Gold Nugget Problems Worksheet

Group Name: ___________________________

Members: ____________________________, ____________________________, ____________________________

Solve the following “gold nugget” math problems. Show all your work and calculations.

1. If 2 pans yield 5 nuggets, how many nuggets would you expect from 14 pans?
   
   
   
   
   
   
   

2. The ratio of gold to sand in a pan sample is 1:6 by weight. If you have 18 g of gold, how much sand is present?
   
   
   
   
   
   
   

3. A mining team recovers 75% of the gold in each pan. If a pan originally contains 80 g of gold, how many grams does the team actually collect?
   
   
   
   
   
   
   

4. A gold nugget costs $60. A buyer negotiates a 20% discount before purchase. What is the discounted price of the nugget?
   
   
   
   
   
   
   

5. You find a nugget that cost you $40 and sell it for a 50% profit. What is your selling price?
   
   
   
   
   
   
   

6. During the adventure, your group answered 9 out of 12 problems correctly.
   a) What percentage of problems did you solve correctly?
   b) If each correct answer earns 1 nugget, how many nuggets did you earn?
   c) If you can trade 4 nuggets for one “super nugget” bonus, how many super nuggets could you claim?
   
   
   
   
   
   
   
   
   
   
   
   

7. Extension Challenge: A prospector increases her number of pans by 25% and finds that her nugget haul increases by 20%. If she originally used 8 pans to find 32 nuggets, how many pans and how many nuggets does she have after improving her strategy?
   
   
   
   
   
   
   
   
   
   
   
   
   

8. Ratio Sharing: A prospector shares her nuggets with two friends in a ratio of 3:2:1. If she has 36 nuggets in total, how many nuggets does each person receive?
   
   
   
   
   
   
   
   
   
   
   
   

9. Trading & Revenue Decision: You have 11 regular nuggets. You can trade 4 regular nuggets for 1 super nugget, which sells for $20. Any leftover regular nuggets sell for $4 each. If you trade as many nuggets as possible for super nuggets and then sell all nuggets, what total revenue will you earn?
   
   
   
   
   
   
   
   
   
   
   
   
   

Gold Nugget Answer Key (Updated)

Below are the step-by-step solutions for all problems on the Gold Nugget Problems Worksheet, including the new problems 8 and 9.

1. Panning Proportion

... (existing solution remains unchanged)

2. Gold-to-Sand Ratio

... (existing solution remains unchanged)

3. Percent Recovery

... (existing solution remains unchanged)

4. Discounted Price

... (existing solution remains unchanged)

5. Profit Calculation

... (existing solution remains unchanged)

6. Group Performance Analysis

... (existing solution remains unchanged)

7. Extension Challenge

... (existing solution remains unchanged)

8. Ratio Sharing

Problem: A prospector shares her nuggets with two friends in a ratio of 3:2:1. If she has 36 nuggets in total, how many nuggets does each person receive?

Solution Steps:

1. Compute total parts: 3 + 2 + 1 = 6 parts.
2. Determine value of one part: 36 nuggets ÷ 6 parts = 6 nuggets per part.
3. Calculate each share:
   • First person (3 parts): 3 × 6 = 18 nuggets
   • Second person (2 parts): 2 × 6 = 12 nuggets
   • Third person (1 part): 1 × 6 = 6 nuggets

Answer: 18 nuggets, 12 nuggets, and 6 nuggets respectively

9. Trading & Revenue Decision

Problem: You have 11 regular nuggets. You can trade 4 regular nuggets for 1 super nugget, which sells for $20. Any leftover regular nuggets sell for $4 each. If you trade as many nuggets as possible for super nuggets and then sell all nuggets, what total revenue will you earn?

Solution Steps:

1. Determine number of super nuggets you can acquire by trading:
   • 11 regular nuggets ÷ 4 nuggets/trade = 2 trades (because 2 × 4 = 8 used)
   • Super nuggets earned = 2
2. Calculate leftover regular nuggets:
   • Leftover = 11 – 8 = 3 regular nuggets
3. Compute revenue:
   • Revenue from super nuggets = 2 × $20 = $40
   • Revenue from leftover regular nuggets = 3 × $4 = $12
   • Total revenue = $40 + $12 = $52

Answer: $52 total revenue

Use these extended solutions to guide grading and reinforce strategies for ratio partitioning and multi-step percent/trading decisions.

Gold Rush Reflection Exit Ticket

Take a moment to reflect on today’s gold panning adventure. Answer the prompts below in complete sentences.

1. Which strategy helped you pan the most gold? Why was it effective?

1. Describe a real-life situation where you could use proportions or percents. How would you apply what you learned?

1. On a scale from 1 (not confident) to 5 (very confident), how do you feel about solving percent problems now? Explain your rating.

1. What is one question or concept from today’s lesson that you would like to review further tomorrow?

Use your reflections to guide our next steps and ensure everyone strikes gold with confidence!

Real-Life Math Applications

Math isn’t just for textbooks—it’s a powerful tool we use every day. Below are real-world scenarios where proportional reasoning and percent calculations help us make smart decisions.

1. Cooking and Recipe Adjustments

Imagine a pancake recipe designed for 4 people that uses:

• 2 cups of flour
• 1½ cups of milk
• 1 egg

What if you’re cooking only for 2 people? Use a proportion: 2 people is half of 4, so you’d use half of each ingredient:

• Flour: 2 cups × ½ = 1 cup
• Milk: 1½ cups × ½ = ¾ cup
• Eggs: 1 egg × ½ = ½ egg (you might round and use just one egg or adjust slightly)

This same approach works whenever you need to scale a recipe up or down.

2. Mixing Paints or Solutions

Painters often mix paint in a 3:1 ratio (3 parts base color to 1 part accent color). If you need 16 cups of final paint, let x be the amount of accent color:

• Total parts = 3 + 1 = 4
• One part = 16 cups ÷ 4 = 4 cups
• Base color = 3 × 4 cups = 12 cups
• Accent color = 1 × 4 cups = 4 cups

Proportional reasoning ensures consistent colors every time.

3. Shopping Discounts and Sales Tax

Percentages help you figure out sale prices and taxes quickly. For example, a $50 jacket is on sale for 30% off:

• 30% of $50 = 0.30 × $50 = $15 discount
• Sale price = $50 – $15 = $35

When you check out, you might pay sales tax of 7%:

• 7% of $35 = 0.07 × $35 = $2.45
• Total cost = $35 + $2.45 = $37.45

4. Map Reading and Scale Models

Maps use scale ratios to represent large distances on paper. A map scale of 1:100,000 means 1 inch (or centimeter) on the map equals 100,000 inches (or centimeters) in real life. If two towns are 2.5 inches apart on the map, the actual distance is:

• 2.5 inches × 100,000 = 250,000 inches
• Convert to miles: 250,000 in ÷ 63,360 in/mile ≈ 3.94 miles

5. Medicine Dosages

Health professionals calculate dosages in proportion to a patient’s weight. A doctor prescribes 5 mg of medicine per kilogram of body weight. For a 60 kg patient:

• Dosage = 5 mg/kg × 60 kg = 300 mg

Accurate proportional calculations help keep patients safe.

6. Personal Finance and Interest Rates

Understanding percentages helps when you earn interest or pay back a loan. If you invest $1,000 at a 4% annual interest rate:

• Interest earned in one year = 0.04 × $1,000 = $40

Knowing how to calculate percent growth or percent decrease is essential for budgeting and saving.

By spotting proportions and percentages in everyday life—from the kitchen to the bank—you’ll see why these math tools are so valuable!

Gold Rush Team Challenges

Bring proportions and percents to life with these three collaborative, game-style group activities. Each challenge earns “gold nuggets” toward class bragging rights!

1. Ratio Relay Race (10–12 minutes)

• Divide the class into teams of 4–5.
• Give each team a stack of ratio challenge cards (e.g., “If 3 pans yield 7 nuggets, how many from 15 pans?”).
• On “Go,” the first student draws a card, solves it on poster paper, and shows the solution to the teacher.
• Once correct, they pass the “gold pan” baton to the next teammate, who draws the next card.
• First team to solve all their cards correctly earns 5 bonus nuggets; others earn 1 nugget per correct answer.

Objectives: Speed up ratio thinking, practice silent checking strategies, build teamwork.

2. Discount Dilemma Auction (15 minutes)

• Each group receives a mock budget of $100 in play money.
• The teacher “auctions” different quantities of gold pans at various percent-off deals (e.g., “10 pans at 15% off,” “5 pans at 25% off,” “20 pans at 5% off”).
• Groups calculate the discounted price for each auction item and decide how many pans to bid on without exceeding their budget.
• After all items are auctioned, groups total their purchased pans.
• Award nuggets: 2 nuggets per pan owned + 5 nuggets to the group with the highest leftover budget (smart spending).

Objectives: Apply percent discount calculations in a decision-making context, weigh cost vs. quantity.

3. Super Nugget Negotiation (15–18 minutes)

• Present a trading scenario: groups start with 12 regular nuggets.
• A “Trading Post” offers to swap 4 regular for 1 super nugget (worth more in final scoring), but each super can also be sold for $20 vs. $4 per regular.
• In teams, students decide: How many trades to make? How many regular to keep to maximize total value?
• Each team records their trade plan, computes total revenue, and prepares a 2-minute pitch arguing why their strategy is best.
• Teams present; peers vote on the most persuasive strategy.
• Nuggets awarded: 3 nuggets for correct optimal strategy + 2 bonus nuggets for winning the vote.

Objectives: Tackle multi-step percent and ratio problems, practice persuasive math communication.

Rotate teams through these challenges or run them concurrently if space allows. Tally nuggets at the end and celebrate your top prospector group!