Grade 6 Mathematics
Student Edition
Real-World Problem Solving for Pre-Algebra Success
Ratios • Integers • Algebra • Geometry • Statistics
GLOBAL SOVEREIGN UNIVERSITY
"Building a Bridge to Freedom Through Education—Not Handouts"
Math in Action: Grade 6 Real-World Problem Solving
Copyright © 2024 Global Sovereign University Press
All rights reserved. First Edition.
FREE EDUCATIONAL RESOURCE
This curriculum is provided at no cost to students and educators worldwide.
Why This Book Is Different: The Nobel Prize Research .................. 4
Chapter 1: The Nutritionist — Ratios and Proportions .................. 8
Chapter 2: The Banker — Integers and Rational Numbers ................. 17
Chapter 3: The Architect — Surface Area and Nets ...................... 26
Chapter 4: The Recipe Developer — Dividing Fractions .................. 35
Chapter 5: The Data Journalist — Statistical Distributions ............ 44
Chapter 6: The Map Maker — Scale Drawings and Proportions ............. 53
Chapter 7: The Stock Trader — Algebraic Expressions ................... 62
Chapter 8: The Event Planner — Percent Applications ................... 71
Chapter 9: The Climate Scientist — Absolute Value and Data ............ 80
Chapter 10·The Entrepreneur — Capstone Project ....................... 89
Extra Practice ........................................................ 98
Challenge Problems .................................................... 106
Why This Book Is Different
Nobel Prize-Winning Research Proves We Need a New Approach
"Students who score 96% on classroom math tests succeed only 1% of the time when solving the same problems in real
life."
— Banerjee & Duflo, Nature, February 2025 (2019 Nobel Prize in Economics)
What the Research Found
Nobel Prize-winning economists Abhijit Banerjee and Esther Duflo conducted a landmark study with over 1,400 children. They discovered something shocking: the math skills students learn in school don't transfer to real life.
Students who aced their classroom tests couldn't solve the same math problems when presented in real-world situations. Meanwhile, children who worked in markets (with no formal education) solved practical problems with 96% accuracy.
The Missing Bridge
The researchers concluded: Schools need to build a bridge between math learned in the classroom and math encountered in real-life situations.
This book IS that bridge.
How This Book Works
In every chapter, you will become a professional who needs math to succeed:
• Chapter 1: You're a Nutritionist calculating ratios and proportions for meal plans
• Chapter 2: You're a Banker working with positive and negative transactions
• Chapter 3: You're an Architect designing 3D structures with surface area
• Chapter 4: You're a Recipe Developer scaling recipes by dividing fractions
• Chapter 5: You're a Data Journalist analyzing statistical distributions
• Chapter 6: You're a Map Maker using scale drawings and proportional reasoning
• Chapter 7: You're a Stock Trader writing algebraic expressions for market trends
• Chapter 8: You're an Event Planner calculating percentages and budgets
• Chapter 9: You're a Climate Scientist working with absolute value and data
• Chapter 10: You're an Entrepreneur running your own startup with ALL skills
Pre-Algebra Foundation
Grade 6 is the critical bridge to algebra. Throughout this book, you'll work with:
• Variables and algebraic expressions
• One-step equations and inequalities
• Negative numbers and the number line
• Ratios, rates, and proportional relationships
By the end of this book, you won't just know math—you'll think like someone who uses math every day.
A Note to Students
You might wonder: Why do I need to learn this?
Here's the truth: Every job worth having uses math. Doctors calculate dosages. Engineers design bridges. Business owners track profits. Scientists analyze data. Even artists use proportions and geometry.
The difference between people who succeed and people who struggle often comes down to one thing: Can they apply what they learned in school to real situations?
This book trains you to do exactly that.
Research Citation
Banerjee, A., Duflo, E., et al. (2025). Children's arithmetic skills do not transfer between applied and academic mathematics. Nature.
Let's build that bridge—together.
🥗
CHAPTER 1 The Nutritionist
Master ratios, rates, and proportions to create balanced nutrition plans
Section 1.1: Understanding Ratios
As a nutritionist, you help people eat better. You need to understand the ratios between different nutrients—how much protein compared to carbs, how many vegetables relative to grains.
What is a Ratio?
A ratio compares two quantities. If a meal has 30 grams of protein and 45 grams of carbohydrates, the ratio of protein to carbs is 30:45 or 30/45.
Ratio of A to B = A : B = A/B
Ratios can be simplified like fractions. 30:45 simplifies to 2:3 (divide both by 15).
WORKED EXAMPLE
A smoothie recipe calls for 2 cups of fruit and 3 cups of yogurt. What is the ratio of fruit to yogurt? Write it in simplest form.
Solution: The ratio is 2:3. Check if it simplifies: GCF of 2 and 3 is 1, so 2:3 is already in simplest form.
Answer: 2:3 (or 2/3)
WORKED EXAMPLE
A patient's meal has 40g protein, 60g carbs, and 20g fat. What is the ratio of protein to carbs to fat?
Solution: Write all three: 40:60:20. Find GCF of all three: 20. Divide each by 20: 40÷20 = 2, 60÷20 = 3, 20÷20 = 1.
Answer: 2:3:1
Practice Problems
1. A salad has 4 cups of lettuce and 2 cups of spinach. What is the ratio of lettuce to spinach in simplest form?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. A protein shake has 25g protein and 35g carbs. Write the ratio of protein to carbs in simplest form.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A meal plan includes 6 servings of vegetables and 3 servings of fruit daily. What is the ratio of vegetables to fruit?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A patient needs 2,400 calories daily: 600 from protein, 900 from carbs, 900 from fat. Write the ratio in simplest form.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A soup recipe uses 3 cups of broth for every 1 cup of vegetables. Write this ratio two different ways.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. In a healthy diet, the ratio of omega-3 to omega-6 should be 1:4. If you consume 8g of omega-6, how much omega-3 should you have?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A nutrition bar has 12g sugar and 18g fiber. What is the ratio of sugar to fiber in simplest form?
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
8. A breakfast plate has 2 eggs, 3 strips of bacon, and 4 pieces of toast. What is the ratio of eggs to bacon to toast?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. The ratio of protein to total calories should be about 30:100. Simplify this ratio.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A dietitian recommends a 3:1 ratio of water to juice. If you drink 9 cups of water, how many cups of juice?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. A meal has 45g carbs and 15g protein. Express this as a unit ratio (how many g carbs per 1g protein).
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Compare: Meal A has protein:carbs ratio of 2:5. Meal B has ratio of 3:8. Which has more protein relative to carbs?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A client's weekly meal plan has 21 servings of protein and 28 servings of vegetables. Simplify this ratio.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. The USDA recommends 2.5 cups of vegetables and 2 cups of fruit daily. What is the ratio of vegetables to fruit?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A nutrition label shows 8g fat and 24g carbs. Write the ratio of fat to carbs, then express how many g carbs per g fat.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 1.2: Unit Rates
A unit rate tells you how much of something per ONE unit of something else. As a nutritionist, you constantly work with unit rates: calories per serving, grams of protein per ounce, cost per meal.
Unit Rate = Total Quantity ÷ Number of Units
Key phrase: 'per' always signals a rate—miles per hour, dollars per pound, calories per serving.
WORKED EXAMPLE
A 24-ounce protein powder contains 720 grams of protein. How many grams of protein per ounce?
Solution: Unit rate = 720 ÷ 24 = 30
Answer: 30 grams per ounce
WORKED EXAMPLE
A client burns 450 calories in 30 minutes of exercise. What is the rate of calories burned per minute?
Solution: Unit rate = 450 ÷ 30 = 15
Answer: 15 calories per minute
Practice Problems
1. A box of 12 protein bars costs $36. What is the cost per bar?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. A chicken breast weighs 6 ounces and has 42 grams of protein. How many grams of protein per ounce?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A client walks 4.5 miles in 90 minutes. What is their speed in miles per minute? In miles per hour?
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
4. A 16-ounce bottle of juice has 240 calories. How many calories per ounce?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A meal delivery service provides 21 meals for $189. What is the cost per meal?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. An apple has 95 calories and weighs 182 grams. How many calories per gram (round to 2 decimal places)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A runner burns 2,400 calories during a 3-hour marathon. What is the rate of calories burned per hour?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A nutrition coach sees 35 clients in 7 hours. What is the rate of clients per hour?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A 32-oz smoothie has 64 grams of sugar. How many grams of sugar per ounce?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Brand A: 20 vitamins for $15. Brand B: 50 vitamins for $35. Which is the better unit price?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. A client loses 12 pounds in 8 weeks. What is the rate of weight loss per week?
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
12. A recipe serves 8 people and uses 2.5 cups of rice. How many cups of rice per person?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A gym charges $360 for 12 months. What is the cost per month? Per week (52 weeks)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. A food blog gets 15,000 views in 30 days. What is the rate of views per day?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A diabetic patient's blood sugar dropped 45 points over 3 hours. What is the rate of decrease per hour?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 1.3: Solving Proportions
A proportion states that two ratios are equal. This is incredibly useful for scaling recipes, converting measurements, and calculating doses.
If a/b = c/d, then a × d = b × c (Cross-Multiplication)
To solve for an unknown, set up a proportion and cross-multiply.
WORKED EXAMPLE
A recipe calls for 3 cups of oats for 4 servings. How many cups do you need for 10 servings?
Solution: Set up proportion: 3/4 = x/10. Cross-multiply: 3 × 10 = 4 × x → 30 = 4x → x = 30 ÷ 4 = 7.5
Answer: 7.5 cups of oats
WORKED EXAMPLE
A medication dosage is 5mg per 20 pounds of body weight. How much should a 140- pound patient receive?
Solution: Set up proportion: 5/20 = x/140. Cross-multiply: 5 × 140 = 20 × x → 700 = 20x → x = 35
Answer: 35 mg
Practice Problems
1. A smoothie recipe uses 2 bananas for 3 servings. How many bananas for 12 servings?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. If 4 ounces of chicken has 28g protein, how much protein in 10 ounces?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A diet plan burns 500 calories in 45 minutes. How many calories in 90 minutes at the same rate?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. The ratio of water to rice is 2:1. How much water for 3.5 cups of rice?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A nutritionist charges $80 for a 2-hour consultation. How much for a 3-hour session at the same rate?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. If 3 cups of flour makes 24 cookies, how many cups for 40 cookies?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A vitamin C tablet provides 500mg per tablet. How many tablets for 1,250mg?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A food scale shows 8 ounces = 225 grams. How many grams is 12 ounces?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. If 6 eggs cost $2.40, how much do 15 eggs cost?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A meal plan uses a ratio of 4 proteins to 6 vegetables per day. With 9 vegetable servings, how many protein?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. A patient burns 3 calories per minute walking. How long to burn 225 calories?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. If 100 grams of pasta has 350 calories, how many calories in 175 grams?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. The recommended calcium is 1,000mg per day. If a glass of milk has 300mg, how many glasses to meet 100%?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. A recipe feeds 6 people with 1.5 lbs of meat. How much meat for 10 people?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. If your heart beats 72 times per minute, how many beats in 2.5 hours?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 1.4: Action Report
Complete this report as the lead nutritionist at Healthy Living Clinic.
1. A client needs a protein:carb:fat ratio of 3:4:1 for their meal plan. If they consume 45g of protein, how many grams of carbs should they have?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Using the same ratio (3:4:1), how many grams of fat should they consume?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. The client's meal plan costs $175 for 7 days. What is the daily cost?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A protein powder costs $45 for 30 servings. A competitor charges $38 for 25 servings. Which is the better value per serving?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. The clinic recommends 64 ounces of water daily. If a client drinks 8-ounce glasses, how many glasses is that?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. A recipe makes 8 portions with 2 cups of quinoa. The client needs 20 portions for a party. How many cups of quinoa?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. The client burns 12 calories per minute jogging. They want to burn 540 calories. How many minutes should they jog?
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
8. A supplement contains 25mg of zinc per tablet. The daily recommendation is 8mg. What fraction of the daily value is one tablet?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. The client's current weight is 180 lbs. Their goal is a ratio of 1 lb muscle gain per 2 lbs fat loss. If they lose 8 lbs of fat, how much muscle should they gain?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Create a weekly meal prep budget: If groceries cost $4.50 per meal and the client eats 3 meals a day for 7 days, what is the weekly cost?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
🏦
CHAPTER 2 The Banker
Work with positive and negative numbers to track credits, debits, and account balances
Section 2.1: Understanding Integers
As a banker, you work with positive numbers (deposits, credits, gains) and negative numbers (withdrawals, debits, losses). Understanding integers is essential for accurate accounting.
The Number Line
Integers include positive whole numbers, negative whole numbers, and zero. On a number line, positive numbers go right, negative numbers go left.
... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...
Key concepts:
• Positive numbers represent deposits, credits, profits, gains
• Negative numbers represent withdrawals, debits, losses, debt
• Zero represents a balanced account (no money, no debt)
WORKED EXAMPLE
A customer has $350 in their account. They withdraw $400. What is their new balance?
Solution: Start: +350. Subtract withdrawal: 350 - 400 = -50
Answer: -$50 (overdrawn by $50)
WORKED EXAMPLE
Order these account balances from least to greatest: $45, -$120, $0, -$30, $15
Solution: On a number line, further left = smaller. Order: -120, -30, 0, 15, 45
Answer: -$120, -$30, $0, $15, $45
Practice Problems
1. A checking account has $500. After a $675 purchase, what is the balance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Order from least to greatest: -45, 23, -12, 0, -50, 18
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A business had a profit of $2,500 in January and a loss of $1,800 in February. Represent each as an integer.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A customer's balance is -$75. They deposit $100. What is the new balance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. The temperature in the bank vault is -5°F. The lobby is 73°F. What is the difference?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Place on a number line and identify which is greater: -25 or -30?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A savings account earns $45 interest but has a $12 fee. What is the net change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Compare using < or >: -156 ___ -149
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
9. A stock drops $8 per share on Monday, rises $12 on Tuesday, then drops $3 on Wednesday. What is the total change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. An account shows: +$250, -$180, +$95, -$200. List these in order from smallest to largest.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. What integer represents: 'The account is overdrawn by $340'?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. The bank's basement is 15 feet below ground level. The roof is 48 feet above. What is the total height from basement to roof?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Compare: Which is further from zero, -45 or 38?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. A loan balance is -$5,000. After a $750 payment, what is the new balance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. List all integers between -4 and 3, inclusive.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 2.2: Adding and Subtracting Integers
Adding and subtracting integers follows specific rules. Master these rules and you can track any financial transaction.
Adding Integers
Same signs: Add absolute values, keep the sign
Different signs: Subtract absolute values, use sign of
larger absolute value
Subtracting Integers
Subtracting = Adding the opposite: a - b = a + (-b)
WORKED EXAMPLE
A customer has -$45 (overdrawn). They overdraw another $30. What is the balance?
Solution: Adding two negatives: (-45) + (-30) = -(45 + 30) = -75
Answer: -$75
WORKED EXAMPLE
An account balance is -$200. A deposit of $350 is made. What is the new balance?
Solution: Different signs: (-200) + (+350) → |350| - |200| = 150. Larger absolute value (350) is positive.
Answer: +$150
WORKED EXAMPLE
Calculate: 25 - (-40)
Solution: Subtracting a negative = adding a positive: 25 - (-40) = 25 + 40 = 65
Answer: 65
Practice Problems
1. Calculate: (-35) + (-42)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Calculate: (-18) + 45
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Calculate: 72 + (-95)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Calculate: (-50) - (-25)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Calculate: 33 - 78
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. An account starts at $250. Transactions: -$80, +$125, -$200, +$50. What is the final balance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Calculate: (-15) + (-8) + 20 + (-12)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Calculate: 100 - (-45) - 30
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A bank starts the day with $5,000 in the vault. Withdrawals total $8,500 and deposits total $4,200. End balance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Calculate: (-125) - (-125)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Calculate: 0 - (-67)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. The temperature dropped from 5°F to -12°F. How many degrees did it drop?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Calculate: (-45) + 45 + (-30) + 30
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. An investor loses $2,400 in Q1 and loses $1,800 in Q2. What is the total change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Calculate: 500 - 250 - (-100) + (-175)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 2.3: Multiplying and Dividing Integers
Multiplication and division of integers follow simple sign rules. These are essential for calculating interest, fees, and investment returns.
Sign Rules for Multiplication and Division
Positive × Positive = Positive (+)(+) = +
Negative × Negative = Positive (−)(−) = +
Positive × Negative = Negative (+)(−) = −
Negative × Positive = Negative (−)(+) = −
Same signs → Positive result. Different signs → Negative result.
WORKED EXAMPLE
A stock loses $12 per day for 5 days. What is the total loss?
Solution: Loss = -12 per day. Total = (-12) × 5 = -60
Answer: -$60 (loss of $60)
WORKED EXAMPLE
A debt of $840 is split equally among 4 partners. How much does each owe?
Solution: Debt = -840. Each share = (-840) ÷ 4 = -210
Answer: -$210 each
Practice Problems
1. Calculate: (-8) × (-9)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Calculate: (-15) × 4
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Calculate: 6 × (-12)
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
4. Calculate: (-144) ÷ (-12)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Calculate: 90 ÷ (-15)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Calculate: (-100) ÷ 25
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A loan charges $25 interest per month. After 8 months, what is the total interest (as a negative)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Calculate: (-5) × (-5) × (-5)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Calculate: (-72) ÷ 8 × (-3)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. An investment loses 3% of its $4,000 value. What is the dollar loss (express as negative)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Calculate: 12 × (-3) × (-2) × (-1)
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
12. A temperature drops 4 degrees per hour. After 6 hours, what is the total change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Calculate: [(-48) ÷ (-6)] × (-4)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Divide a loss of $1,200 among 6 investors. What is each person's share (as negative)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Calculate: (-2)⁴ (that is: -2 × -2 × -2 × -2)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 2.4: Action Report
Complete this report as a personal banker at First National Bank.
1. A new customer opens an account with $500. Their first month's transactions: +$1,200 (paycheck), -$450 (rent), -$85 (utilities), -$120 (groceries), +$50 (refund), -$75 (subscription). What is the ending balance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. The customer above wants to know their average transaction amount. Calculate the mean of all 6 transactions (not including the opening deposit).
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A savings account starts at $2,000. It earns $15 interest but has a $4 monthly fee. What is the net gain?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Compare two account options: Account A charges -$12/month but pays +$20 in rewards. Account B charges -$8/month with no rewards. Which is better and by how much?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. An investor's portfolio: Stock A lost $450, Stock B gained $680, Stock C lost $225. What is the net change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. A customer is overdrawn by $125. What is the minimum deposit needed to bring the balance to exactly $0?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A loan balance is -$15,000. Monthly payments of $450 are made. How many months until the balance reaches -$10,500?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Calculate the total: Start at -$300, add $150, subtract $75, add -$100, subtract -$200
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Temperature in the bank vault: Monday -2°F, Tuesday 5°F, Wednesday -8°F, Thursday 3°F, Friday -5°F. What is the average temperature?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A credit card has a -$2,400 balance. The customer pays $200/month. If no new charges occur, what will the balance be after 8 months?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
🏗️
CHAPTER 3 The Architect
Calculate surface area and volume for 3D structures and understand nets
Section 3.1: Surface Area of Rectangular Prisms
As an architect, you need to know how much material covers the outside of a structure. This is surface area—the total area of all faces of a 3D shape.
Surface Area of a Rectangular Prism
A rectangular prism has 6 faces: top, bottom, front, back, left side, right side.
SA = 2lw + 2lh + 2wh
Where l = length, w = width, h = height. Each pair of opposite faces has the same area.
WORKED EXAMPLE
A storage building is 20 ft long, 15 ft wide, and 10 ft tall. What is the total surface area to paint (all 6 sides)?
Solution: SA = 2(20×15) + 2(20×10) + 2(15×10) = 2(300) + 2(200) + 2(150) = 600 + 400 + 300 = 1,300
Answer: 1,300 square feet
WORKED EXAMPLE
A gift box is 8 in × 6 in × 4 in. How much wrapping paper is needed to cover it completely?
Solution: SA = 2(8×6) + 2(8×4) + 2(6×4) = 2(48) + 2(32) + 2(24) = 96 + 64 + 48 = 208
Answer: 208 square inches
Practice Problems
1. Find the surface area of a cube with sides of 5 cm.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. A room is 12 ft × 10 ft × 8 ft. Find the surface area of all walls (4 sides only, not floor or ceiling).
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A shipping container is 40 ft × 8 ft × 8.5 ft. Calculate the total surface area.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Find the surface area: l = 9 in, w = 6 in, h = 4 in.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A rectangular pool is 30 ft × 15 ft × 6 ft. What is the surface area of the bottom and four sides (not the top)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. How much cardboard is needed to make an open-top box that is 10 in × 8 in × 5 in?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A cube has a surface area of 150 sq cm. What is the length of one side?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Find the surface area: l = 2.5 m, w = 1.5 m, h = 2 m.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. An architect needs to cover a building with siding. The building is 60 ft × 40 ft × 25 ft. What is the area of all four walls?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A rectangular prism has a surface area of 94 sq in. If l = 5 in and w = 3 in, find h.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Compare: Box A is 4×4×4. Box B is 2×4×8. Which has greater surface area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Find the surface area of a rectangular prism with dimensions 7.5 ft × 4 ft × 3 ft.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A jewelry box is 6 in × 4 in × 2 in. The outside will be covered with fabric. How much fabric is needed?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. A storage unit is 10 ft × 8 ft × 9 ft. Paint costs $0.50 per sq ft. What is the cost to paint all surfaces?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Find the missing dimension: SA = 158 sq m, l = 7 m, w = 5 m, h = ?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 3.2: Nets of 3D Figures
A net is a 2D pattern that folds into a 3D shape. Architects use nets to plan how materials will be cut and assembled.
Identifying Nets
A valid net for a cube has 6 squares that fold into a closed cube. A valid net for a rectangular prism has 6 rectangles (pairs of equal rectangles for opposite faces).
• Cube net: 6 equal squares in a cross or stair pattern
• Rectangular prism net: 3 pairs of equal rectangles
• Triangular prism net: 2 triangles + 3 rectangles
• Pyramid net: 1 base + triangular faces meeting at a point
WORKED EXAMPLE
Describe the net for a rectangular prism that is 4 in × 3 in × 2 in.
Solution: The net has 6 rectangles: Two 4×3 (top/bottom), Two 4×2 (front/back), Two 3×2 (sides).
Answer: 2 rectangles of 4×3, 2 rectangles of 4×2, 2 rectangles of 3×2
Practice Problems
1. How many faces does a cube have? Describe the net.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. A net for a rectangular prism shows rectangles with areas: 24, 24, 18, 18, 12, 12 sq in. What are the prism's dimensions?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Draw and label a net for a rectangular prism: 6 cm × 4 cm × 2 cm. List the dimensions of each rectangle.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A triangular prism has triangular bases with area 10 sq cm each and three rectangular faces (6×5, 6×4, 6×3). Find total SA.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Can a net with 5 squares form a cube? Explain.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. A net shows 6 equal squares, each with area 16 sq in. What is the side length of the cube it forms?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Describe the net for a square pyramid (square base, 4 triangular sides).
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A net for a cereal box shows rectangles: 12×8, 12×8, 12×3, 12×3, 8×3, 8×3. What are the box dimensions?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. If you unfold a 5 cm × 5 cm × 5 cm cube, what is the total area of the net?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A net has 2 triangles (base 6, height 4) and 3 rectangles (8×6, 8×5, 8×5). What shape does it form?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Which uses less cardboard: one 8×6×4 box or two 4×4×4 boxes?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. A net for a rectangular prism uses 40 sq in of material. If two faces are 3×4, two are 3×5, what is the area of the last two faces?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Can you make a closed rectangular prism from a net missing one face? Explain.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. A gift box net has rectangles 10×6, 10×6, 10×4, 10×4, 6×4, 6×4. Verify this is a valid net and find total area.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. An architect cuts a net from sheet metal. The prism is 12×8×6 ft. How many sq ft of metal is needed?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 3.3: Volume with Fractional Edges
Real-world dimensions aren't always whole numbers. As an architect, you must calculate volume accurately even with fractional measurements.
Volume = length × width × height
When dimensions include fractions, convert to decimals or multiply fractions carefully.
WORKED EXAMPLE
A planter box is 4½ ft × 2 ft × 1½ ft. What is its volume?
Solution: V = 4.5 × 2 × 1.5 = 9 × 1.5 = 13.5 (or: 9/2 × 2 × 3/2 = 9 × 3/2 = 27/2 = 13.5)
Answer: 13.5 cubic feet
WORKED EXAMPLE
A brick is 2¼ in × 3¾ in × 8 in. Find its volume.
Solution: V = 2.25 × 3.75 × 8 = 8.4375 × 8 = 67.5
Answer: 67.5 cubic inches
Practice Problems
1. Find the volume: 3½ ft × 2 ft × 4 ft
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Find the volume: 5 in × 2½ in × 6 in
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A concrete slab is 10 ft × 8 ft × ½ ft. How many cubic feet of concrete is needed?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Find the volume: 2¼ cm × 4 cm × 3½ cm
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
5. A foundation is 24 ft × 18 ft × ¾ ft. Calculate the volume.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Find the volume: 6½ in × 4½ in × 2 in
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A room is 12.5 ft × 10 ft × 8.5 ft. What is the volume?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A container holds 24 cubic feet. If it is 4 ft × 3 ft × h, find h.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Find the volume: 1½ m × 2½ m × 3 m
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A pool is 20 ft × 10 ft × 4½ ft. How many cubic feet of water does it hold?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Find the volume: 7.5 cm × 4 cm × 2.5 cm
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. A garden bed is 6 ft × 2½ ft × ⅔ ft. What is the volume?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A box has volume 45 cubic inches. If l = 5 in and w = 3 in, find h.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Compare volumes: Box A is 4 × 3 × 2. Box B is 3½ × 3½ × 2. Which is larger?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A shipping crate is 5½ ft × 4 ft × 3½ ft. Find the volume.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 3.4: Action Report
Complete this report as the lead architect at Modern Design Studio.
1. A client wants a garden shed: 10 ft × 8 ft × 7 ft. Calculate the surface area of all 6 sides.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. The shed (above) needs exterior paint. If one gallon covers 350 sq ft, how many gallons are needed? (Round up)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Describe the net for the shed. List dimensions of all 6 rectangles.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. The shed floor will be poured concrete, 4 inches (⅓ ft) thick. Calculate the volume of concrete needed.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A skylight will be cut from the roof: 3 ft × 2 ft. What is the new roof surface area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Design a storage bench: 4 ft × 1½ ft × 1½ ft. Find the volume.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. The storage bench will be covered with cedar planks on all 6 sides. Find the total surface area.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Compare two planter designs: Design A is 3 ft × 3 ft × 2 ft. Design B is 4 ft × 2 ft × 2.5 ft. Which has more volume?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A brick wall uses bricks that are 8 in × 4 in × 2.5 in. What is the volume of one brick?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. If the wall needs 500 bricks, what is the total volume of all bricks in cubic inches? Convert to cubic feet.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
👨🍳
CHAPTER 4 The Recipe Developer
Master dividing fractions to scale recipes up and down with precision
Section 4.1: Dividing Fractions by Whole Numbers
As a recipe developer, you often need to divide ingredients. If a recipe serves 8 but you want 4 servings, you divide each ingredient by 2. But what about dividing ¾ cup by 2?
The Rule: Multiply by the Reciprocal
a/b ÷ c = a/b × 1/c = a/(b×c)
Dividing by a whole number is the same as multiplying by its reciprocal (1 over that number).
WORKED EXAMPLE
A recipe calls for ¾ cup of sugar for 6 servings. How much sugar per serving?
Solution: ¾ ÷ 6 = ¾ × = 3/24 = 1/8 ⅙
Answer: ⅛ cup per serving
WORKED EXAMPLE
Divide 5/8 cup of flour among 4 portions.
Solution: 5/8 ÷ 4 = 5/8 × 1/4 = 5/32
Answer: 5/32 cup per portion
Practice Problems
1. Calculate: ½ ÷ 4
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
2. Calculate: ⅔ ÷ 3
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Calculate: ¾ ÷ 2
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Calculate: 5/6 ÷ 5
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A recipe uses 2/3 cup of honey for 4 servings. How much per serving?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Calculate: 7/8 ÷ 7
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Calculate: 3/4 ÷ 6
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Split 5/6 lb of butter among 10 recipes. How much per recipe?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Calculate: 9/10 ÷ 3
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A 3/4 gallon of milk is split into 8 equal portions. How much each?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Calculate: 4/5 ÷ 4
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Calculate: 11/12 ÷ 11
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A bag contains 7/8 lb of flour. If split into 2 batches, how much per batch?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Calculate: 2/3 ÷ 8
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Calculate: 5/8 ÷ 10
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 4.2: Dividing Fractions by Fractions
Sometimes you need to know how many times one fraction fits into another. How many ¼ cup portions are in ¾ cup? This is fraction division.
a/b ÷ c/d = a/b × d/c (Multiply by the reciprocal)
To divide by a fraction, flip it (find the reciprocal) and multiply.
WORKED EXAMPLE
How many ¼ cup servings are in ¾ cup?
Solution: ¾ ÷ ¼ = ¾ × 4/1 = 12/4 = 3
Answer: 3 servings
WORKED EXAMPLE
Divide: 5/6 ÷ 2/3
Solution: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4 = 1¼
Answer: 1¼ (or 5/4)
Practice Problems
1. Calculate: ½ ÷ ¼
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Calculate: ⅔ ÷ ⅓
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Calculate: ¾ ÷ ⅜
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Calculate: 5/8 ÷ ¼
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
5. How many ⅓ cup portions are in 2/3 cup?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Calculate: 4/5 ÷ 2/5
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Calculate: 7/8 ÷ ½
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A recipe needs ¾ cup of oil. If each batch uses ⅛ cup, how many batches?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Calculate: 9/10 ÷ 3/5
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Calculate: 5/6 ÷ 5/12
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Calculate: ⅔ ÷ 4/9
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. How many ⅜ lb portions in 1½ lbs?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Calculate: 11/12 ÷ 1/3
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Calculate: 3/4 ÷ 9/8
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A bag has ⅔ lb sugar. Each cookie needs 1/12 lb. How many cookies?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 4.3: Dividing Mixed Numbers
Mixed numbers (like 2½) must be converted to improper fractions before dividing.
Convert mixed to improper: 2½ = 5/2, then divide using
reciprocals
WORKED EXAMPLE
Divide: 3½ ÷ ¾
Solution: Convert: 3½ = 7/2. Then: 7/2 ÷ 3/4 = 7/2 × 4/3 = 28/6 = 14/3 = 4⅔
Answer: 4⅔
WORKED EXAMPLE
Divide: 2¼ ÷ 1½
Solution: Convert: 2¼ = 9/4, 1½ = 3/2. Then: 9/4 ÷ 3/2 = 9/4 × 2/3 = 18/12 = 3/2 = 1½
Answer: 1½
Practice Problems
1. Calculate: 1½ ÷ ½
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Calculate: 2⅓ ÷ ⅔
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Calculate: 3¼ ÷ 1½
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Calculate: 4½ ÷ ¾
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A recipe uses 2¼ cups flour total. Each batch uses ¾ cup. How many batches?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Calculate: 5⅓ ÷ 2⅔
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Calculate: 1⅞ ÷ ⅝
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A roast weighing 3½ lbs will be cut into ½ lb portions. How many portions?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Calculate: 2½ ÷ 1¼
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Calculate: 4⅔ ÷ ⅓
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Calculate: 6¼ ÷ 2½
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. A chef has 5½ lbs of potatoes. Each dish uses ¾ lb. How many dishes?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Calculate: 3⅜ ÷ 1⅛
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
14. Calculate: 7½ ÷ 2½
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A punch bowl holds 4¾ gallons. If each glass is ⅜ gallon, how many glasses?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 4.4: Action Report
Complete this report as head recipe developer at Gourmet Test Kitchen.
1. A brownie recipe serves 16 and uses 1½ cups of cocoa. How much cocoa per serving?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. The same recipe uses ⅔ cup of butter for 16 servings. How much for 4 servings?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. You have 3¾ cups of flour. The recipe uses ¾ cup per batch. How many batches can you make?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Scale down: Original uses 2⅔ cups sugar for 12 servings. How much for 3 servings?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A cake recipe uses 1½ cups milk. You want to make ⅔ of the recipe. How much milk?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. You have 2½ lbs of ground beef. Each burger uses ⅓ lb. How many burgers?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A pie recipe serves 8 with ¾ cup of berries. Scale to serve 2. How many cups of berries?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A pasta recipe uses ⅝ lb of noodles for 5 servings. How much per serving?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. You have 4⅓ cups of broth. Each portion uses ⅔ cup. How many full portions?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Create a ratio: If ¾ cup of oil is needed for 6 muffins, express this as a unit rate (cups per muffin).
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
📊
CHAPTER 5 The Data Journalist
Analyze statistical distributions and communicate data stories using box plots and
histograms
Section 5.1: Measures of Center and Spread
As a data journalist, you turn numbers into stories. Understanding how data is centered and spread helps you accurately report on trends and patterns.
Review: Mean, Median, Mode, Range
Mean = Sum of values ÷ Number of values
Median = Middle value when ordered
Mode = Most frequent value
Range = Maximum - Minimum
WORKED EXAMPLE
Test scores: 78, 85, 92, 85, 88, 95, 72. Find the mean, median, mode, and range.
Solution: Mean: (78+85+92+85+88+95+72) ÷ 7 = 595 ÷ 7 = 85. Ordered: 72, 78, 85, 85, 88, 92, 95. Median: 85 (middle). Mode: 85 (appears twice). Range: 95-72 = 23.
Answer: Mean: 85, Median: 85, Mode: 85, Range: 23
Practice Problems
1. Dataset: 12, 15, 18, 15, 22, 15, 20. Find mean, median, and mode.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Salaries (in thousands): 45, 52, 48, 125, 50, 47, 51. Find mean and median. Which better represents typical salary?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Temperature readings: 68, 72, 75, 71, 69, 73, 70. Find the range and mean.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Test scores: 88, 92, 76, 88, 95, 88, 82. What is the mode? What does it tell you?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Two datasets: A = {10, 20, 30} and B = {18, 20, 22}. Both have mean 20. Which has greater range?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Add one number to {5, 10, 15, 20} so the mean becomes 12. What number?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Dataset: 3, 7, 7, 9, 11, 15. Find the median.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Home prices (in thousands): 250, 275, 280, 310, 975. Which measure is misleading and why?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Rainfall (inches): 2.1, 3.4, 0.8, 5.2, 2.9, 1.6. Find mean rounded to nearest tenth.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Dataset: 100, 105, 110, 115, 120. If you add 10 to each value, what happens to the mean? The range?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Find the missing value: Mean of 8, 12, x, 18, 22 is 14. What is x?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Which has less spread: {10, 30, 50} or {25, 30, 35}? Explain.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Dataset: 5, 5, 5, 5, 5. Find mean, median, mode, and range.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. After removing an outlier of 200 from {20, 25, 30, 35, 200}, how do mean and median change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Create a dataset of 5 numbers with mean 10, median 8, and range 12.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 5.2: Mean Absolute Deviation (MAD)
Range tells us the gap between extremes, but MAD tells us how spread out all values are from the center on average.
MAD = Sum of |each value - mean| ÷ Number of values
A smaller MAD means data is clustered near the mean. A larger MAD means data is spread out.
WORKED EXAMPLE
Find the MAD for: 2, 4, 6, 8, 10
Solution: Mean = 30 ÷ 5 = 6. Deviations: |2-6|=4, |4-6|=2, |6-6|=0, |8-6|=2, |10-6|=4. Sum = 12. MAD = 12 ÷ 5 = 2.4
Answer: MAD = 2.4
Practice Problems
1. Find MAD: 5, 5, 5, 5, 5 (Hint: what happens when all values equal the mean?)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Find MAD: 10, 20, 30, 40, 50
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Find MAD: 8, 10, 10, 12, 10
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Dataset A: 20, 20, 20. Dataset B: 10, 20, 30. Find MAD for each. Which is more consistent?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Find MAD: 3, 5, 7, 9, 11 (mean = 7)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Find MAD: 100, 102, 98, 104, 96
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Which has greater MAD without calculating: {1, 1, 1, 10} or {1, 3, 5, 7}? Explain.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Find MAD: 15, 18, 12, 20, 15
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A journalist reports 'average commute is 25 min with MAD of 2 min.' What does this mean?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Find MAD: 50, 60, 70, 80, 90
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. If you add 10 to every value in a dataset, what happens to the MAD?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Find MAD for test scores: 82, 88, 75, 95, 80
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Two stores have same mean sales ($500). Store A has MAD of $20, Store B has MAD of $150. Which is more predictable?
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
14. Find MAD: 4, 8, 6, 8, 4
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Create a dataset of 4 numbers with mean = 10 and MAD = 0.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 5.3: Box Plots and Quartiles
A box plot (box-and-whisker plot) shows the five-number summary: minimum, Q1, median, Q3, maximum.
Finding Quartiles
• Q1 (First Quartile): Median of lower half
• Q2 (Median): Middle of entire dataset
• Q3 (Third Quartile): Median of upper half
• IQR (Interquartile Range): Q3 - Q1
WORKED EXAMPLE
Find the five-number summary for: 12, 15, 18, 22, 25, 28, 30, 35, 40
Solution: Min = 12, Max = 40. Median (Q2) = 25 (5th value). Lower half: 12, 15, 18, 22 → Q1 = (15+18)/2 = 16.5. Upper half: 28, 30, 35, 40 → Q3 = (30+35)/2 = 32.5.
Answer: Min: 12, Q1: 16.5, Median: 25, Q3: 32.5, Max: 40
Practice Problems
1. Find the five-number summary: 5, 8, 12, 15, 18, 20, 25
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Find Q1, median, Q3 for: 10, 12, 14, 16, 18, 20, 22, 24, 26
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Find the IQR for: 3, 5, 7, 9, 11, 13, 15
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Dataset: 20, 25, 30, 35, 40, 45, 50, 55, 60. Find all quartiles and IQR.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. What percent of data falls between Q1 and Q3?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Find five-number summary: 100, 105, 110, 115, 120, 125, 130, 135
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Two box plots have same median. Plot A has IQR of 10, Plot B has IQR of 30. Which shows more variability?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Find Q1 and Q3: 2, 4, 6, 8, 10, 12
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Dataset: 50, 60, 70, 80, 90, 100. Find IQR.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. If Min=10, Q1=25, Median=40, Q3=55, Max=80, what is the IQR?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Find five-number summary: 1, 1, 2, 3, 5, 8, 13, 21
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. The 'box' in a box plot represents what portion of the data?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Ages: 22, 25, 28, 30, 32, 35, 38, 42, 45. Find quartiles.
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
14. Create a dataset of 7 numbers where Q1=10, Median=15, Q3=20.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Find five-number summary: 65, 70, 72, 78, 80, 82, 85, 88, 92, 95
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 5.4: Action Report
Complete this report as a data journalist at Metro News.
1. City A temperatures (°F): 45, 52, 48, 55, 50, 47, 53. City B: 42, 58, 35, 62, 48, 55, 50. Find the mean for each city.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Which city (above) has a larger range? What does this tell you about weather consistency?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. For City A (above), find the MAD. Is the weather consistent or variable?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Home prices (thousands): 250, 275, 280, 295, 300, 310, 325, 350, 850. Find the median and mean. Which is a better headline?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. For the home prices above, find the five-number summary.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Calculate the IQR for the home prices. What does this tell you about the middle 50% of prices?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Is $850,000 an outlier? Use the rule: Outlier if beyond Q1 - 1.5(IQR) or Q3 + 1.5(IQR).
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
8. Commute times (min): 15, 18, 20, 22, 25, 28, 30, 32, 35. Find Q1, median, and Q3.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Write a headline summarizing the commute data: use median and IQR.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Compare two schools' test scores: School A has median 78 with IQR 15. School B has median 80 with IQR 35. Which school would you send your child to? Explain.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
🗺️
CHAPTER 6 The Map Maker
Use scale drawings and proportional reasoning to create accurate maps and blueprints
Section 6.1: Understanding Scale
As a cartographer (map maker), you must represent large real-world distances on small pieces of paper. A scale tells you the relationship between map distance and actual distance.
Reading Scales
A scale of 1 inch : 50 miles means 1 inch on the map represents 50 miles in real life.
Actual Distance = Map Distance × Scale Factor
Map Distance = Actual Distance ÷ Scale Factor
WORKED EXAMPLE
On a map with scale 1 in : 25 mi, two cities are 3.5 inches apart. What is the actual distance?
Solution: Actual = Map × Scale Factor = 3.5 × 25 = 87.5
Answer: 87.5 miles
WORKED EXAMPLE
Two cities are 180 miles apart. Using scale 1 in : 30 mi, how far apart should they be on the map?
Solution: Map = Actual ÷ Scale = 180 ÷ 30 = 6
Answer: 6 inches
Practice Problems
1. Scale: 1 in : 10 mi. Map distance is 4.5 in. Find actual distance.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Scale: 1 cm : 25 km. Actual distance is 150 km. Find map distance.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Scale: 1 in : 100 ft. A building is 450 ft tall. How tall on the drawing?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Scale: 1:50,000. A road is 3 cm on the map. How long in reality (in meters)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Two points are 7 inches apart on a map with scale 1 in : 40 mi. Find actual distance.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Scale: 1 cm : 5 m. A room is 8 m × 6 m. What are the dimensions on the blueprint?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A 600-mile flight appears as 4 inches on a map. What is the scale?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Scale: 1 in : 75 mi. How far apart should cities be if actual distance is 300 miles?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Scale: 2 cm : 50 km. Map shows 7 cm. Find actual distance.
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
10. A football field (100 yards) is 5 inches on a drawing. Find the scale.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Scale: 1:24. A model car is 8 inches long. How long is the real car (in feet)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Scale: 1 in : 20 ft. A house is 60 ft × 40 ft. Find blueprint dimensions.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. On a map, 2.5 inches = 125 miles. What does 1 inch represent?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Scale: 1 cm : 15 km. Two cities are 120 km apart. Map distance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A state is 8 inches wide on a map (scale 1 in : 60 mi). How wide is the actual state?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 6.2: Scale Factors and Similar Figures
When shapes are similar (same shape, different size), all corresponding lengths have the same scale factor.
Scale Factor = New Length ÷ Original Length
If scale factor is 2, the new figure is twice as big. If scale factor is 0.5, it's half the size.
WORKED EXAMPLE
A rectangle is 8 cm × 6 cm. A similar rectangle has length 12 cm. Find the width and scale factor.
Solution: Scale factor = 12 ÷ 8 = 1.5. Width = 6 × 1.5 = 9 cm.
Answer: Width: 9 cm, Scale factor: 1.5
Practice Problems
1. Original: 4 in × 6 in. Scale factor: 3. Find new dimensions.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Original: 10 cm × 15 cm. New: 4 cm × ?. Find the missing dimension and scale factor.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A model train is 1:87 scale. If the real engine is 52.2 ft, how long is the model (in inches)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Triangle sides: 3, 4, 5. Similar triangle has shortest side 9. Find other two sides.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Photo: 4 in × 6 in. Enlarged to 10 in × ?. Find missing dimension.
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
6. Scale factor is 0.25. Original is 80 ft × 120 ft. Find new dimensions.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Original rectangle: 12 cm × 8 cm. Reduced copy is 9 cm × ?. Find missing dimension.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A 6-foot person appears 2 inches tall in a photo. What is the scale factor?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Similar triangles: Triangle A has sides 5, 12, 13. Triangle B has longest side 39. Find all sides of B.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Blueprint scale: 1 in : 4 ft. A room is 3.5 in × 4 in on paper. Find actual dimensions.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Scale factor 2.5. If perimeter of original is 40 cm, what is perimeter of new figure?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Map scale: 1:50,000. Two mountains are 4 cm apart on map. Actual distance in km?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A mural is 12 ft × 8 ft. A postcard version is 6 in × ?. Find missing dimension.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Original square: side 5 m. New square: side 7.5 m. Find scale factor.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Scale factor is 1:4. Model building is 15 inches tall. How tall is actual building (in feet)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 6.3: Area and Scale
When you scale a figure, area changes differently than length!
If length scale factor = k, then Area scale factor = k²
Double the length (k=2), and area quadruples (k²=4).
WORKED EXAMPLE
A square has side 5 cm (area 25 sq cm). If you double each side, what is the new area?
Solution: New side = 10 cm. New area = 10² = 100 sq cm. Or: Area factor = 2² = 4, so 25 × 4 = 100.
Answer: 100 sq cm (4× the original)
Practice Problems
1. Original: 4 cm × 6 cm = 24 sq cm. Scale factor: 3. Find new area.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. A rectangle's length and width are both tripled. By what factor does area increase?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Original area: 50 sq in. Scale factor: 2. New area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A map uses scale 1 in : 100 ft. A park is 2 in × 3 in on the map. Find actual area in sq ft.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Scale factor: 0.5. Original area: 400 sq cm. New area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. A room is 12 ft × 10 ft. A model (scale 1:4) has what dimensions and area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Original square: 8 in side. New square: 4 in side. Scale factor? Area factor?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Blueprint: 1 in : 5 ft. A room is 3 in × 4 in = 12 sq in on paper. Actual area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A poster is enlarged by factor 1.5. Original area: 200 sq in. New area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Two similar rectangles. Smaller: 6 cm × 4 cm. Larger has length 15 cm. Find larger area.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. If area increases by factor of 9, what is the linear scale factor?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Scale: 1:50. Model floor is 0.5 m². Actual floor area?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A tile design: 2 in × 2 in. Scaled up to 6 in × 6 in. Area multiplied by what factor?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Original garden: 8 m × 5 m. Scaled version: 4 m × 2.5 m. Find scale factor and area ratio.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. If you reduce a figure by half (k=0.5), area becomes what fraction of original?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 6.4: Action Report
Complete this report as a cartographer at Atlas Geographic.
1. Your state map uses scale 1 in : 40 mi. The state capital to the coast is 7.5 inches on the map. Actual distance?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. A nature reserve is 200 miles × 150 miles. Using scale 1 in : 50 mi, find map dimensions.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Two cities are 280 miles apart. You want them 4 inches apart on your map. What scale should you use?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Find the area of the nature reserve on the map (from problem 2). Then verify by calculating actual area and converting.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Blueprint scale: 1 in : 8 ft. A room is 24 ft × 20 ft. Find blueprint dimensions.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. The room (above) has area 480 sq ft. What is its area on the blueprint (in sq in)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A model skyscraper is 1:500 scale. The model is 30 inches tall. How tall is the real building in feet?
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
8. On your map, a lake measures 1.5 in × 2 in. Scale is 1 in : 10 mi. Find the actual area of the lake.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. You're reducing a 24 in × 36 in poster to fit in a 4 in × 6 in frame. What is the scale factor?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. The original poster has 864 sq in of art. How much art (in sq in) will fit in the frame?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
📈
CHAPTER 7 The Stock Trader
Write, evaluate, and solve algebraic expressions and equations for market analysis
Section 7.1: Writing Algebraic Expressions
As a stock trader, you track investments using formulas with variables. A variable is a letter that represents an unknown or changing value.
Translating Words to Algebra
• Addition: sum, plus, increased by, more than, total
• Subtraction: difference, minus, decreased by, less than, fewer
• Multiplication: product, times, of, twice, double, triple
• Division: quotient, divided by, ratio, per, split
Let n = number of shares, p = price per share
Total Value = n × p or np
WORKED EXAMPLE
Write an expression: 'A stock's price increased by $5.'
Solution: Let p = original price. 'Increased by' means add. Expression: p + 5
Answer: p + 5
WORKED EXAMPLE
Write an expression: 'Three times the number of shares, minus 10.'
Solution: Let n = number of shares. Three times: 3n. Minus 10: 3n - 10
Answer: 3n - 10
Practice Problems
1. Write an expression: 'A stock price plus $12'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Write an expression: 'Double the number of shares'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Write an expression: 'The price decreased by $8'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Write an expression: 'The quotient of total profit and 4'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Write an expression: '15 less than the stock price'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Write an expression: 'The sum of two investments, x and y'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Write an expression: '5 more than triple a number'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Write an expression: 'A number divided by 6'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Write an expression: 'The product of 7 and a number, decreased by 3'
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
10. Write an expression: 'Half of the total investment'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Define variables and write: 'Total cost of buying n shares at p dollars each'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Write an expression: 'The difference between selling price s and buying price b'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Write an expression: '20% of the investment value v' (Hint: 20% = 0.20)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Write an expression: 'Commission is $10 plus 2% of the sale amount'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Write an expression using two variables: 'Total portfolio = stocks plus bonds'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 7.2: Evaluating Expressions
Once you write an expression, you can evaluate it by substituting numbers for variables.
To evaluate: Replace each variable with its value, then
calculate
WORKED EXAMPLE
Evaluate 3x + 7 when x = 5
Solution: Replace x with 5: 3(5) + 7 = 15 + 7 = 22
Answer: 22
WORKED EXAMPLE
Evaluate 2a - b when a = 8 and b = 3
Solution: Replace a with 8 and b with 3: 2(8) - 3 = 16 - 3 = 13
Answer: 13
Practice Problems
1. Evaluate 4x when x = 9
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Evaluate n + 15 when n = 27
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Evaluate 5y - 12 when y = 8
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Evaluate 2a + 3b when a = 4 and b = 5
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Evaluate 24 ÷ m when m = 6
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Evaluate x² + 5 when x = 3
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Evaluate 3(n - 4) when n = 10
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Evaluate 2p + q - 5 when p = 6 and q = 9
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Evaluate 100 - 4x when x = 15
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. A stock's value is 25n (n = shares). Find value when n = 40.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Evaluate (a + b) ÷ 2 when a = 18 and b = 22
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Evaluate 0.08x (8% of x) when x = 500
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Evaluate 5x² when x = 4
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
14. Profit = Revenue - Cost = r - c. Find profit when r = 850 and c = 620.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Evaluate 2(l + w) when l = 12 and w = 8
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 7.3: Solving One-Step Equations
An equation states that two expressions are equal. Solving means finding the value of the variable that makes the equation true.
Inverse Operations
Addition ↔ Subtraction (undo each other)
Multiplication ↔ Division (undo each other)
Whatever you do to one side, do to the other side to keep the equation balanced.
WORKED EXAMPLE
Solve: x + 15 = 42
Solution: Subtract 15 from both sides: x + 15 - 15 = 42 - 15 → x = 27. Check: 27 + 15 = 42 ✓
Answer: x = 27
WORKED EXAMPLE
Solve: 5n = 85
Solution: Divide both sides by 5: 5n ÷ 5 = 85 ÷ 5 → n = 17. Check: 5(17) = 85 ✓
Answer: n = 17
WORKED EXAMPLE
Solve: y - 23 = 41
Solution: Add 23 to both sides: y - 23 + 23 = 41 + 23 → y = 64. Check: 64 - 23 = 41 ✓
Answer: y = 64
Practice Problems
1. Solve: x + 8 = 25
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Solve: n - 14 = 36
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
3. Solve: 4y = 48
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Solve: m ÷ 5 = 12
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Solve: 15 + a = 52
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Solve: b - 27 = 45
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Solve: 9x = 108
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Solve: p ÷ 8 = 7
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Solve: 35 = c + 18
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Solve: 72 = 6n
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Solve: z - 100 = 250
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Solve: w ÷ 4 = 25
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A stock gained $x and is now worth $156. It started at $120. Solve: 120 + x = 156
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. You split $y equally among 5 accounts, putting $45 in each. Solve: y ÷ 5 = 45
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. After losing $38, your portfolio is worth $412. Solve: p - 38 = 412
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 7.4: Writing and Solving Inequalities
Sometimes you need to express 'at least,' 'at most,' 'more than,' or 'less than.' These use inequalities.
Inequality Symbols
• < means 'less than'
• > means 'greater than'
• ≤ means 'less than or equal to' (at most)
• ≥ means 'greater than or equal to' (at least)
WORKED EXAMPLE
Write and solve: 'A number plus 5 is greater than 12'
Solution: Inequality: x + 5 > 12. Solve: x > 12 - 5 → x > 7. Any number greater than 7 works.
Answer: x > 7
WORKED EXAMPLE
Write and solve: 'To avoid fees, you need at least $500. You have $350. How much more do you need?'
Solution: Let x = additional amount. 350 + x ≥ 500. Solve: x ≥ 150.
Answer: x ≥ $150
Practice Problems
1. Write as inequality: 'x is greater than 10'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Write as inequality: 'The price p is at most $50'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Write as inequality: 'You need at least 100 shares'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Solve: x + 7 > 15
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Solve: n - 4 ≤ 20
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Solve: 3y < 27
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Solve: m ÷ 2 ≥ 8
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Write and solve: 'Five more than a number is less than 30'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Write and solve: 'A number divided by 3 is at least 9'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. You have $x in savings. You want more than $1,000. Write and interpret the inequality.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Solve: 25 + p > 40
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Solve: 6n ≤ 54
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
13. A broker requires at least $2,500 to open an account. You have $1,800. How much more? Write and solve.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Solve: z - 15 ≥ 45
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Stock must be above $75 to sell. Current: $60. How much must it rise? Write inequality.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 7.5: Action Report
Complete this report as a junior analyst at Summit Trading.
1. Write an expression for total investment: n shares at p dollars per share.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Evaluate your expression from #1 when n = 50 shares and p = $32 per share.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Write an expression: 'Profit equals selling price minus buying price, times number of shares.'
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A stock rose $x and is now at $78. It started at $65. Write and solve an equation to find x.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. You want to buy shares at $25 each with $400. Write and solve: 25n ≤ 400. How many shares can you buy?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Commission is 2% of sale value plus $10. Write the expression using variable s for sale value.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Evaluate your commission expression when s = $5,000.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Write and solve: Your portfolio needs to grow by at least $2,000 this year. After 6 months, you've gained $1,350. How much more do you need? Use inequality.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A stock dropped from $92 to an unknown price p after losing $17. Write and solve the equation.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Challenge: Write an expression for net profit after buying n shares at $40 each, selling them at $52 each, and paying a $25 commission.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
🎉
CHAPTER 8 The Event Planner
Apply percent calculations to budgets, markups, discounts, and tips
Section 8.1: Percent of a Number
As an event planner, you calculate deposits (often 25%), tips (15-20%), taxes (varies), and markups. Mastering percents is essential.
Percent of a Number = Percent × Number
Convert percent to decimal: move decimal 2 places left
(25% = 0.25)
WORKED EXAMPLE
Find 35% of $240
Solution: Convert: 35% = 0.35. Calculate: 0.35 × 240 = 84
Answer: $84
WORKED EXAMPLE
A venue requires a 20% deposit on $4,500. How much is the deposit?
Solution: 20% = 0.20. Deposit = 0.20 × 4,500 = 900
Answer: $900
Practice Problems
1. Find 15% of 80
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Find 40% of $350
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Find 8.5% of $1,200
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A caterer charges 18% gratuity on $2,400. How much is the tip?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Find 125% of 60 (percents can be over 100%!)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Find 6% sales tax on a $850 rental
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Find 33⅓% of 270 (hint: 33⅓% = ⅓)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A DJ requires 50% upfront on a $600 fee. How much is due now?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Find 2.5% of $8,000
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Find 75% of 48
Work:
______________________________________________________________________ ______________________________________________________________________
Answer: ______________________________
11. A venue offers 15% off a $3,200 rental. What is the discount amount?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Find 110% of 200
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Insurance costs 4% of the total budget of $12,500. How much?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Find 66⅔% of 90
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A florist adds 12% for delivery on a $425 order. What is the delivery fee?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 8.2: Finding the Whole from a Percent
Sometimes you know the part and the percent, but need to find the whole.
If Part = Percent × Whole, then Whole = Part ÷ Percent
WORKED EXAMPLE
A 25% deposit is $600. What is the total cost?
Solution: Whole = Part ÷ Percent = 600 ÷ 0.25 = 2,400
Answer: $2,400
WORKED EXAMPLE
If 15% of the guests are vegetarian and that's 12 people, how many total guests?
Solution: Total = 12 ÷ 0.15 = 80
Answer: 80 guests
Practice Problems
1. 20% of a number is 45. Find the number.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. A $180 deposit is 30% of the total. Find the total.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. If 40% of attendees arrived early (that's 28 people), how many total attendees?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A 15% tip was $22.50. What was the bill before tip?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. 8% of a budget is $640. What is the total budget?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. A 25% discount saved you $75. What was the original price?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. 12 vegetarian meals are 15% of the order. How many total meals?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Sales tax of 7% added $56 to a rental. What was the rental before tax?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A 5% deposit is $250. Find the total contract value.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. If 60% of tickets are sold (that's 360 tickets), how many total tickets?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. A $90 gratuity was 18% of the catering bill. Find the bill.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. 10% of the flowers are roses (that's 45 roses). How many total flowers?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A 35% markup added $140 to the cost. What was the original cost?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Insurance at 3% costs $450. What is the total event budget?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. If 80% capacity is 240 people, what is 100% capacity?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 8.3: Percent Change
When prices increase or decrease, you often express the change as a percent.
Percent Change = (New - Original) ÷ Original × 100
Positive result = increase. Negative result = decrease.
WORKED EXAMPLE
A venue raised prices from $2,000 to $2,400. What is the percent increase?
Solution: Change = 2,400 - 2,000 = 400. Percent = 400 ÷ 2,000 × 100 = 20%
Answer: 20% increase
WORKED EXAMPLE
An early-bird price dropped from $80 to $60. What is the percent decrease?
Solution: Change = 60 - 80 = -20. Percent = -20 ÷ 80 × 100 = -25%
Answer: 25% decrease
Practice Problems
1. Original: $50. New: $65. Find percent change.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Original: $200. New: $150. Find percent change.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A caterer raised prices from $25/person to $30/person. Percent increase?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Attendance went from 120 to 180. Find percent change.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Original price: $400. After discount: $340. Percent discount?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. A venue that charged $1,500 now charges $1,800. Percent increase?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Budget was $5,000, now $4,500. Find percent change.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Guest count went from 80 to 100. Percent increase?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A photographer dropped rates from $500 to $400. Percent decrease?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Last year's cost: $3,200. This year: $3,520. Percent change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Original quote: $750. Final price: $600. Percent saved?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Ticket sales went from 200 to 320. Find percent change.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A DJ raised fee from $400 to $450. Percent increase?
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
14. Food cost dropped from $40/plate to $35/plate. Percent decrease?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Event budget grew from $8,000 to $10,000. Percent increase?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 8.4: Action Report
Complete this report as lead planner at Celebrations Unlimited.
1. A wedding venue costs $8,500. The 25% deposit is due now. How much?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Catering is $45 per person for 120 guests. Add 20% gratuity and 8% tax (on food only). Total?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. A florist's original quote was $800. They offered 15% off. What is the new price?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. A DJ charges $650. Last year the same DJ charged $500. Percent increase?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Photography is $1,200. A 30% deposit ($360) was paid. How much remains?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. The venue increased capacity from 150 to 200 guests. What is the percent increase?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. A client's budget is $15,000. They've spent $10,500. What percent remains?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A 6% sales tax on decorations is $42. What was the decoration cost before tax?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Compare two caterers: Caterer A is $50/person. Caterer B is $45/person but adds 22% service charge. For 100 guests, which is cheaper?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Final budget breakdown: Venue 35%, Catering 40%, Photography 15%, Other 10%. If total is $20,000, find the dollar amount for each category.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
🌡️
CHAPTER 9 The Climate Scientist
Apply absolute value and analyze data with positive and negative values
Section 9.1: Absolute Value
As a climate scientist, you work with temperatures above and below zero, elevations above and below sea level, and measurements that can be positive or negative. Absolute value helps you find distance from zero regardless of direction.
|x| = distance from x to 0 on the number line
Absolute value is always positive (or zero). It measures magnitude without direction.
WORKED EXAMPLE
Find: |-15| and |15|
Solution: Both -15 and 15 are 15 units from zero.
Answer: |-15| = 15 and |15| = 15
WORKED EXAMPLE
The temperature dropped from 0°F to -23°F. How many degrees did it drop?
Solution: Distance from 0 to -23 is |-23| = 23 degrees.
Answer: 23 degrees
Practice Problems
1. Find: |8|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Find: |-25|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Find: |0|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Compare: |-12| and |10|. Which is greater?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Find: |-3| + |7|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Find: |5 - 12|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Find: |-8| × |-4|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A submarine is at -450 feet. How far below sea level is it?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Order from least to greatest absolute value: -3, 7, -10, 2, -5
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Find: |−20| − |15|
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
11. The Dead Sea is at -430 meters. Mt. Everest is at +8,849 meters. Which has the greater absolute value for elevation?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Find: |-6|²
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. If |x| = 9, what are the possible values of x?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Find: |4 - 10| + |10 - 4|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. A temperature of -40°C equals -40°F. What is |-40|?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 9.2: Comparing and Ordering Rational Numbers
Climate data includes decimals, fractions, and negative numbers. You must compare and order these rational numbers accurately.
Comparing Rational Numbers
• On a number line, numbers increase from left to right
• Any positive number > any negative number
• For negatives: further from zero = smaller value
WORKED EXAMPLE
Order from least to greatest: -2.5, 1.3, -0.8, 0, 2.1
Solution: Arrange on number line: -2.5 is furthest left, then -0.8, then 0, then 1.3, then 2.1.
Answer: -2.5, -0.8, 0, 1.3, 2.1
Practice Problems
1. Compare using < or >: -5 ___ -8
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Compare: 3.2 ___ -3.2
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Compare: -0.5 ___ -0.25
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Order from least to greatest: 4, -7, 2, -3, 0
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. Compare: -⅔ ___ -¾ (Hint: convert to decimals)
Work:
______________________________________________________________________
______________________________________________________________________ Answer: ______________________________
6. Order: 1.5, -2.5, 0.5, -0.5, -1.5
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Which is colder: -15°C or -12°C?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Order temperatures: 32°F, 0°F, -10°F, 45°F, -5°F
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Compare: |-4| ___ |3|
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Compare: -1.25 ___ -1.3
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Order elevations: -50m, 120m, -200m, 0m, 80m
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Compare: -⅝ ___ -½
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Find two numbers between -3 and -2.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Order: 2.75, -2.75, 2.5, -2.5, 0
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. Which depth is deeper: -85 feet or -90 feet?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 9.3: Graphing on the Coordinate Plane
Climate scientists plot data using the coordinate plane. Both x and y can be positive or negative, creating four quadrants.
The Four Quadrants
• Quadrant I: (+, +) — upper right
• Quadrant II: (-, +) — upper left
• Quadrant III: (-, -) — lower left
• Quadrant IV: (+, -) — lower right
WORKED EXAMPLE
In which quadrant is the point (-3, 5)?
Solution: x is negative, y is positive: Quadrant II (upper left).
Answer: Quadrant II
Practice Problems
1. Name the quadrant: (4, 7)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Name the quadrant: (-2, -6)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Name the quadrant: (5, -3)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Name the quadrant: (-8, 4)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. What quadrant is (0, 5) in? (Trick question!)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Plot and identify quadrant: (-4, -2)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. If a point is in Quadrant III, what are the signs of x and y?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Give the coordinates of a point in Quadrant IV.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. Where is (-6, 0) located?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Reflect (3, -4) over the x-axis. New coordinates?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
11. Reflect (-2, 5) over the y-axis. New coordinates?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Distance from (0, 0) to (3, 0)? From (0, 0) to (0, -5)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. A temperature sensor is at position (-5, 8). Which quadrant?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Move (2, 3) left 5 units and down 7 units. New position?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. If a point moves from Quadrant I to Quadrant III, what must change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Section 9.4: Action Report
Complete this report as a researcher at the Global Climate Institute.
1. Arctic temperatures: -35°C, -28°C, -42°C, -31°C, -38°C. Find the mean temperature.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Which temperature (above) has the greatest absolute value? What does this represent?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Find the range of the Arctic temperatures.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. Ocean depths at research sites (meters): -120, -85, -200, -150, -95. Order from shallowest to deepest.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. A weather balloon rises from -50 meters (underground launch) to +12,000 meters. What is the total change in elevation?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
6. Temperature change from midnight to noon: -8°C to +15°C. Calculate the change.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. Plot these data points: Day 1: (1, -5°C), Day 2: (2, -2°C), Day 3: (3, 4°C), Day 4: (4, 1°C). What quadrants are used?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. Find |−42| − |−28| from the Arctic data. What does this represent?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. A glacier elevation changed from -15 meters (below sea level) to +22 meters (above). What is the absolute change?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. Compare two measurement errors: Site A had error of +3.5°C. Site B had error of - 4.2°C. Which had greater absolute error?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
💼
CHAPTER 10 The Entrepreneur
Apply ALL Grade 6 skills to launch and run your own startup business
Welcome, Entrepreneur!
This is your capstone project. You will apply every skill from Grade 6 to plan, launch, and analyze a business. No single-skill problems here—this is the real world, where problems combine multiple concepts.
YOUR BUSINESS: You are launching a mobile food cart
selling gourmet tacos.
Part 1: Market Research (Ratios & Proportions)
1. You survey 120 people. The ratio of those who would buy tacos to those who wouldn't is 5:3. How many would buy?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
2. Of those who would buy, 60% prefer chicken, 25% prefer beef, 15% prefer veggie. How many prefer each?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
3. Your competitor sells 450 tacos in 6 hours. At what rate (tacos per hour)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
4. You project selling at 80% of that rate. How many tacos would you sell in 8 hours?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
5. If ingredients cost $1.80 per taco and you charge $5, what is your profit ratio per taco?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Part 2: Startup Budget (Integers & Percents)
6. Startup costs: Cart $3,500, Equipment $1,200, Permits $450, Initial inventory $800, Marketing $350. Calculate total startup costs.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
7. You have $4,000 saved. You borrow the rest from family (interest-free). Express your debt as a negative integer.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
8. A grant covers 15% of startup costs. How much do you receive?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
9. After the grant, recalculate your debt.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
10. If you repay $500/month, write and solve an equation to find when debt = 0.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Part 3: Pricing Strategy (Algebra)
11. Write an expression for daily revenue: Let t = number of tacos sold at $5 each.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
12. Write an expression for daily profit: Revenue minus ingredient cost ($1.80 per taco) minus daily fixed costs ($75).
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
13. Simplify your profit expression from #12.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
14. Evaluate daily profit if you sell 150 tacos.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
15. You want daily profit of at least $300. Write and solve an inequality: profit ≥ 300.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Part 4: Cart Design (Geometry)
16. Your cart is 8 ft × 4 ft × 6 ft tall. Find the volume.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
17. You need to wrap the cart in weather-resistant vinyl (all 6 sides). Find the surface area.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
18. Vinyl costs $2.50 per square foot. What is the total cost?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
19. You want a refrigerator inside: 2.5 ft × 2 ft × 3 ft. What percent of cart volume does it occupy?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
20. A scale model of your cart is 1:8. What are the model's dimensions?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Part 5: First Month Analysis (Statistics)
21. Daily sales (Week 1): 85, 120, 95, 140, 180, 210, 195. Find mean, median, range.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
22. Calculate the MAD for Week 1 sales. Is your business consistent?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
23. Week 2 sales: 105, 145, 130, 155, 190, 225, 200. Find the percent change in mean sales from Week 1 to Week 2.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
24. Combine all 14 days. Find Q1, median, Q3, and IQR.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
25. Create a summary: Based on your statistics, write a sentence describing your business's first two weeks.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Part 6: Expansion Planning (Scale & Proportions)
26. You want to add a second cart. If one cart serves a 3-mile radius, what area does it cover? (A = πr², use π ≈ 3.14)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
27. Two carts together cover twice the area. What is the total coverage?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
28. A city map uses scale 1 inch : 2 miles. How big is your 3-mile service radius on the map?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
29. You're designing a logo. Original is 4 in × 3 in. You need it 10 inches wide. What's the new height?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
30. The enlarged logo uses how many times more ink (by area)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Part 7: Final Business Report
Synthesize your work into a final summary.
31. Calculate your first month's total revenue (use Week 1 + Week 2 daily sales × $5 per taco).
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
32. Calculate first month's total profit using your expression from Part 3. (Remember to multiply daily fixed costs by number of days.)
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
33. What percent of startup costs have you recovered after Month 1?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
34. At this profit rate, how many months until you pay off your family loan (from Part 2)?
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
35. Write a one-paragraph business summary using at least 5 statistics from your analysis.
Work:
______________________________________________________________________ ______________________________________________________________________ Answer: ______________________________
Congratulations! You have completed the Grade 6 capstone project.
Extra Practice
Additional problems organized by chapter for targeted review
Chapter 1·Ratios, Rates, and Proportions
1. Simplify the ratio 48:64.
Answer: ________________________________________
2. A recipe uses 5 cups of flour for 20 cookies. Write the unit rate.
Answer: ________________________________________
3. Solve the proportion: 4/7 = x/35
Answer: ________________________________________
4. If 3 apples cost $2.25, how much do 8 apples cost?
Answer: ________________________________________
5. A car travels 280 miles on 8 gallons. Find miles per gallon.
Answer: ________________________________________
6. The ratio of boys to girls is 5:7. If there are 35 boys, how many girls?
Answer: ________________________________________
7. Solve: 9/12 = 15/x
Answer: ________________________________________
8. Which is the better buy: 6 oz for $4.50 or 10 oz for $7.00?
Answer: ________________________________________
9. A map scale is 1 in : 30 mi. Two cities are 4.5 inches apart. Find actual distance.
Answer: ________________________________________
10. The ratio of protein to carbs in a meal is 2:5. If there are 30g of carbs, how much protein?
Answer: ________________________________________
Chapter 2·Integers and Operations
1. Calculate: (-15) + (-23)
Answer: ________________________________________
2. Calculate: 45 + (-67)
Answer: ________________________________________
3. Calculate: (-8) - (-12)
Answer: ________________________________________
4. Calculate: 25 - 38
Answer: ________________________________________
5. Calculate: (-6) × 9
Answer: ________________________________________
6. Calculate: (-72) ÷ (-8)
Answer: ________________________________________
7. Order from least to greatest: -12, 5, -3, 0, -8, 7
Answer: ________________________________________
8. A bank account: Start $200, withdraw $350, deposit $100. Final balance?
Answer: ________________________________________
9. Calculate: (-4) × (-5) × (-2)
Answer: ________________________________________
10. Evaluate: -15 + 8 - (-3) + (-10)
Answer: ________________________________________
Chapter 3·Surface Area and Volume
1. Find surface area of a cube with side 7 cm.
Answer: ________________________________________
2. Find surface area: l=10, w=6, h=4 inches.
Answer: ________________________________________
3. A box is 5 ft × 3 ft × 2 ft. How much cardboard for all 6 sides?
Answer: ________________________________________
4. Find volume: 8 in × 5 in × 3 in.
Answer: ________________________________________
5. Find volume: 2.5 m × 4 m × 3 m.
Answer: ________________________________________
6. A rectangular prism has SA = 148 sq cm. If l=6 and w=4, find h.
Answer: ________________________________________
7. Find volume: 3½ ft × 2 ft × 4 ft.
Answer: ________________________________________
8. Describe the net for a cube: how many squares and what size?
Answer: ________________________________________
9. A pool is 25 ft × 12 ft × 5 ft. Find volume in cubic feet.
Answer: ________________________________________
10. Find surface area of the four walls only: 12 ft × 10 ft × 8 ft room.
Answer: ________________________________________
Chapter 4·Dividing Fractions
1. Calculate: ¾ ÷ 2
Answer: ________________________________________
2. Calculate: ⅔ ÷ ½
Answer: ________________________________________
3. Calculate: 5/8 ÷ ¼
Answer: ________________________________________
4. Calculate: 2½ ÷ ½
Answer: ________________________________________
5. Calculate: 4⅓ ÷ ⅔
Answer: ________________________________________
6. How many ¼ cup servings in 3 cups?
Answer: ________________________________________
7. Calculate: 7/8 ÷ 7/16
Answer: ________________________________________
8. A recipe uses ⅔ cup sugar. You have 4 cups. How many batches?
Answer: ________________________________________
9. Calculate: 3¾ ÷ 1½
Answer: ________________________________________
10. Calculate: 5/6 ÷ 5/12
Answer: ________________________________________
Chapter 5·Statistics
1. Find mean: 12, 18, 15, 21, 14.
Answer: ________________________________________
2. Find median: 8, 3, 12, 7, 15, 9, 11.
Answer: ________________________________________
3. Find range: 45, 52, 38, 67, 41.
Answer: ________________________________________
4. Find MAD for: 10, 12, 14, 16, 18 (mean = 14).
Answer: ________________________________________
5. Find Q1 and Q3: 5, 8, 12, 15, 18, 22, 25.
Answer: ________________________________________
6. Calculate IQR from the dataset above.
Answer: ________________________________________
7. Dataset: 20, 25, 25, 30, 35, 40. Find mode and median.
Answer: ________________________________________
8. Find five-number summary: 10, 15, 20, 25, 30, 35, 40.
Answer: ________________________________________
9. Which measure is affected most by outliers: mean or median?
Answer: ________________________________________
10. Find MAD: 5, 5, 10, 15, 15 (mean = 10).
Answer: ________________________________________
Chapter 6·Scale Drawings
1. Scale 1 in : 50 mi. Map distance 3.5 in. Find actual distance.
Answer: ________________________________________
2. Actual distance 240 miles. Scale 1 in : 40 mi. Find map distance.
Answer: ________________________________________
3. Original: 6 cm × 8 cm. Scale factor 2.5. Find new dimensions.
Answer: ________________________________________
4. Similar rectangles: small is 4 × 6, large has length 10. Find large width.
Answer: ________________________________________
5. Scale factor is 3. Original area is 20 sq cm. New area?
Answer: ________________________________________
6. Blueprint: 1 in : 8 ft. Room is 2.5 in × 3 in on paper. Actual dimensions?
Answer: ________________________________________
7. A model car is 1:24 scale. Real car is 12 ft. Model length in inches?
Answer: ________________________________________
8. If area scale factor is 9, what is the linear scale factor?
Answer: ________________________________________
9. Scale 1:100. Model is 15 cm tall. Actual height in meters?
Answer: ________________________________________
10. Photo: 4 × 6 inches. Enlarged with factor 1.5. New area?
Answer: ________________________________________
Chapter 7·Algebraic Expressions and Equations
1. Write expression: 'A number increased by 12'
Answer: ________________________________________
2. Write expression: 'The product of 8 and a number, minus 5'
Answer: ________________________________________
3. Evaluate 4x + 7 when x = 6.
Answer: ________________________________________
4. Evaluate 3a - 2b when a = 5 and b = 4.
Answer: ________________________________________
5. Solve: x + 18 = 45
Answer: ________________________________________
6. Solve: n - 27 = 53
Answer: ________________________________________
7. Solve: 7y = 91
Answer: ________________________________________
8. Solve: m ÷ 6 = 12
Answer: ________________________________________
9. Write and solve: 'A number plus 15 is greater than 40'
Answer: ________________________________________
10. Solve: 5x ≤ 75
Answer: ________________________________________
Chapter 8·Percent Applications
1. Find 45% of 80.
Answer: ________________________________________
2. Find 8% of $650.
Answer: ________________________________________
3. 20% of what number is 36?
Answer: ________________________________________
4. What percent of 80 is 20?
Answer: ________________________________________
5. A $120 item is discounted 25%. New price?
Answer: ________________________________________
6. A price increased from $50 to $65. Percent increase?
Answer: ________________________________________
7. Sales tax is 6.5% on a $240 purchase. Total cost?
Answer: ________________________________________
8. 15% tip on a $84 bill. How much?
Answer: ________________________________________
9. A 30% deposit is $450. What is the total?
Answer: ________________________________________
10. Original: $80. Final: $60. Percent decrease?
Answer: ________________________________________
Chapter 9·Absolute Value and Coordinate Plane
1. Find: |-18|
Answer: ________________________________________
2. Find: |7| + |-12|
Answer: ________________________________________
3. Compare: |-15| ___ |12|
Answer: ________________________________________
4. Order: -8, 3, -5, 0, -2, 6 from least to greatest.
Answer: ________________________________________
5. If |x| = 11, what are possible values of x?
Answer: ________________________________________
6. Name quadrant: (-4, 7)
Answer: ________________________________________
7. Name quadrant: (5, -2)
Answer: ________________________________________
8. Reflect (3, -5) over x-axis. New point?
Answer: ________________________________________
9. Find: |-9| × |-4|
Answer: ________________________________________
10. Point is in Quadrant III. What are signs of (x, y)?
Answer: ________________________________________
Challenge Problems
Advanced multi-step problems for students ready to go deeper
Challenge Set A: Mixed Operations
1. A store buys shirts at $15 each, marks them up 60%, then offers 20% off the marked price. What is the final price and profit per shirt?
Answer: ________________________________________
2. You have 3¾ cups of flour. Recipe A uses ½ cup per batch. Recipe B uses ⅔ cup per batch. How many more batches of A can you make than B?
Answer: ________________________________________
3. Temperature dropped from 8°C to -15°C over 5 hours. What was the average change per hour?
Answer: ________________________________________
4. A rectangular garden is 12 ft × 8 ft. You want to triple the area by increasing both dimensions by the same amount. What is the new length?
Answer: ________________________________________
5. Data set: 15, 18, 21, x, 27. If the mean is 20, find x. Then find the MAD.
Answer: ________________________________________
Challenge Set B: Multi-Step Applications
1. A pool is 20 ft × 15 ft × 6 ft. Water costs $0.004 per gallon. One cubic foot = 7.48 gallons. How much to fill the pool?
Answer: ________________________________________
2. Investment A earns 5% annually. Investment B loses 3% annually. If you put $1,000 in each, what is the combined value after one year?
Answer: ________________________________________
3. Map scale is 1:250,000. Two cities are 8 cm apart on the map. If you drive 60 km/h, how long is the trip?
Answer: ________________________________________
4. A recipe serves 6 and uses 2¼ cups flour, ¾ cup sugar, ½ cup butter. Scale to serve 10. Give all ingredient amounts.
Answer: ________________________________________
5. Stock A: -$5, +$12, -$3, +$8. Stock B: +$4, -$2, +$7, -$6. Which had better total performance and by how much?
Answer: ________________________________________
Challenge Set C: Pre-Algebra Preview
1. Solve the two-step equation: 3x + 7 = 22
Answer: ________________________________________
2. Solve: 2(n - 4) = 14
Answer: ________________________________________
3. The perimeter of a rectangle is 38 cm. The length is 3 more than the width. Find both dimensions. (Hint: P = 2l + 2w)
Answer: ________________________________________
4. Solve: 5x - 12 > 28
Answer: ________________________________________
5. A cell phone plan costs $25/month plus $0.10 per text. Write an expression for monthly cost with t texts. If you spent $43, how many texts?
Answer: ________________________________________
6. Solve for x: x/4 + 5 = 12
Answer: ________________________________________
7. Two numbers add to 45. One is 9 more than the other. Find both numbers.
Answer: ________________________________________
8. Solve: 4(x + 2) - 3 = 25
Answer: ________________________________________
9. A triangle has angles in ratio 1:2:3. Find all three angles. (Hint: angles sum to 180°)
Answer: ________________________________________
10. If 2x + 3y = 21 and y = 3, find x.
Answer: ________________________________________
Final Mastery Check
Comprehensive review covering all Grade 6 standards
1. Simplify: 36:48
Answer: ________________________________________
2. Solve the proportion: 5/8 = 30/x
Answer: ________________________________________
3. Calculate: (-24) + 15 - (-8)
Answer: ________________________________________
4. Calculate: (-6) × (-7) × 2
Answer: ________________________________________
5. Find surface area: l=9, w=5, h=3 cm
Answer: ________________________________________
6. Find volume: 4½ ft × 3 ft × 2 ft
Answer: ________________________________________
7. Calculate: 5/6 ÷ 2/3
Answer: ________________________________________
8. Calculate: 3¼ ÷ 1½
Answer: ________________________________________
9. Find mean and median: 12, 18, 15, 22, 18, 25
Answer: ________________________________________
10. Find MAD for: 6, 8, 10, 12, 14 (mean = 10)
Answer: ________________________________________
11. Scale 1 in : 25 mi. Actual distance 175 miles. Map distance?
Answer: ________________________________________
12. Scale factor 4. Original area 15 sq in. New area?
Answer: ________________________________________
13. Evaluate 5x - 2y when x = 4 and y = 3
Answer: ________________________________________
14. Solve: n + 34 = 81
Answer: ________________________________________
15. Solve: 6y = 78
Answer: ________________________________________
16. Solve: x - 15 > 42
Answer: ________________________________________
17. Find 35% of $180
Answer: ________________________________________
18. A price increased from $40 to $52. Percent increase?
Answer: ________________________________________
19. 20% of a number is 45. Find the number.
Answer: ________________________________________
20. Find: |-23| + |8|
Answer: ________________________________________
21. Order: -7, 4, -2, 0, -9, 5 (least to greatest)
Answer: ________________________________________
22. Name quadrant: (-5, -8)
Answer: ________________________________________
23. A box is 12 in × 8 in × 6 in. You wrap it completely. How much paper?
Answer: ________________________________________
24. Unit rate: 450 miles in 9 hours. Miles per hour?
Answer: ________________________________________
25. Write expression: 'Triple a number, decreased by 7'
Answer: ________________________________________
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This curriculum is based on Nobel Prize-winning research showing that traditional math education fails to transfer to real-world situations. By embedding every problem in professional contexts, we build the bridge that research shows is missing.
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