing cleaning? Answer:

6. 10 birds total, 3 are parrots. Fraction that are parrots? Answer:

7. 24 animals total, 6 are reptiles. Fraction that are reptiles? Answer:

8. Water bowl is 2/3 full. Fraction that is empty? Answer:

9. 15 fish, 9 are goldfish. Fraction that are goldfish? Answer:

Page: 36 Dr. Gene A Constant - Author 10. 20 cages, 8 are empty. Fraction that are occupied? Answer:

11. Treat jar has 16 treats, 10 given away. Fraction remaining? Answer:

12. Pet shop open 5 days out of 7 days per week. Fraction open? Answer:

13. 30 bags of food, 12 are dog food. Fraction that is dog food? Answer:

14. Cat food bowl 5/6 full. Fraction empty? Answer:

15. 18 leashes, 6 are red. Fraction that are red? Answer:

16. Fish tank 7/8 full of water. Fraction empty? Answer:

17. 25 customers today, 15 bought something. Fraction that bought? Answer:

Global Sovereign University Press Page: 37 18. 12 puppies sleeping, 5 are awake. Fraction sleeping? Answer: Section 2: Equivalent Fractions @@ The Skill Equivalent fractions are different fractions that represent the same amount. You can find them by multiplying or dividing both the numerator and denominator by the same number. *%. Worked Example: Finding Equivalents: 2/4 = 1/2 Divide both numerator and denominator by 2: 2+2=1 4+2=2 So: 2/4 = 1/2 To go UP: 1/2 x 2/2 = 2/4, or 1/2 x 3/3 = 3/6 *~ Worked Example: Simplifying 8/12 Find a common factor of 8 and 12: Both divisible by 4 8+4=2 12+4=3 Simplified: 8/12 = 2/3 *% Worked Example: Finding a Missing Numerator 3/4 = 2/12 What times 4 equals 12? — 3 Multiply numerator by same: 3 x 3 = 9 Answer: 3/4 = 9/12 @@ Practice: Equivalent Fractions 1. Find equivalent: 3/6 = 2/2 Answer: 2. Find equivalent: 2/5 = 7/10 Answer: 3. Simplify: 4/8 Answer: Page: 38 Dr. Gene A Constant - Author 4. Simplify: 6/9 Work:

Answer: 5. Are 2/3 and 4/6 equivalent? Prove it. Work:

Answer: 6. Find equivalent: 3/4 = 2/12 Work:

Answer: 7. Simplify: 10/15 Work:

Answer: 8. Find three fractions equivalent to 1/2. Work:

Answer: 9. Simplify: 8/12 Work

Answer: 10. Which is in simplest form: 3/9, 2/5, or 4/6? Work

Answer: 11. Find equivalent: 4/6 = 2/3 Work:

Answer:

Global Sovereign University Press Page: 39 12. Simplify: 12/16 Work:

Answer: 13. Find equivalent: 5/6 = ?/18 Work:

Answer: 14. Simplify: 15/20 Work:

Answer: 15. Are 3/4 and 9/12 equivalent? Work:

Answer: 16. Find equivalent: 2/3 = ?/15 Work:

Answer: 17. Simplify: 9/27 Work:

Answer: 18. Find equivalent: 1/4 = 2/20 Work:

Answer: Page: 40 Dr. Gene A Constant - Author Section 3: Comparing Fractions ‘% Worked Example: Comparing 3/4 and 2/3 Method: Find a common denominator LCD of 4 and 3 is 12 3/4 = 9/12 2/3 = 8/12 9/12 > 8/12 Answer: 3/4 > 2/3 *% Worked Example: Comparing with Same Numerator Compare 2/5 and 2/7 Same numerator: Larger denominator = smaller fraction 2/5 has smaller pieces than 2/7 Answer: 2/5 > 2/7 @@ Practice: Comparing Fractions 1.Compare: 1/2 2/5 Answer: 2. Compare: 3/4__—5/8 Answer: 3. Compare: 2/3 3/5 Answer: 4. Order least to greatest: 1/2, 1/3, 1/4 Answer: 5. Compare: 5/6___7/8 Answer: Global Sovereign University Press Page: 41 6. Which is more food: 2/5 of a bag or 3/8 of a bag? Work: Answer: 7. Order greatest to least: 3/4, 2/3, 5/6 Work: Answer: 8. Cat ate 3/8, dog ate 2/6 of same-size bowl. Who ate more? Work: Answer: 9. Compare: 4/5 7/10 Work: Answer: 10. Order: 2/3, 5/6, 3/4, 7/12 from least to greatest Work: Answer: 11. Compare: 3/8 2/5 Work: Answer: 12. Which is less: 5/12 or 3/8? Work Answer: 13. Compare: 7/10 2/3 Work Answer: Page: 42 Dr. Gene A Constant - Author 14. Order greatest to least: 1/2, 3/5, 7/10 Answer: 15. Compare: 4/95/12 Answer:

Section 4: Adding & Subtracting Fractions ‘~ Worked Example: Same Denominators: 1/4 + 2/4 When denominators match, just add the numerators:

1/4 + 2/4 = 3/4 The denominator stays the same! ‘%. Worked Example: Different Denominators: 2/3 + 1/6 Step 1: Find common denominator (LCD of 3 and 6 is 6) Step 2: Convert 2/3 to sixths: 2/3 = 4/6 Step 3: Add: 4/6 + 1/6 = 5/6 Answer: 5/6 *%. Worked Example: Subtracting: 7/8 - 1/4 Convert 1/4 to eighths: 1/4 = 2/8 7/8 - 2/8 = 5/8 Answer: 5/8 of the tank remains @¢@ Practice: Fraction Operations 1. Add: 2/5 + 1/5 Answer: 2. Add: 3/8 + 2/8 Answer: Global Sovereign University Press Page: 43 3. Subtract: 5/6 - 2/6 Work:

Answer: 4. Add: 1/4 + 1/2 Work:

Answer: 5. Subtract: 3/4 - 1/2 Work:

Answer: 6. Morning feeding: 1/3 cup. Evening: 1/6 cup. Total? Work:

Answer: 7. Add: 2/3 + 1/4 Work:

Answer: 8. Tank was 7/8 full. Used 1/4 for water change. How full now? Work:

Answer: 9. Add: 1/2 + 1/3 + 1/6 Work:

Answer: 10. Subtract: 5/6 - 1/3 Work:

Answer: Page: 44 Dr. Gene A Constant - Author 11. Add: 3/8 + 1/4 Work:

Answer: 12. Had 7/8 bag of food. Used 3/8. What fraction remains? Work:

Answer: 13. Add: 2/5 + 3/10 Work:

Answer: 14. Subtract: 4/5 - 1/2 Work:

Answer: 15. Add: 1/6 + 2/3 Work:

Answer: 16. Bowl 5/6 full, drank 1/3. How full now? Work:

Answer: 17. Add: 3/4 + 1/8 Work:

Answer: 18. Subtract: 11/12 - 3/4 Work:

Answer:

Global Sovereign University Press Page: 45 Chapter 3 Action Report: Pet Shop Weekly Summary 1. INVENTORY: 24 animals total. 1/3 are dogs, 1/4 are cats. How many dogs? How many cats? Answer: 2. FEEDING: Dog needs 3/4 cup AM + 2/4 cup PM. Daily total? Answer: 3. CLEANING: 12 tanks, 8 need cleaning. What fraction? Simplify. Answer: ——‘—s—sSCSCSS 4. SUPPLIES: Cat food 2/3 full, dog food 5/8 full. Which has more? Answer: 5. USAGE: Used 5/8 of treats Monday + 1/4 Tuesday. Total fraction used? Answer: 6. SPACE: Dogs 3/8, cats 2/8, fish 1/8 of store. Fraction for small animals? Answer: 7. MEASURE: Food scoop holds 2/6 cup. Simplify this fraction. Answer: 8. COMPARISON: Puppies weigh 3/4 Ib, 2/3 Ib, 5/6 Ib. Order least to greatest. Answer: Page: 46 Dr. Gene A Constant - Author CHAPTER 4 The Recipe Master Chapter Goal: Use fractions and mixed numbers to scale recipes and measure ingredients.

Welcome to the school cafeteria kitchen! As Recipe Master, you'll double recipes for big events, halve them for small groups, and measure ingredients precisely. Cooking is applied mathematics— and hungry students are counting on your accuracy! Section 1: Understanding Mixed Numbers @@ The Skill A mixed number combines a whole number and a fraction: 2 1/2 means 2 whole things plus 1/2 more. An improper fraction has a numerator larger than its denominator: 5/2 means five halves.

*% Worked Example: Converting Mixed to Improper: 2 1/2 Step 1:

Multiply whole number x denominator: 2 x 2 = 4

Step 2: Add the numerator: 4+ 1=5

Step 3: Keep the same denominator: 5/2

Answer: 2 1/2 = 5/2

*% Worked Example: Converting Improper to Mixed: 11/4 Step 1:

Divide numerator by denominator: 11 + 4 = 2 remainder 3

Step 2: Whole number is the quotient: 2

Step 3: Remainder becomes new numerator: 3

Step 4: Keep same denominator: 4

Answer: 11/4 = 2 3/4

*% Worked Example: Comparing Mixed Numbers

Which is larger: 2 3/4 or 11/4?

Convert 2 3/4 to improper: (2*4)+3 = 11, so 2 3/4 = 11/4

Answer: They are equal! 2 3/4 = 11/4 @@ Practice: Mixed Numbers 1. Convert to improper fraction: 3 1/4

Answer: Global Sovereign University Press Page: 47 2. Convert to improper fraction: 2 2/3 Work:

Answer: 3. Convert to mixed number: 9/4 Work:

Answer: 4. Convert to mixed number: 17/5 Work:

Answer: 5. Convert to improper fraction: 4 1/2 Work:

Answer: 6. Convert to mixed number: 23/6 Work:

Answer: 7. Which is larger: 2 3/4 or 11/4? Prove it. Work:

Answer: 8. Recipe calls for 1 3/4 cups flour. Write as improper fraction. Work:

Answer: 9. Convert to mixed number: 19/8 Work:

Answer: Page: 48 Dr. Gene A Constant - Author 10. Convert to improper fraction: 5 2/3 Work:

Answer: 11. Convert to mixed number: 25/4 Work:

Answer: 12. Convert to improper fraction: 3 5/8 Work:

Answer: 13. Convert to mixed number: 31/6 Work:

Answer: 14. Convert to improper fraction: 6 1/3 Work:

Answer: 15. Which is larger: 3 1/2 or 10/3? Work:

Answer: 16. Convert to mixed number: 47/10 Work:

Answer: 17. Convert to improper fraction: 2 7/8 Work:

Answer:

Global Sovereign University Press Page: 49 18. Convert to mixed number: 33/8 Answer: Section 2: Adding Mixed Numbers ‘% Worked Example: Adding: 2 3/4 + 1 2/4 Step 1: Add the whole numbers: 2 + 1 =3 Step 2: Add the fractions: 3/4 + 2/4 = 5/4 Step 3: Convert improper fraction: 5/4 = 1 1/4 Step 4: Add to whole number: 3 + 1 1/4 = 4 1/4 Answer: 4 1/4 ‘% Worked Example: Adding with Different Denominators: 1 1/2 + 2 1/3 Step 1: Find common denominator: LCD of 2 and 3 is 6 Step 2: Convert fractions: 1/2 = 3/6 and 1/3 = 2/6 Step 3: Add: 1 3/6 + 2 2/6 = 3 5/6 Answer: 3 5/6 “ Worked Example: Recipe Application Morning batch: 2 1/4 cups flour. Afternoon batch: 1 3/4 cups flour. 2 1/4 + 1 3/4 =3 4/4 = 4 cups total flour needed @@ Practice: Adding Mixed Numbers 1. Add: 2 1/4 + 3 2/4 Answer: 2. Add: 1 2/5 + 2 1/5 Answer: 3. Add: 3 1/2 + 2 1/2 Answer: 4. Add: 1 3/4 + 2 3/4 Answer: Page: 50 Dr. Gene A Constant - Author 5. Add: 2 2/3 + 1 2/3 Work: Answer: 6. 1 1/2 cups milk + 2 1/4 cups water. Total liquid? Work: Answer: 7. Add: 4 5/8 + 2 7/8 Work: Answer: 8. Morning: 3 2/3 cups. Afternoon: 2 2/3 cups. Total? Work: Answer: 9. Add: 2 1/3 + 3 1/2 Work: Answer: 10. Add: 1 3/4 + 2 2/3 Work: Answer: 11. Add: 5 1/6 + 2 5/6 Work: Answer: 12. Add: 3 2/5 + 4 4/5 Work Answer: Global Sovereign University Press Page: 51 13. Add: 2 1/2 + 1 1/3 + 1 1/6 Answer: 14. Recipe: 1 1/4 cups sugar + 2 1/2 cups flour. Total dry ingredients? Answer: 15. Add: 6 3/8 + 2 5/8 Answer: 16. Add: 4 2/3 + 3 5/6 Answer: Section 3: Subtracting Mixed Numbers % Worked Example: Subtracting: 4 3/4 - 2 1/4 Fractions have same denominator, and 3/4 > 1/4 Whole numbers: 4 - 2 = 2 Fractions: 3/4 - 1/4 = 2/4 = 1/2 Answer: 2 1/2 “Worked Example: Subtracting with Borrowing: 5 1/4 - 2 3/4 Problem: Can't subtract 3/4 from 1/4! Step 1: Borrow 1 from the 5: 5 1/4 becomes 4 + 1 1/4 = 4 5/4 Step 2: Now subtract: 4 5/4 - 2 3/4 Whole numbers: 4 - 2 = 2 Fractions: 5/4 - 3/4 = 2/4 = 1/2 Answer: 2 1/2 ‘~ Worked Example: Recipe Subtraction Had 5 cups sugar. Used 2 1/3 cups. How much remains? 5 = 5 0/3 = 4 3/3 (borrow to subtract) 4 3/3 - 2 1/3 = 2 2/3 cups remaining Page: 52 Dr. Gene A Constant - Author @¢@ Practice: Subtracting Mixed Numbers 1. Subtract: 4 3/4 - 2 1/4 Work:

Answer: 2. Subtract: 5 2/3 - 3 1/3 Work:

Answer: 3. Subtract: 3 1/4 - 1 3/4 (borrowing needed!) Work:

Answer: 4. Subtract: 6 1/2 - 2 3/4 Work:

Answer: 5. Had 4 cups sugar. Used 1 2/3 cups. Remaining? Work:

Answer: 6. Subtract: 7 1/8 - 4 5/8 Work:

Answer: 7. 10 pounds flour - 6 3/4 pounds used. Left? Work:

Answer: 8. Subtract: 8 - 3 2/5 Work:

Answer:

Global Sovereign University Press Page: 53 9. Subtract: 5 1/3 - 2 2/3 Work:

Answer: 10. Subtract: 9 1/4 - 5 3/4 Work:

Answer: 11. Had 6 1/2 cups. Used 2 3/4 cups. Remaining? Work:

Answer: 12. Subtract: 7 2/5 - 3 4/5 Work:

Answer: 13. Subtract: 10 1/6 - 4 5/6 Work:

Answer: 14. Started with 8 gallons. Used 3 5/8 gallons. Remaining? Work:

Answer: 15. Subtract: 12 - 5 3/4 Work:

Answer: 16. Subtract: 6 1/3 - 2 5/6 Work:

Answer: Page: 54 Dr. Gene A Constant - Author Section 4: Multiplying Fractions %. Worked Example: Multiplying Two Fractions: 1/2 x 3/4 Step 1: Multiply numerators: 1 x 3 = 3 Step 2: Multiply denominators: 2 x 4 = 8 Answer: 3/8 ‘% Worked Example: Multiplying Fraction by Whole Number: 2/3 * 6 Write 6 as fraction: 6/1 Multiply: 2/3 x 6/1 = 12/3 = 4 Answer: 4 ‘% Worked Example: Finding Half of a Recipe Recipe needs 2/3 cup oil. Making half batch. 1/2 x 2/3 = 2/6 = 1/3 cup oil needed ‘% Worked Example: Multiplying Mixed Numbers 21/2 «2 Convert: 2 1/2 = 5/2 §/2 x 2=10/2=5 Answer: 5 @@ Practice: Multiplying Fractions 1. Multiply: 1/2 x 1/4 Answer: 2. Multiply: 2/3 x 3/4 Answer: 3. Multiply: 1/4 x 8 Answer: 4. Multiply: 3/5 x 2/3 Answer: Global Sovereign University Press Page: 55 5. Half of 2/3 cup is how much? Work:

Answer: 6. Multiply: 4/5 x 5/8 Work:

Answer: 7. Triple the recipe: 3 x 2/3 cup = ? Work:

Answer: 8. Multiply: 2 1/2 x 2 Work:

Answer: 9. Multiply: 3/4 = 2/5 Work:

Answer: 10. Multiply: 5/6 x 3 Work:

Answer: 11. Quarter of a recipe: 1/4 x 3/4 cup = ? Work:

Answer: 12. Multiply: 7/8 x 4/7 Work:

Answer: Page: 56 Dr. Gene A Constant - Author 13. Multiply: 2/3 x 9 Work:

Answer: 14. Multiply: 1 1/2 x 4 Work:

Answer: 15. Multiply: 5/8 x 2/3 Work:

Answer: 16. Double batch: 2 x 1 3/4 cups = ? Work:

Answer: Chapter 4 Action Report: Kitchen Math 1. CONVERSION: Recipe needs 3 2/5 cups. Write as improper fraction. Work:

Answer: 2. DOUBLE BATCH: Original recipe: 1 3/4 cups milk. Doubled amount? Work:

Answer: 3. COMBINED: Cake needs 2 1/2 cups flour. Frosting needs 1 3/4 cups. Total flour? Work

Global Sovereign University Press Page: 57 Answer: 4. REMAINING: Started with 5 cups sugar. Used 2 1/3 cups. How much left? Answer: 5. HALF BATCH: Full recipe uses 2/3 cup oil. Half batch needs? Answer: 6. TRIPLE: Recipe uses 1 1/4 cups butter. Triple batch needs? Answer: 7. SERVINGS: Recipe makes 2 1/2 gallons. Need 7 1/2 gallons. How many batches? Answer: 8. TOTAL: Breakfast used 3 2/3 cups flour. Lunch used 4 5/6 cups. Total today? Answer: Page: 58 Dr. Gene A Constant - Author CHAPTER 5 The Construction Crew Chapter Goal: Use measurement, conversion, and geometry to complete building projects. Welcome to the Construction Crew! You're helping build a new playground for the elementary school. You'll measure lumber, convert between units, calculate surface areas, and figure out how much fencing to order. Hard hats on—let's build! Section 1: Units of Length @@ Key Conversion Facts Inches and Feet: 1 foot = 12 inches Feet and Yards: 1 yard = 3 feet = 36 inches ‘~ Worked Example: Converting Feet to Inches: 8 ft = ? in 1 foot = 12 inches 8 feet = 8 x 12 = 96 inches Answer: 96 inches ‘“ Worked Example: Converting Inches to Feet: 54 inches = ? ft ? in Divide by 12: 54 + 12 = 4 remainder 6 Answer: 4 feet 6 inches ‘% Worked Example: Converting Yards to Feet: 5 yards = ? feet 1 yard = 3 feet 5 yards = 5 x 3 = 15 feet Answer: 15 feet @@ Practice: Length Conversions 1.5feet=_ inches Answer: 2.36 inches =___ feet Answer: 3.2 yards=____ feet Answer: Global Sovereign University Press Page: 59 4.4 feet 3inches =____ inches total Work:

Answer: 5.72 inches =____ feet Work:

Answer: 6.7 feet=_ inches Work:

Answer: 7.15 feet=_ yards Work:

Answer: 8.100 inches=__feet___ inches Work:

Answer: 9.6 yards =___ inches Work:

Answer: 10.30 feet=_ yards Work:

Answer: 11. 3 feet 8 inches =___ inches total Work:

Answer: Page: 60 Dr. Gene A Constant - Author 12.60 inches =____ feet Answer: 13.4 yards 2 feet=___ feet total Answer: 14.90 inches=__feet___ inches Answer: 15.18 feet=_ yards Answer: 16. 2 yards 1 foot =___ inches total Answer: Section 2: Perimeter @@ The Skill Perimeter: The distance around a shape. Add all sides! Rectangle formula: P = 2 x length + 2 x width (or P = 2L + 2W) ‘~ Worked Example: Rectangle Perimeter: 12 ft 8 ft P = 2(12) + 2(8) = 24 + 16 = 40 feet Or add all sides: 12 + 8 + 12 + 8 = 40 feet Answer: 40 feet of fencing needed ‘~ Worked Example: Finding Missing Side from Perimeter Rectangle perimeter is 48 ft. Length is 14 ft. Find width. P=2L+2W Global Sovereign University Press Page: 61 48 = 2(14) + 2W 48 = 28+ 2W 20 = 2W Width: 10 feet @¢@ Practice: Perimeter 1. Rectangle 12 ft x 8 ft. Perimeter? Answer: 2. Square with sides 9 ft. Perimeter? Answer: 3. Garden 15 ft x 10 ft. Fence needed? Answer: 4. Picture frame 24 in x 18 in. Border length? Answer: 5. Playground 50 ft x 30 ft. Perimeter? Answer: 6. Square perimeter is 48 ft. Side length? Answer: 7. Rectangle P = 60 ft, length = 18 ft. Width? Answer: Page: 62 Dr. Gene A Constant - Author 8. Triangle sides: 7 ft, 8 ft, 10 ft. Perimeter? Answer: 9. Room 14 ft x 12 ft. Baseboard needed? Answer: 10. Rectangle P = 100 ft, width = 20 ft. Length? Answer: 11. Square perimeter 64 ft. Side length? Answer: 12. Rectangle 25 ft x 15 ft. Perimeter? Answer: 13. Fence costs $8/ft. Rectangle 40 x 30 ft. Total fence cost? Answer: 14. Triangle P = 36 ft. Two sides are 12 ft and 14 ft. Third side? Answer: 15. Rectangle P = 84 ft. Length is 3x width. Find both. Answer: Global Sovereign University Press Page: 63 16. Square garden. 120 ft of fence available. Maximum side length? Answer: Section 3: Area @@ The Skill Area: The space inside a shape, measured in square units. Rectangle formula: A = length x width *% Worked Example: Finding Area: 15 ft x 12 ft room A= 15 x 12 = 180 square feet Answer: 180 sq ft ‘% Worked Example: Finding Missing Side from Area Rectangle area is 72 sq ft. Width is 8 ft. Find length. A=LxW 72=Lx8 L=72+8=9 Length: 9 feet ‘%. Worked Example: Real-World Application: Flooring Cost Room: 20 ft x 18 ft. Flooring costs $4 per square foot. Area: 20 x 18 = 360 sq ft Cost: 360 x $4 = $1,440 @@ Practice: Area 1. Rectangle 15 ft x 12 ft. Area? Answer: 2. Square side 8 ft. Area? Answer: 3. Floor 20 ft x 18 ft. Square feet? Answer: Page: 64 Dr. Gene A Constant - Author 4. Wall 12 x 9 ft. Paint covers 50 sq ft/gal. How many gallons? Answer: 5. Two rooms: 10x12 and 8x10 ft. Combined area? Answer: 6. Grass seed $2/sq ft. Lawn 30x20 ft. Cost? Answer: 7. Square area is 144 sq ft. Side length? Answer: 8. Rectangle area is 72 sq ft, width is 8 ft. Length? Answer: 9. Carpet $5/sq ft. Room 15x12 ft. Total cost? Answer: 10. Driveway 40 ft x 12 ft. Square feet? Answer: 11. Rectangle area 96 sq ft, length 12 ft. Width? Answer: Global Sovereign University Press Page: 65 12. Three rooms: 12x10, 1412, 108 ft. Total area? Answer: 13. Square area 225 sq ft. Side length? Answer: 14. Tile costs $3/sq ft. Bathroom 8x6 ft. Cost? Answer: 15. Playground 60x45 ft. Surface material $1.50/sq ft. Cost? Answer: 16. Rectangle 24x18 ft. Area in square yards? (9 sq ft = 1 sq yd) Answer: Section 4: Weight and Capacity @@ Key Facts Weight: 1 pound = 16 ounces, 1 ton = 2,000 pounds Capacity: 1 gallon = 4 quarts = 8 pints = 16 cups ‘% Worked Example: Converting Pounds to Ounces 5 pounds = ? ounces 5 x 16 = 80 ounces Answer: 80 ounces *%. Worked Example: Converting Gallons to Quarts 3 gallons = ? quarts 3 x 4= 12 quarts Page: 66 Dr. Gene A Constant - Author Answer: 12 quarts @@ Practice: Weight and Capacity 1.3 pounds =___ ounces Work: Answer: 2.48 ounces =____ pounds Work: Answer: 3.2 gallons =___ quarts Work: Answer: 4.1.5 tons=_ pounds Work: Answer: 5.5 gallons =___ pints Work Answer: 6.24 cups =___ quarts Work ____ Answer: 7. 3,500 pounds=___—tons___—s pounds Work: Answer: Global Sovereign University Press Page: 67 8. Need 960 Ibs of sand. Bags hold 80 Ibs. How many bags? Work:

Answer: 9.4 quarts =_ cups Work:

Answer: 10. 64 ounces =____ pounds Work:

Answer: 11.6 gallons =_ cups Work:

Answer: 12. 1 ton 500 Ibs =___ pounds total Work:

Answer: 13. 32 pints =___ gallons Work:

Answer: 14. Recipe needs 2 quarts. How many cups? Work:

Answer: 15. Truck holds 3 tons. Crates weigh 250 lbs each. Max crates? Work:

Answer: Page: 68 Dr. Gene A Constant - Author 16. Pool holds 5,000 gallons. How many quarts? Answer: Chapter 5 Action Report: Construction Summary 1. LUMBER: Need boards 18 ft total. Boards come in 6 ft lengths. How many? Answer: 2. CONVERSION: Blueprint shows 156 inches. Convert to feet. Answer: 3. FENCE: Playground 60x45 ft. Fence around perimeter? Answer: 4. SURFACE: Same 60x45 ft. Safety mulch costs $2/sq ft. Total cost? Answer: 5. CONCRETE: Need 1,200 Ibs. Bags hold 40 Ibs each. How many bags? Answer: 6. PAINT: Wall 15x10 ft. Gallon covers 100 sq ft. Enough with 1 gallon? Answer: 7. SANDBOX: Perimeter 24 ft, length 8 ft. Width? Area? Answer: Global Sovereign University Press Page: 69 8. TOTAL AREA: Three play areas: 12x10, 8x6, 5x5 ft. Combined sq ft? Answer: Page: 70 Dr. Gene A Constant - Author CHAPTER 6 The Sports League Manager Chapter Goal: Collect, organize, and analyze data using tables, graphs, and statistics. Welcome to Youth Sports League! As league manager, you'll track team scores, calculate batting averages, create standings, and make graphs to show performance. Data analysis helps you make fair decisions about playoffs, awards, and team improvements! Section 1: Reading and Creating Data Tables @@ The Scenario You need to track the performance of 4 teams throughout the season. Tables help organize large amounts of information clearly. ‘“ Worked Example: Reading a Team Standings Table Team | Wins | Losses | Ties | Total Games Eagles | 8|2|1| 11 Tigers |7|3]1|11 Bears |5|5|1| 11 Lions |2| 8 |1| 11 Eagles lead with 8 wins. Lions have most losses. ‘~ Worked Example: Calculating Win Percentage Eagles: 8 wins out of 11 games Win fraction: 8/11 Win percentage: 8 + 11 = 0.727 = about 73% @@ Practice: Data Tables 1. Eagles won 8 of 11 games. What fraction of games did they win? Answer: 2. Which team won exactly half their games? Answer: 3. What is the total number of wins across all four teams? Answer: Global Sovereign University Press Page: 71 4. Playoffs require 6 or more wins. Which teams qualify? Answer:

5. If Lions win 3 more games, what would be their new record? Answer:

6. What is the average number of wins per team? Answer:

7. What fraction of Bears' games were ties? Answer:

8. What is the combined number of losses for Eagles and Tigers? Answer:

9. Which team has the worst win-loss record? Answer:

10. If Tigers win 2 more games next week, what's their total? Answer:

11. Eagles lost what fraction of their games? Answer:

Page: 72 Dr. Gene A Constant - Author 12. How many more wins do Eagles have than Lions? Answer: 13. What percentage of Lions' games were losses? (Round to nearest %) Answer: 14. Total games played by all teams combined? Answer: 15. If all teams played 5 more games each, total games for league? Answer: 16. Bears need 2 more wins for playoffs. What would their record be? Answer: Section 2: Bar Graphs and Line Plots Basketball team scores this week: Monday 42, Tuesday 38, Wednesday 51, Thursday 45, Friday 44 *%. Worked Example: Reading Bar Graph Data Highest bar = best score: Wednesday with 51 points Shortest bar = lowest score: Tuesday with 38 points Range: 51 - 38 = 13 points between best and worst Total: 42 + 38 + 51 + 45 + 44 = 220 points @¢@ Practice: Graphs 1. What was the highest score this week? Answer: Global Sovereign University Press Page: 73 2. What is the range (highest minus lowest)? Answer:

3. What is the total points scored all five days? Answer:

4. Which two days had the closest scores? Answer:

5. Goal was 45 points per day. How many days met the goal? Answer:

6. How many more points were scored Wednesday than Tuesday? Answer:

7. What is the average daily score? Answer:

8. If Thursday's score increased by 5, what would it be? Answer:

9. Which day was closest to the average? Answer:

Page: 74 Dr. Gene A Constant - Author 10. Total points Monday through Wednesday? Answer: 11. How many points below the goal was Tuesday? Answer: 12. If Friday's score doubled, what would it be? Answer: 13. Difference between highest and second-highest day? Answer: 14. Order the days from lowest to highest score. Answer: 15. What fraction of total points came from Wednesday? Answer: 16. If every day had scored 45 points, what would week total be? Answer: Global Sovereign University Press Page: 75 Section 3: Mean, Mode, and Range @@ Key Definitions Mean (Average): Add all values, divide by count Mode: The value that appears most often Range: Difference between highest and lowest values % Worked Example: Finding the Mean Scores: 45, 52, 48, 52, 55 Step 1: Add all values: 45 + 52 + 48 + 52 + 55 = 252 Step 2: Count values: 5 Step 3: Divide: 252 + 5 = 50.4 Mean: 50.4 points ‘%. Worked Example: Finding the Mode Scores: 48, 52, 48, 55, 48, 52 48 appears 3 times (most frequent) 52 appears 2 times 55 appears 1 time Mode: 48 *%. Worked Example: Finding the Range Scores: 45, 52, 48, 52, 55 Highest: 55, Lowest: 45 Range: 55 - 45 = 10 Range: 10 points @¢@ Practice: Statistics 1. Find the mean: 12, 15, 18, 15 Answer: 2. Find the mean: 85, 90, 88, 92, 95 Answer: 3. Find the mode: 24, 28, 24, 30, 24 Answer: Page: 76 Dr. Gene A Constant - Author 4. Find the mean: 42, 38, 51, 45, 44 Work:

Answer: 5. Player scored 8, 12, 6, 10, 14 points in 5 games. Average? Work:

Answer: 6. Find the range: 23, 45, 31, 28, 40 Work:

Answer: 7. Find the mode: 12, 14, 12, 15, 12, 13 Work:

Answer: 8. Test scores: 75, 82, 78, 85. Average? Work:

Answer: 9. Find the mode: 5, 7, 5, 8, 5, 9, 7 Work:

Answer: 10. Find the range: 100, 85, 92, 78, 95 Work:

Answer: 11. Mean of 6 scores is 80. Sum of all scores? Work:

Answer:

Global Sovereign University Press Page: 77 12. Scores: 90, 85, 90, 75, 90. What's the mode? Answer: 13. Find mean: 123, 145, 156, 132, 144 Answer: 14. Range is 25, lowest is 60. What's the highest? Answer: 15. Find mode: 3, 5, 3, 7, 3, 5, 5, 3 Answer: 16. Average of 4 tests is 88. Sum of all tests? Answer: Section 4: Making Predictions from Data ‘% Worked Example: Using Average to Predict Team averages 45 points per game. Season has 20 games. Predicted total: 45 x 20 = 900 points for the season ‘% Worked Example: Using Percentages to Predict Team wins 60% of games. Playing 20 games total. Predicted wins: 60% of 20 = 0.60 x 20 = 12 wins Page: 78 Dr. Gene A Constant - Author @¢@ Practice: Predictions 1. Average 3 goals per game. Predict total for 15-game season. Answer: 2. Scoring 8 points per game. Predict 25-game season total. Answer: 3. Average 250 attendance per game. Predict total for 12 home games. Answer: 4. Run a mile in 8 minutes. Predict time for 5 miles. Answer: 5. Win 60% of games. In 20 games, predict number of wins. Answer: 6. Scored 180 points in first 4 games. Predict total for 10 games. Answer: 7. Score 12 runs every 3 games. Predict runs in 9 games. Answer: 8. Sell 50 tickets per hour. Predict sales for 8 hours. Answer: Global Sovereign University Press Page: 79 9. Average 15 points per game. Need 200 points. How many games? Answer:

10. Win rate is 75%. In 24 games, predicted wins? Answer:

11. Score 2.5 goals per game. Predict total for 18 games. Answer:

12. Average $450 in sales per day. Predict weekly (7-day) sales. Answer:

Chapter 6 Action Report: Season Summary

1. RECORD: Team has 12 wins, 6 losses, 2 ties. What fraction are wins? Answer:

2. SCORING: Week's scores: 52, 48, 61, 55, 44. Find the average. Answer:

3. RANGE: Highest score 78, lowest 42. What is the range? Answer:

4. PREDICTION: Average 48 points/game. Predict 15-game season total. Answer:

Page: 80 Dr. Gene A Constant - Author 5. MODE: Game times (minutes): 15, 18, 15, 20, 15, 17. Find the mode. Answer: 6. LEAGUE TOTAL: Four teams scored 45, 52, 38, 49. League total? Answer: 7. COMPARISON: Team A averages 42, Team B averages 45. Difference over 10 games? Answer: 8. GOAL CHECK: Need 50+ average. Scores: 48, 52, 46, 55. Will they make it? Answer: Global Sovereign University Press Page: 81 CHAPTER 7 The Savings Account Chapter Goal: Master decimals through banking, shopping, and money management. Welcome to Junior Banking! You'll manage a savings account, compare prices at different stores, calculate discounts, and track your balance. Understanding decimals is essential for financial success—every cent counts! Section 1: Decimal Place Value ‘ Worked Example: Understanding $42.75 4 is in the tens place = $40.00 2 is in the ones place = $2.00 7 is in the tenths place = $0.70 (70 cents) 5 is in the hundredths place = $0.05 (5 cents) Total: $40 + $2 + $0.70 + $0.05 = $42.75 ‘“ Worked Example: Rounding Money Round $34.67 to nearest dollar: Look at tenths (6). Is it 5 or more? YES! Round UP: $34.67 — $35.00 Round $8.943 to nearest cent: Look at thousandths (3). Is it 5 or more? NO! Round DOWN: $8.943 — $8.94 @@ Practice: Decimal Place Value 1. In 56.83, what is the value of the digit 8? Answer: 2. Write 23.45 in expanded form. Answer: 3. Write in standard form: 6 + 0.3 + 0.09 Answer: Page: 82 Dr. Gene A Constant - Author 4. In $125.49, what is the value of the digit 4? Work:

Answer: 5. Round $34.67 to the nearest dollar. Work:

Answer: 6. Round $8.943 to the nearest cent. Work:

Answer: 7. What digit is in the tenths place of 45.82? Work

Answer: 8. Write 7 dollars and 8 cents as a decimal. Work:

Answer: 9. What digit is in the hundredths place of 123.45? Work:

Answer: 10. Round $99.95 to the nearest dollar. Work:

Answer: 11. Write in expanded form: $156.72 Work

Answer:

Global Sovereign University Press Page: 83 12. Round $4.997 to the nearest cent. Answer: 13. What is 0.5 as a fraction? Answer: 14. Write 3 dollars 5 cents as a decimal. Answer: 15. Round $199.49 to the nearest dollar. Answer: 16. In 78.456, what is the value of the 5? Answer: Section 2: Comparing Decimals ‘% Worked Example: Comparing $24.95 and $24.59 Line up decimal points and compare left to right: Ones: both have 24 Tenths: 9 vs5>9>5 Answer: $24.95 > $24.59 (Store B is cheaper!) ‘% Worked Example: Ordering Decimals Order from least to greatest: 5.6, 5.06, 5.60, 5.066 Rewrite with same decimal places: 5.600, 5.060, 5.600, 5.066 Order: 5.06, 5.066, 5.6 = 5.60 Page: 84 Dr. Gene A Constant - Author @¢@ Practice: Comparing Decimals 1.Compare:3.5 3.50 Work:

Answer: 2. Compare: 4.25 4.3 Work:

Answer: 3. Compare: 12.09 12.1 Work:

Answer: 4. Order least to greatest: 5.6, 5.06, 5.60, 5.066 Work:

Answer: 5. Which costs less: $15.99 or $15.90? Work:

Answer: 6. Order greatest to least: 8.4, 8.04, 8.44, 8.404 Work:

Answer: 7. Compare: 0.5 (0.50 Work:

Answer: 8. Which is the better deal: $29.99 or $30.00? Work:

Answer:

Global Sovereign University Press Page: 85 9. Order least to greatest: 7.1, 7.01, 7.10, 7.001 Work:

Answer: 10. Compare: 6.789 ___—«6..79 Work:

Answer: 11. Which is more: 0.45 or 0.405? Work:

Answer: 12. Order greatest to least: 3.03, 3.3, 3.033, 3.303 Work:

Answer: 13. Compare: 9.90 9.9 Work:

Answer: 14. Which is less: $45.09 or $45.90? Work:

Answer: 15. Order: 0.25, 0.3, 0.205, 0.35 from least to greatest Work:

Answer: 16. Compare: 15.050 15.05 Work:

Answer: Page: 86 Dr. Gene A Constant - Author Section 3: Adding and Subtracting Decimals ‘% Worked Example: Adding: $45.67 + $23.45 Line up decimal points: 45.67 + 23.45 Answer: $69.12 ‘ Worked Example: Subtracting: $100.00 - $67.85 Line up decimal points: 100.00 - 67.85 Answer: $32.15 @¢@ Practice: Decimal Operations 1. Add: 45.67 + 23.45 Answer: 2. Subtract: 100.00 - 67.85 Answer: 3. Balance $234.56, deposit $45.00. New balance? Answer: 4. Add: 12.5 + 8.75 + 3.25 Answer: 5. Had $50.00, spent $23.47. Remaining? Answer: Global Sovereign University Press Page: 87 6. Add: 6.4 + 12.85 + 0.75 Work:

Answer: 7. Subtract: 85.00 - 36.78 Work:

Answer: 8. Check has $125.40. Spent $45.99, $32.50, $18.75. Remaining? Work:

Answer: 9. Add: 234.56 + 78.9 + 12.345 Work

Answer: 10. Subtract: $500.00 - $267.89 Work

Answer: 11. Balance $1,234.56. Withdraw $789.99. New balance? Work:

Answer: 12. Add: 0.5 + 0.75 + 1.25+0.5 Work:

Answer: 13. Subtract: 50 - 12.75 Work:

Answer: Page: 88 Dr. Gene A Constant - Author 14. Start $200, deposit $75.50, withdraw $48.25. Balance? Answer: 15. Add: 99.99 + 45.50 + 12.01 Answer: 16. Subtract: 1,000 - 456.78 Answer: Section 4: Multiplying Decimals ‘ Worked Example: Multiplying: $2.45 x 6 Step 1: Multiply as whole numbers: 245 x 6 = 1,470 Step 2: Count decimal places in factors: 2 (from 2.45) Step 3: Place decimal: 14.70 Answer: $14.70 ‘% Worked Example: Multiplying Two Decimals: 1.5 x 2.5 15 x 25 = 375 Decimal places: 1+ 1=2 Answer: 3.75 @¢@ Practice: Multiplying Decimals 1. Multiply: 3.5 x 4 Answer: 2. Multiply: 2.25 x 8 Answer: 3. $4.99 x 3 items. Total? Answer: Global Sovereign University Press Page: 89 4. Multiply: 1.5 x 2.5 Work:

Answer: 5. Gas costs $3.45 per gallon. 10 gallons costs? Work:

Answer: 6. Multiply: 12.50 x 4 Work:

Answer: 7. Tickets are $8.50 each. 5 people costs? Work:

Answer: 8. Multiply: 0.75 x 12 Work:

Answer: 9. $6.99 x 7 items. Total? Work:

Answer: 10. Multiply: 2.5 x 3.5 Work:

Answer: 11. Hourly wage $15.50. Worked 8 hours. Earnings? Work:

Answer: Page: 90 Dr. Gene A Constant - Author 12. Multiply: 4.25 x 6 Work: Answer: 13. $12.75 per yard. 5 yards costs? Work: Answer: 14. Multiply: 0.5 x 0.5 Work: Answer: 15. Tax is 8% ($0.08) on $25. Tax amount? Work: Answer: 16. Multiply: 3.14 = 10 Work: Answer: Chapter 7 Action Report: Banking Summary 1. BALANCE: Start $245.80, deposit $75.25, withdraw $50.00. Final balance? Work: Answer: 2. COMPARISON: Store A: $34.99. Store B: $35.09. Which is cheaper? Work: Answer: Global Sovereign University Press Page: 91 3. SHOPPING: Items cost $12.45, $8.99, $5.50. Total? Answer:

4. CHANGE: Pay $50.00 for $37.82 purchase. Change due? Answer:

5. PURCHASE: 6 books x $8.95 each. Total cost? Answer:

6. ORDERING: Arrange least to greatest: 3.45, 3.405, 3.5, 3.54 Answer:

7. ROUNDING: Round $156.847 to the nearest cent. Answer:

8. SAVINGS: Save $12.50 per week x 8 weeks. Total saved? Answer:

Page: 92 Dr. Gene A Constant - Author CHAPTER 8 The Delivery Driver Chapter Goal: Calculate elapsed time, read schedules, and plan efficient routes. Welcome to Express Delivery! Calculate how long deliveries take, read bus schedules, and make sure packages arrive on time. Time management is essential for keeping customers happy! Section 1: Telling Time and Time Intervals @@ Key Facts Minutes and Hours: 60 minutes = 1 hour Seconds and Minutes: 60 seconds = 1 minute ‘% Worked Example: Finding Time Intervals From 9:20 to 9:45 = how many minutes? Count: 9:20 — 9:45 = 25 minutes Or subtract: 45 - 20 = 25 minutes ‘% Worked Example: Adding Time 45 minutes after 10:30 AM is what time? 10:30 + 30 min = 11:00 11:00 + 15 min = 11:15 AM @¢@ Practice: Telling Time 1.9:20 to 9:45 =_ minutes Answer: 2. 2:30 PM to 3:00 PM=___ minutes Answer: 3. 45 minutes after 10:30 AM is what time? Answer: Global Sovereign University Press Page: 93 4. 20 minutes before 4:15 PM is what time? Work:

Answer: 5. 11:45 AM to 12:15 PM = how long? Work:

Answer: 6. 1 hour 15 minutes after 9:50 AM is what time? Work:

Answer: 7. 35 minutes after 7:40 PM is what time? Work:

Answer: 8. 50 minutes before 3:05 PM is what time? Work:

Answer: 9. 8:25 to 9:10 =___s minutes Work

Answer: 10. 2 hours 20 minutes after 6:45 AM is what time? Work

Answer: 11. 7:55 to 8:30 =____s minutes Work:

Answer: Page: 94 Dr. Gene A Constant - Author 12. 1 hour 45 minutes before 2:30 PM is what time? Answer: 13. 10:40 to 11:25=_ minutes Answer: 14. 55 minutes after 11:35 PM is what time? Answer: 15. 3:15 to 5:00 =_——s hours__ minutes Answer: 16. 25 minutes before 12:10 PM is what time? Answer: Section 2: Elapsed Time *% Worked Example: 10:45 AM to 2:20 PM Method: Count in chunks 10:45 AM — 11:00 AM = 15 minutes 11:00 AM — 2:00 PM = 3 hours 2:00 PM — 2:20 PM = 20 minutes Total: 3 hours 35 minutes *% Worked Example: Finding End Time Start: 2:45 PM. Duration: 2 hours 35 minutes 2:45 + 2 hours = 4:45 PM 4:45 + 35 minutes = 5:20 PM End time: 5:20 PM Global Sovereign University Press Page: 95 @¢@ Practice: Elapsed Time 1. 8:30 AM to 11:45 AM = ? Work: Answer: 2. 1:15 PM to 4:30 PM = ? Work: Answer: 3. Movie starts 7:45 PM, ends 10:10 PM. Length? Work: Answer: 4. Flight departs 6:30 AM, arrives 9:15 AM. Duration? Work: Answer: 5. Work 8:00 AM to 4:30 PM. Total hours? Work: Answer: 6. Game starts 2:45 PM, lasts 2 hr 35 min. End time? Work: Answer: 7. School 8:15 AM to 3:30 PM. Total hours? Work: Answer: 8. Show starts 7:30 PM, ends 11:00 PM. Length? Work: Answer: Page: 96 Dr. Gene A Constant - Author 9. Practice 3:45 PM to 6:00 PM. Duration? Answer: 10. Leave home 7:20 AM, arrive 9:05 AM. Travel time? Answer: 11. Meeting 10:30 AM, lasts 1 hr 45 min. End time? Answer: 12. Party 4:00 PM to 7:30 PM. Duration? Answer: 13. Train departs 5:55 PM, journey 3 hr 20 min. Arrival? Answer: 14. Store hours 9:00 AM to 9:00 PM. Open how long? Answer: y 15. Baking starts 2:15 PM, takes 1 hr 50 min. Done when? Answer: 16. Event 11:30 AM to 3:45 PM. Duration? Answer: Global Sovereign University Press Page: 97 Section 3: Planning with Schedules ‘% Worked Example: Route Planning 5 deliveries x 25 minutes each = 125 minutes 125 minutes = 2 hours 5 minutes Start 9:00 AM — Finish 11:05 AM ‘% Worked Example: Working Backward Must arrive by 3:00 PM. Trip takes 45 minutes. 3:00 PM - 45 minutes = 2:15 PM Leave by: 2:15 PM at latest @@ Practice: Schedules 1.3 stops x 20 minutes each. Total time? Answer: 2. Start 8:30 AM, 4 deliveries x 15 min each. Finish time? Answer: 3. Must arrive by 3:00 PM. Trip takes 45 min. Latest departure? Answer: 4. 8 deliveries x 30 min=___ hours Answer: 5. Work 10:00 AM to 12:00 PM, break, 12:30 PM to 3:00 PM. Total work time? Answer: 6. Need 4 hr 30 min for task. Start 7:45 AM. End time? Answer: Page: 98 Dr. Gene A Constant - Author 7. 6 stops x 25 min each. Start 10:00 AM. Finish? Answer: 8. Due 5:00 PM. Takes 2 hr 15 min. Latest start? Answer: 9. Bus every 20 min starting 6:00 AM. Third bus arrives? Answer: 10. 5 tasks: 45, 30, 60, 25, 40 min. Total time? Answer: 11. Start 9:15 AM. Tasks: 1 hr 20 min, 45 min, 1 hr 10 min. End? Answer: 12. Need to finish by 4:30 PM. Tasks total 3 hr 45 min. Latest start? Answer: Section 4: Time Conversions *%. Worked Example: 185 minutes = ? hours ? minutes Divide by 60: 185 + 60 = 3 remainder 5 Answer: 3 hours 5 minutes ‘% Worked Example: 2 hr 45 min = ? minutes 2 hours = 2 x 60 = 120 minutes 120 + 45 = 165 minutes Answer: 165 minutes Global Sovereign University Press Page: 99 @@ Practice: Time Conversions 1.150 min=_hr___smin Work:

Answer: 2.2 hr45 min =____ minutes Work:

Answer: 3.200 min=_ohr__s min Work:

Answer: 4.3.5 hours =___ minutes Work:

Answer: 5.90 seconds=___smin____ sec Work:

Answer: 6.4 hr 20 min=____ minutes total Work:

Answer: 7.275 min=__shr__ min Work:

Answer: 8.5.25 hours =__ohr__min Work:

Answer: Page: 100 Dr. Gene A Constant - Author 9.180 seconds =___ minutes Work:

Answer: 10.6hr15min=____ minutes Work:

Answer: 11.320 min=_shr__ min Work:

Answer: 12. 1.75 hours =___ minutes Work:

Answer: Chapter 8 Action Report: Delivery Day Summary 1. ROUTE: Left depot 7:45 AM, returned 2:15 PM. Time on route? Work:

Answer: 2. DELIVERIES: 6 stops x 35 min each. Start 9:00 AM. Finish time? Work:

Answer: 3. CONVERSION: Route took 255 min. Express in hours and minutes. Work:

Answer: 4. DEADLINE: Package due 4:30 PM. Delivery takes 1 hr 45 min. Latest pickup? Work

Answer: Global Sovereign University Press Page: 101 5. TOTAL: Morning 2 hr 15 min, afternoon 3 hr 40 min. Total work time? Answer: 6. WORK DAY: Shift 8 AM to 5 PM with 45-min lunch. Hours worked? Answer: CHAPTER 9 The Garden Designer Chapter Goal: Use patterns, variables, and equations to plan beautiful gardens. Welcome to Green Thumb Landscapes! You'll discover patterns in plant arrangements, use variables to write formulas, and solve equations to figure out how many supplies to order. Algebra starts here! Section 1: Number Patterns ‘%. Worked Example: Finding the Pattern: 4, 7, 10, 13... Look at differences between numbers: 7-4=3, 10-7=3, 13-10=3 Rule: Add 3 each time Next number: 13 + 3 = 16 Row 10: Start at 4, add 3 nine times = 4 + 27 = 31 *%. Worked Example: Geometric Pattern: 3, 6, 12, 24... Look at relationships: 6+3=2, 12+6=2, 24+12=2 Rule: Multiply by 2 each time Next: 24 x 2 = 48 @@ Practice: Patterns 1.2, 5,8, 11,__. What's next? Answer: Page: 102 Dr. Gene A Constant - Author 2. 3, 6,12, 24, _. What's next? Work:

Answer:

3. 100, 90, 80, 70, __—. What's next? Work:

Answer: 4. Row 1: 5 plants, Row 2: 8, Row 3: 11. Row 5? Work:

Answer: 5.1,4,9, 16, _. What's next? (Hint: Square numbers!) Work:

Answer:

6. Fence posts: 4, 7, 10, 13. Section 8? Work:

Answer:

7. 2,6, 18, 54, What's next? Work:

Answer:

8. 50, 45, 40, 35,___—. What's next? Work:

Answer: 9.1, 1, 2, 3,5, 8,__. What's next? (Fibonacci!) Work:

Answer:

Global Sovereign University Press Page: 103 10. 64, 32, 16,8, __—. What's next? Work:

Answer: 11. Pattern +4: First term is 3. What's the 6th term? Work:

Answer: 12. Tiles: 1, 3,6, 10, __. What's next? (Triangular numbers) Work:

Answer: 13.5, 10, 20,40, _—. What's next? Work:

Answer: 14. Pattern: 7, 14, 21, 28. What's the 10th term? Work:

Answer: 15. 81, 27,9, 3,__. What's next? Work:

Answer: 16. Flowers: Row 1 has 6. Each row adds 4 more. Row 8? Work:

Answer: Page: 104 Dr. Gene A Constant - Author Section 2: Understanding Variables A variable is a letter that represents an unknown number. We use variables to write general rules. ‘% Worked Example: Using Variables Each flower needs w gallons of water. 12 flowers need: 12 x w gallons If w = 2: 12 x 2 = 24 gallons needed *% Worked Example: Evaluating Expressions Evaluate 3n + 2 whenn =4 Substitute: 3(4) +2=12+2=14 Answer: 14 @@ Practice: Variables 1. Write an expression: 8 more than n Answer: 2. Write an expression: 5 times x Answer: 3. Evaluate: 3n + 2 whenn =4 Answer: 4. Evaluate: 2x - 5 when x = 10 Answer: 5. Cost = 6p. If p = 15, what is the cost? Answer: Global Sovereign University Press Page: 105 6. Area =s *s. If s = 7, what is the area? Work:

Answer: 7. Evaluate: 4n + 3n when n =5 Work:

Answer: 8. Perimeter = 4s. If P = 36, what is s? Work:

Answer: 9. Evaluate: 5x - 3 when x = 8 Work:

Answer: 10. Distance = 60t. If t = 3 hours, what is distance? Work:

Answer: 11. Write expression: n divided by 4 Work:

Answer: 12. Evaluate: 2a + 3b when a=5 andb=4 Work:

Answer: 13. Write expression: 7 less than twice x Work:

Answer: Page: 106 Dr. Gene A Constant - Author 14. Evaluate: n? + 5 when n =6 Answer: 15. If y = 3x + 1 and x = 5, find y. Answer: 16. Cost = 4.50n. Find cost when n = 8. Answer: Section 3: Writing and Solving Equations ‘% Worked Example: Solving n + 5 = 18 What number plus 5 equals 18? Think: 18 - 5 = 13 Answer: n = 13 Check: 13+ 5=18V % Worked Example: Solving 3n = 24 What number times 3 equals 24? Think: 24 + 3=8 Answer: n = 8 Check: 3 x 8= 24 V/V @@ Practice: Equations 1. Solve:n+7=15 Answer: 2. Solve: x - 4 = 12 Answer: Global Sovereign University Press Page: 107 3. Solve: 3n = 24 Work:

Answer: 4. Solve: n + 12 = 30 Work:

Answer: 5. Solve: 5x = 45 Work:

Answer: 6. Solve: n- 8 = 25 Work:

Answer: 7. Write and solve: A number plus 9 equals 21. Work:

Answer: 8. Write and solve: 4 times a number equals 32. Work:

Answer: 9. Solve: 2n + 3 = 11 Work:

Answer: 10. Solve:n+4=8 Work:

Answer: Page: 108 Dr. Gene A Constant - Author 11. Solve: 15-n=7 Work: Answer: 12. Solve: 6x = 54 Work: Answer: 13. Write and solve: A number minus 15 equals 23. Work: Answer: 14. Solve:n+n+n=27 Work: Answer: 15. Solve: 4n- 5 = 19 Work: Answer: 16. Solve: 100 +n = 25 Work Answer: Section 4: Input-Output Tables *%. Worked Example: Finding the Rule Pots: 1 — $3, 2 > $6, 3 — $9, 4 — $12 Pattern: Each output is 3 times the input Rule: Cost = 3 x Pots (or y = 3x) Global Sovereign University Press Page: 109 @¢@ Practice: Input-Output Tables 1. Rule: x4. Input 5. Output? Work:

Answer: 2. Rule: +6. Input 12. Output? Work:

Answer: 3. In: 2,4,6,8. Out: 7,9,11,13. What's the rule? Work:

Answer: 4. In: 1,2,3,4. Out: 5,10,15,20. What's the rule? Work:

Answer: 5. y = 2x + 1. If x = 6, what is y? Work

Answer: 6. y = 3x - 2. If y = 10, what is x? Work:

Answer: 7. In: 3,5,7,9. Out: 9,15,21,27. What's the rule? Work:

Answer: 8. y = 4x. If y = 36, what is x? Work:

Answer: Page: 110 Dr. Gene A Constant - Author 9. Rule: x3 then -1. Input 7. Output? Work Answer: 10. In: 10,20,30,40. Out: 2,4,6,8. What's the rule? Work: Answer: 11. y =x +8. Complete: If x = 15, y=? Work Answer: 12. In: 2,4,6,8. Out: 1,2,3,4. What's the rule? Work Answer: Chapter 9 Action Report: Garden Planning 1. PATTERN: Sections have 6, 10, 14, 18 flowers. What's next? Work Answer: 2. VARIABLE: Each garden bed needs b bags of soil. 8 beds need how many? Work: Answer: 3. EXPRESSION: Plants = 4n + 2. If n = 7, how many plants? Work Answer: 4. EQUATION: Started with some plants, added 12, now have 35. How many at start? Work Answer: Global Sovereign University Press Page: 111 5. SOLVE: 6n = 42 Answer:

6. RULE: In: 3,5,7,9. Out: 12,20,28,36. What's the rule? Answer:

7. PREDICT: Pattern adds 5 each row. Row 1 has 8. Row 12 has? Answer:

8. COST: Shrubs cost $15 each. Write cost equation. Find cost of 9 shrubs. Answer:

Page: 112 Dr. Gene A Constant - Author CHAPTER 10 The Business Plan Chapter Goal: Apply ALL your mathematical skills to create and analyze a real business.

Congratulations! You've learned place value, operations, fractions, decimals, measurement, data analysis, time management, and algebraic thinking. Now you'll use EVERYTHING to create your very own Lemonade Stand business! Part 1: Startup Costs (Decimals & Operations) Supplies needed: Cups $12.50, Lemons $18.75, Sugar $8.25, Pitcher $15.99 1. What is the total startup cost?

Answer: 2. You have $75.00 saved. After buying supplies, how much remains?

Answer: 3. If cups cost $2.50 more, what would new total be?

Answer: Part 2: Recipe Scaling (Fractions) One batch (makes 8 cups): 1 1/2 cups lemon juice, 3/4 cup sugar, 6 cups water 4. Triple the recipe: How much lemon juice needed?

Answer: 5. Triple the recipe: How much sugar needed?

Answer:

Global Sovereign University Press Page: 113 6. Triple batch makes how many cups of lemonade? Work: Answer: 7. Half batch: How much lemon juice? Work: Answer: Part 3: Pricing & Profit (Multiplication) Selling price: $2.00 per cup. Cost to make: $0.50 per cup. 8. What is the profit per cup (price minus cost)? Work: Answer: 9. Revenue from selling 45 cups? Work: Answer: 10. Total profit from 45 cups? Work Answer: 11. How many cups to earn $60 profit? Work: Answer: Part 4: Time Management (Elapsed Time) Stand hours: 10:00 AM to 2:00 PM 12. How many hours is the stand open? Work: Answer: Page: 114 Dr. Gene A Constant - Author 13. 45 cups in 4 hours. Average cups per hour? Work Answer: 14. 2 minutes per customer. Customers per hour? Work Answer: 15. If you start setup at 9:15 AM and need 45 min, when do you finish? Work Answer: Part 5: Data Analysis (Statistics) Week 1 sales: Mon 38, Tue 42, Wed 45, Thu 52, Fri 48 16. Total cups sold this week? Work Answer: 17. Average daily sales? Work Answer: 18. Range of daily sales? Work Answer: 19. If Saturday sells 20% more than average, how many cups? Work Answer: Global Sovereign University Press Page: 115 Part 6: Growth Patterns (Algebra) Sales growth: Week 1: 225, Week 2: 270, Week 3: 315, Week 4: 360 20. What is the pattern (how many cups added each week)? Answer: 21. Predict Week 5 sales. Answer: 22. Write an equation for the pattern (let w = week number). Answer: Part 7: Stand Layout (Geometry) Stand space: 8 ft x 6 ft. Table: 4 ft x 2 ft. Cooler: 2 ft x 2 ft. 23. What is the total area of your stand space? Answer: 24. What is the perimeter (for decorative ribbon)? Answer: 25. Area remaining after placing table and cooler? Answer: Page: 116 Dr. Gene A Constant - Author Part 8: Final Business Report (All Skills) 26. Week 1 Revenue: 225 cups x $2.00 = ? Answer: 27. Week 1 Costs: 225 cups x $0.50 = ? Answer: 28. Week 1 Net Profit: Revenue minus Costs = ? Answer: 29. If you save 1/2 of profit and reinvest 1/2, how much each? Answer: 30. Goal: $500 profit. At $1.50 profit per cup, how many cups needed? Answer: Congratulations, Fourth Grade Mathematician! You've completed an entire year of real-world mathematics! You can now: ¥ Work with numbers to millions and decimals to hundredths Vv Add, subtract, multiply, and divide with confidence V Use fractions in recipes, measurements, and comparisons V Calculate area, perimeter, and convert between units V Analyze data, find averages, and make predictions V Manage time and plan schedules v Recognize patterns and write algebraic equations V Apply mathematics to real business decisions You're ready for fifth grade and beyond. Great work! About Global Sovereign University "Building a Bridge to Freedom Through Education—Not Handouts" Global Sovereign University Press Page: 117 Global Sovereign University is a 501(c)(3) educational foundation with a simple mission: We believe every person deserves access to quality education that builds real capabilities—not temporary fixes. This textbook is provided FREE to students because learning should never be limited by economics. When you master mathematics, you gain tools for independence and success that no one can take away. For more free educational resources, visit:

www.globalsovereignuniversity.org Teachers: A separate Teacher's Guide with complete answer keys, lesson plans, pacing guides, and assessment rubrics is available for purchase to support your instruction. About the Author Author | Historian | Educator | Visionary His work with GSU focuses on ending economic poverty through capability-building education delivered by retired professional mentors called "Civilization Builders." His other works include the "History of the Americans" series (6 volumes), the "Teach a Man to Fish" trilogy, the "Survival in an Al World" series (4 volumes), and numerous guides on mathematics education, personal development, and relationship psychology. He hosts the "Voice of Sovereignty" podcast, which reaches global audiences in ten languages. Dr. Constant believes that every human being bears the image of God and possesses untapped potential waiting to be awakened. This theological conviction drives his life's work of helping people move from dependency to sovereignty, from poverty to flourishing, and from ignorance to capability. Dr. Gene A Constant, DBA, is a prolific American author and the founder of the Foundation for Global Instruction. With more than 100 published titles ranging from civic education to self-help, business, leadership, and history, Dr. Constant's mission is to empower individuals through knowledge, legacy, and personal transformation. A veteran of both the United States Navy and the United States Marine Corps, he combines firsthand experience in service and discipline with decades of scholarship. His honors include being inducted into the Phi Theta Kappa Honor Society (1983) and his gubernatorial appointment as Honorary Lieutenant Colonel Aide-de-camp in the Alabama National Guard (1975). Raised in Springfield, Illinois—just blocks from the legacy of Abraham Lincoln—Dr. Constant carries forward the American tradition of principled leadership. His writing speaks to parents, teachers, dreamers, and defenders of liberty, blending patriotic themes with personal testimony and historical insight. His most notable works include Page: 118 Dr. Gene A Constant - Author There Can Be a Better Life, The Second American Civil War (2024), Digital Farm, and Guardian Angel of the American Spirit. He is also the visionary behind “Legacy Learning for the Common Man,” a global adult education initiative that champions traditional values, multilingual instruction, and practical knowledge for all. Multilingual Closing: Hy: FAVE Ee MAAStH ALBA. (My works are dedicated to readers around the world.) fed: AY qeret ai Sexa Want Usd sik Wa HT S| (The purpose of my books is to empower and inspire everyone.) Cazes Galil on Dey 4d peal 55 Gl} Langs (tS An all, (My books aim to spread knowledge and hope among all people.) For more information about Global Sovereign University and the Civilization Builder program, visit GlobalSovereignUniversity.org