Gold Rush Ratios

Katie McFarland

Tier 1

Lesson Plan

Gold Rush Ratios Lesson Plan

Students will apply ratios, proportions, and percentages to Gold Rush scenarios by calculating yields, comparing profits, and making trade-off decisions.

This lesson connects abstract math to a historical event, boosting proportional reasoning and problem-solving through engaging, real-world applications.

Audience

8th Grade

Time

60 minutes

Approach

Use themed tasks to practice ratios in context

Materials

Gold Panning Scenario Cards, - Gold Yield Calculation Worksheet, - Proportion Practice Handout, - Gold Rush Assessment Quiz, - Calculators, and - Whiteboard and markers

Prep

Teacher Preparation

15 minutes

Print and/or duplicate Gold Panning Scenario Cards, Gold Yield Calculation Worksheet, Proportion Practice Handout, and Gold Rush Assessment Quiz
Cut and shuffle the Gold Panning Scenario Cards into sets of 3–4 cards per student group
Review the mathematical steps in each handout to anticipate student questions
Set up the whiteboard with a sample ratio problem from the Gold Rush context
Ensure calculators or digital tools are available for each student

Step 1

Introduction & Hook

10 minutes

Display a brief Gold Rush overview and the historical importance of striking gold
Write a sample ratio on the whiteboard (e.g., nuggets to river buckets) and solve together
Explain today’s goals: using ratios, proportions, and percentages to simulate Gold Rush yields

Step 2

Scenario Card Exploration

10 minutes

Distribute Gold Panning Scenario Cards to each group
Instruct students to identify the ratio of gold nuggets to pans for their scenarios
Have groups share one ratio and explain its meaning to the class

Step 3

Yield Calculations

15 minutes

Hand out the Gold Yield Calculation Worksheet
Students calculate total gold yield and convert to ounces or grams using given conversions
Circulate to support proportional setups and percentage conversions

Step 4

Proportion & Percentage Practice

15 minutes

Distribute the Proportion Practice Handout
Students solve word problems on trade-offs (e.g., trading gold for supplies using percentage marks)
Encourage use of calculators and check against peer answers for accuracy

Step 5

Wrap-Up & Assessment

10 minutes

Review key takeaways: setting up ratios, solving proportions, converting to percentages
Administer the Gold Rush Assessment Quiz as an exit ticket
Collect quizzes and highlight strong student explanations on the whiteboard

0 educators
use Lenny to create lessons.

No credit card needed

Slide Deck

Gold Rush Ratios

Explore ratios, proportions, and percentages through a fun Gold Rush scenario.

• 8th Grade Math • 60 minutes

Welcome students! Introduce our Gold Rush adventure and today’s math goals.

Hook: The 1849 Gold Rush

• Tens of thousands traveled to California seeking fortune.
• Panning for gold required skill and math.
• Today: you are prospectors calculating yields and profits!

Show a brief map or image of 1849 California. Explain why people rushed west.

Sample Ratio Warm-Up

If 3 gold nuggets are found in 5 buckets of river sand, how many nuggets in 25 buckets?

Set up proportion: 3/5 = x/25

Write “Nuggets : Buckets = 3 : 5” on board. Solve 3/5 = x/25 together.

Scenario Card Exploration

Each group receives Gold Panning Scenario Cards.
Identify the ratio of nuggets to pans.
Share one ratio and explain its meaning.

Explain scenario cards and group work. Each group gets 3–4 cards.

Example Scenarios

• Scenario A: 8 nuggets : 10 pans
• Scenario B: 15 nuggets : 20 pans

What do these ratios tell us about yield efficiency?

Display two example cards on screen: e.g., 8 nuggets in 10 pans, 15 in 20.

Yield Calculation Worksheet

• Calculate total nuggets found.
• Convert nuggets to ounces (1 nugget = 0.1 oz).
• Write your work and answer in grams or ounces.

Hand out the worksheet. Model one problem step by step.

Worked Example

Find mass of 12 nuggets:

Nuggets to ounces: 12 × 0.1 = 1.2 oz
Ounces to grams: 1.2 × 28.35 ≈ 34.02 g

Work through: 12 nuggets = ? oz (12 × 0.1 = 1.2 oz). Then to grams (1 oz ≈ 28.35 g).

Your Turn: Yield Problems

20 nuggets → ounces and grams
7 nuggets → ounces and grams
25 nuggets → ounces and grams

Encourage partners to compare answers after 5 minutes.

Proportion & Percentage Practice

• Trade gold for supplies at a 20% markup.
• If you trade 10 oz for tools, how much gold must you give for 12 oz of tools?
• Set up ratio and solve.

Explain percentage markup when trading gold for supplies.

Wrap-Up: Key Takeaways

• Set up and simplify ratios
• Solve proportions
• Convert between units and percentages
• Apply math to real-world scenarios

Summarize key math steps and invite final questions before quiz.

Exit Quiz

Answer these on your quiz:

Ratio of 9 nuggets to 15 pans.
Convert 18 nuggets to grams.
Trade 5 oz gold at 10% markup: how many oz for purchase?

Distribute the Gold Rush Assessment Quiz. Students have 5 minutes.

Worksheet

Gold Panning Scenario Cards

Cut into individual cards and distribute 3–4 to each student group. Each card describes a gold panning scenario. Students identify the ratio of nuggets to pans.

Scenario 1
You find 7 gold nuggets after panning 10 pans of river sediment.

Scenario 2
You recover 12 nuggets from 18 pans.

Scenario 3
In one day you pan 8 pans and find 5 nuggets.

Scenario 4
A prospector finds 15 nuggets in 20 pans.

Scenario 5
After a long day you collect 9 nuggets from 12 pans.

Scenario 6
You pan 6 pans of sediment and uncover 4 nuggets.

Scenario 7
Your group yields 11 nuggets from 14 pans.

Scenario 8
An expert panner finds 16 nuggets in 25 pans.

Scenario 9
You strike a rich spot: 20 nuggets in 30 pans.

Scenario 10
A busy day yields 13 nuggets from 22 pans.

Worksheet

Gold Yield Calculation Worksheet

Instructions: Use the conversions below and show all your work:
• 1 nugget = 0.1 oz
• 1 oz = 28.35 g

1. You find 12 gold nuggets.

Ounces of gold: ______ oz
Grams of gold: ______ g

2. You recover 20 gold nuggets.

Ounces of gold: ______ oz
Grams of gold: ______ g

3. You pan 7 gold nuggets.

Ounces of gold: ______ oz
Grams of gold: ______ g

4. You strike a rich spot with 25 nuggets.

Ounces of gold: ______ oz
Grams of gold: ______ g

5. A prospector collects 30 gold nuggets.

Ounces of gold: ______ oz
Grams of gold: ______ g

6. Reverse conversion: If you have 3 ounces of gold, how many nuggets did you find?
________ nuggets

7. Reverse conversion: If you collected 100 grams of gold, how many ounces and how many nuggets?

Ounces: ______ oz
Nuggets: ______ nuggets

When you’re done, check your work with the Proportion Practice Handout or try problems on the Gold Rush Assessment Quiz. Good luck, prospectors!

Worksheet

Proportion Practice Handout

Instructions: Set up proportions and percentage equations to solve each problem. Show all your work and include units.

1. Tool Set Markup

A prospector finds a tool set priced at 10 oz of gold. The supplier applies a 20% markup on the gold price.
How many ounces of gold must the prospector trade to purchase the tool set?

2. Food Supplies Trade

A miner has 15 oz of gold to trade for food. The trader adds a 10% markup.
What is the maximum value (in oz of gold) of supplies the miner can get?

3. Clothing Exchange

A dealer demands a 25% markup on gold when exchanging for clothing.
If a prospector wants clothing worth 40 oz of gold, how many ounces of gold must he trade?

4. Panning Proportion

If the ratio of gold nuggets to pans is 3 : 5, how many nuggets will you find after panning 35 pans?
Set up and solve a proportion.

5. Nuggets to Supplies

A prospector pans 8 gold nuggets.

Convert your nuggets to ounces of gold.
If supplies cost a 30% markup in gold, how many ounces of supplies can you receive for your gold?

6. Reverse Conversion & Markup

You receive 84 grams of supplies for your gold at a 15% markup.

What was the mass of your gold in ounces?
How many nuggets did you trade?
(Use 1 oz = 28.35 g and 1 nugget = 0.1 oz.)

When you finish, check your work with the Gold Yield Calculation Worksheet or try the Gold Rush Assessment Quiz. Good luck, prospectors!

Quiz

Gold Rush Assessment Quiz

Answer Key

Gold Rush Assessment Answer Key

Question 1: Ratio Identification

Write the ratio of gold nuggets to pans if a prospector finds 9 nuggets in 15 pans.
Solution:

Start with 9 : 15
Divide both terms by their greatest common divisor (3): 9÷3=3, 15÷3=5
Answer: 3 : 5

Question 2: Unit Conversion

You discover 18 gold nuggets. Calculate the total mass in grams of the gold collected.
(Use 1 nugget = 0.1 oz and 1 oz = 28.35 g.)
Solution:

Convert nuggets → ounces: 18 nuggets × 0.1 oz/nugget = 1.8 oz
Convert ounces → grams: 1.8 oz × 28.35 g/oz = 51.03 g
Answer: 51.03 g

Question 3: Trade with Markup

A trader applies a 10% markup when exchanging gold for supplies. How many ounces of gold must you give to receive supplies valued at 5 oz of gold?
Solution:

Let x = ounces you give. After 10% markup, you get supplies worth x·1.10.
Set up equation: x·1.10 = 5
Solve for x: x = 5 ÷ 1.10 ≈ 4.545 oz
Answer: ≈ 4.545 oz

Question 4: Proportion Application

If 6 nuggets are found in 8 pans, how many pans are needed to find 24 nuggets?
Solution:

Set up proportion: 6/8 = 24/x
Cross-multiply: 6·x = 8·24
Solve: x = (8·24) ÷ 6 = 192 ÷ 6 = 32
Answer: 32 pans

Question 5: Reverse Conversion

If you have 100 grams of gold, how many ounces and how many nuggets is that?
(Use 1 oz = 28.35 g and 1 nugget = 0.1 oz.)
Solution:

Convert grams → ounces: 100 g ÷ 28.35 g/oz ≈ 3.53 oz
Convert ounces → nuggets: 3.53 oz ÷ 0.1 oz/nugget = 35.3 nuggets
Answer: ≈ 3.53 oz (≈ 35.3 nuggets)

Answer Key

Gold Yield & Proportion Answer Key

Section 1: Gold Yield Calculation Worksheet

(See Gold Yield Calculation Worksheet for prompts.)

You find 12 gold nuggets.
- Ounces: 12 × 0.1 = 1.2 oz
- Grams: 1.2 × 28.35 = 34.02 g
You recover 20 gold nuggets.
- Ounces: 20 × 0.1 = 2.0 oz
- Grams: 2.0 × 28.35 = 56.70 g
You pan 7 gold nuggets.
- Ounces: 7 × 0.1 = 0.7 oz
- Grams: 0.7 × 28.35 = 19.845 g (≈19.85 g)
You strike a rich spot with 25 nuggets.
- Ounces: 25 × 0.1 = 2.5 oz
- Grams: 2.5 × 28.35 = 70.875 g (≈70.88 g)
A prospector collects 30 gold nuggets.
- Ounces: 30 × 0.1 = 3.0 oz
- Grams: 3.0 × 28.35 = 85.05 g
Reverse conversion: If you have 3 ounces of gold, how many nuggets did you find?
- Nuggets: 3.0 ÷ 0.1 = 30 nuggets
Reverse conversion: If you collected 100 grams of gold, how many ounces and how many nuggets?
1. Ounces: 100 ÷ 28.35 ≈ 3.53 oz
2. Nuggets: 3.53 ÷ 0.1 ≈ 35.3 nuggets

Section 2: Proportion Practice Handout

(See Proportion Practice Handout for prompts.)

Tool Set Markup
- Let x = ounces of gold traded. After 20% markup, you pay x·1.20 = 10 oz.
- Solve: x = 10 ÷ 1.20 = 8.33 oz
Food Supplies Trade
- You have 15 oz of gold; supplies cost 10% extra. If y = value of supplies, then y·1.10 = 15.
- Solve: y = 15 ÷ 1.10 ≈ 13.64 oz of supplies
Clothing Exchange
- Desired value 40 oz; markup 25%. Let x·1.25 = 40 → x = 40 ÷ 1.25 = 32 oz
Panning Proportion
- Ratio nuggets : pans = 3 : 5. For 35 pans, nuggets x satisfy 3/5 = x/35.
- Solve: x = (3 × 35) ÷ 5 = 21 nuggets
Nuggets to Supplies
- 8 nuggets → 8×0.1 = 0.8 oz of gold.
- Supplies cost 30% markup: let y·1.30 = 0.8 → y = 0.8 ÷ 1.30 ≈ 0.62 oz of supplies
Reverse Conversion & Markup
- You receive 84 g of supplies. Convert to ounces: 84 ÷ 28.35 ≈ 2.96 oz.
- Let x = ounces of gold traded; x·1.15 = 2.96 → x = 2.96 ÷ 1.15 ≈ 2.57 oz
- Nuggets traded: 2.57 ÷ 0.1 ≈ 25.7 nuggets

Teacher’s Notes: Students should show all work: setting up multiplication for unit conversions, proportions, and percentage equations. Answers may vary slightly due to rounding.
Happy prospecting!