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Golden Ratio Dig

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Lesson Plan

Golden Ratio Dig Lesson Plan

Students will pan for “gold” and sand, calculate gold-to-sand ratios, express them as fractions and percentages, and compare their findings to build proportional reasoning.

This Gold Rush-themed lesson deepens understanding of ratios, fractions, and percentages through a hands-on activity, making abstract concepts concrete and engaging for 6th graders.

Audience

6th Grade

Time

30 minutes

Approach

Hands-on panning activity with data recording and calculation.

Materials

Hands-On Gold Panning Kits, Gold Ratio Panning Worksheet, Plastic Gold Flakes, Sand Samples, Bowls, Rulers, Timers, Chart Paper and Markers, Calculators (Optional), and Golden Ratio Dig Slide Deck

Prep

Teacher Preparation

10 minutes

  • Gather all physical materials: panning kits, sand, gold flakes, bowls, rulers, timers, chart paper, and markers.
  • Ensure students can access digital resources: Gold Ratio Panning Worksheet and Golden Ratio Dig Slide Deck.
  • Set up panning stations or distribution plan for efficient transitions.
  • Review slide deck and worksheet to anticipate student questions and examples.

Step 1

Introduction & Activation

5 minutes

  • Display Golden Ratio Dig Slide Deck slide on ratios.
  • Ask: “What is a ratio? Where have you seen ratios in real life?”
  • Connect to Gold Rush history: miners panned for gold, comparing gold to sand.
  • Introduce learning goal: calculate gold-to-sand ratios and convert to fractions and percentages.

Step 2

Demonstration

5 minutes

  • Model a panning demonstration: sift sand and collect gold flakes in a bowl.
  • Measure and record quantities of gold and sand using a ruler or volume estimation.
  • Show how to write the ratio (e.g., 3 gold : 12 sand), simplify to a fraction (3/12 = 1/4), and convert to a percentage (25%).
  • Display example on chart paper.

Step 3

Student Panning Activity

15 minutes

  • Distribute panning kits, sand samples, and gold flakes to student pairs.
  • Students pan, collect gold, measure quantities, and record data on Gold Ratio Panning Worksheet.
  • Calculate and simplify ratios, write fractions, and convert to percentages.
  • Differentiation:
    • Support: provide guided prompts and simplified data sets.
    • Extension: challenge advanced learners to find samples approximating the golden ratio (~1.618:1).

Step 4

Group Discussion & Analysis

3 minutes

  • Invite pairs to share one ratio/fraction/percentage from their worksheet.
  • Discuss differences in results and strategies for more accurate panning.
  • Highlight connections to proportional reasoning and the golden ratio concept.

Step 5

Assessment & Reflection

2 minutes

  • Collect worksheets to assess accuracy of calculations and conversions.
  • Quick exit ticket: “Write one way a miner could use percentages to decide if a pan is worth keeping.”
  • Provide oral feedback and note any misconceptions for reteaching.
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Slide Deck

Golden Ratio Dig!

A Gold Rush–Themed Math Adventure

Grade 6 • 30 Minutes

Objective: Pan for “gold” and sand, calculate gold‐to‐sand ratios, express as fractions and percentages, and compare results.

Welcome the class and introduce the lesson. Explain that today we’re combining history with math in a Gold Rush–themed activity to learn about ratios, fractions, and percentages.

What Is a Ratio?

• A ratio compares two quantities by division.
• Written as a :b, a/b, or “a to b.”
• Examples:
– 2 apples : 3 oranges
– 4 cups : 1 cup sugar (recipe)

Ask students: “What is a ratio? Where have you seen ratios in real life?” Solicit examples (recipes, maps, sports stats). Define ratio formally.

The Gold Rush & Ratios

• Miners sifted sand and gravel to find flecks of gold.
• They recorded how much gold they found versus how much sand.
• That gold‐to‐sand ratio told them if it was worth digging deeper.

Provide a brief Gold Rush overview: in 1849, miners panned riverbeds to separate gold flakes from sand and gravel. Explain that miners used ratios to estimate yield.

Demonstration Steps

  1. Sift sand and collect gold flakes in bowl.
  2. Measure quantities (by volume or count).
  3. Record: e.g., 3 gold : 12 sand.
  4. Simplify ratio: 3/12 = 1/4.
  5. Convert to percentage: (1/4)×100 = 25%.

Demonstrate each step clearly. Show real or mock panning kit. Record measurements on chart paper as you go.

Your Panning Activity

• In pairs, use kits to pan for gold and sand.
• Record counts on Gold Ratio Panning Worksheet.
• Simplify each ratio to a fraction and convert to a percentage.
• Extension: Find a sample close to the golden ratio (~1.618 : 1).

Explain logistics: pairs, materials, worksheet. Circulate to support and challenge students. Remind about simplification and conversion.

Reflect & Share

• Share one ratio, fraction, and percentage from your data.
• Exit Ticket: “How could a miner use percentages to decide if a pan is worth keeping?”

Invite a few pairs to share their ratios and percentages. Collect worksheets. Have students write the exit ticket before leaving.

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Worksheet

Gold Ratio Panning Worksheet

Name: _______________________ Date: ________________ Period: _______

Instructions: In this activity, you will pan for gold flakes and sand, record your counts, calculate ratios, simplify them, and convert to fractions and percentages. Answer all parts below.

Part 1: Data Collection

Record your counts for each pan sample.

Pan #1

  • Number of gold flakes: __________

  • Number of sand particles: __________

Pan #2

  • Number of gold flakes: __________

  • Number of sand particles: __________

Pan #3

  • Number of gold flakes: __________

  • Number of sand particles: __________

Part 2: Ratios & Simplification

For each pan, write the ratio of gold to sand and then simplify it to lowest terms.

Pan #1
Gold : Sand = __________ : __________

Simplified = __________ : __________


Pan #2
Gold : Sand = __________ : __________

Simplified = __________ : __________


Pan #3
Gold : Sand = __________ : __________

Simplified = __________ : __________


Part 3: Fraction & Percentage Conversion

Convert each simplified ratio into a fraction and then into a percentage.

Pan #1
Fraction = __________

Percentage = __________%


Pan #2
Fraction = __________

Percentage = __________%


Pan #3
Fraction = __________

Percentage = __________%


Part 4: Golden Ratio Challenge (Extension)

The golden ratio is approximately 1.618 : 1. Which pan came closest to this value? Show your comparison.

Pan # ______ came closest because my ratio of __________ (or my percentage of __________%) is nearest to 1.618 : 1.




Part 5: Reflection

Write one way a miner could use percentages to decide if a pan is worth keeping.

___________________________________________________________________________





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