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Golden Gold Rush Math

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Lesson Plan

Golden Gold Rush Math Plan

Students will use a Gold Rush–themed hands-on activity with colored counters to model ratios, solve proportions, and set up basic algebraic equations.

Contextualizing ratios and proportions in a fun Gold Rush scenario boosts engagement and helps students grasp abstract concepts through real-world application.

Audience

7th Grade

Time

30 minutes

Approach

Hands-on gold panning exploration with guided practice.

Materials

Prep

Prepare Materials and Review Resources

10 minutes

  • Print enough copies of the Gold Rush Worksheet for each student.
  • Gather colored counters (gold, silver, copper) and small panning trays.
  • Load the Gold Rush Slide Deck on the classroom projector.
  • Review the slide deck to familiarize yourself with the ratio and proportion problem scenarios.

Step 1

Warm-Up Discussion

5 minutes

  • Display the first slide of the Gold Rush Slide Deck featuring a simple gold-to-dirt ratio.
  • Ask students to discuss with a partner what a ratio represents in everyday life.
  • Solicit examples (recipes, sports stats) and note them on the whiteboard.

Step 2

Gold Panning Exploration

10 minutes

  • Distribute panning trays and counters.
  • Present a slide problem: “Your pan has 12 gold pieces and 48 dirt pieces. What’s the gold-to-total ratio?”
  • Students pan for “gold,” count each color, calculate and simplify their ratios.
  • Circulate to support correct ratio language and calculations.

Step 3

Worksheet Practice

10 minutes

  • Instruct students to complete selected problems on the Gold Rush Worksheet involving proportions and basic algebra (e.g., if the ratio of gold to dirt must be 1:4, find x when gold = x).
  • Encourage setting up and solving simple equations based on their panning data.
  • Provide hints or prompts as needed.

Step 4

Cool-Down Reflection

5 minutes

  • Lead a class discussion: Which strategies helped simplify ratios or solve for x?
  • Have students share one real-world application of ratios and proportions.
  • Summarize key takeaways and preview how these skills connect to future algebra lessons.
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Slide Deck

Golden Gold Rush Math

Welcome, 7th graders! Today we’ll dig into ratios, proportions, and simple algebra through a fun Gold Rush–themed activity. Ready to pan for gold?

Introduce the lesson, grab attention with the Gold Rush theme. Mention today we’ll “pan” for gold to learn ratios, proportions, and basic algebra.

What Is a Ratio?

• A ratio compares two quantities by division.
• Written as 3:1, 3 to 1, or 3/1.
Everyday examples: recipe ingredient ratios, sports statistics, map scales.

Ask students to turn and talk. Listen for everyday ratio examples and write a couple on the board.

Warm-Up Problem

“Your pan has 12 gold pieces and 48 dirt pieces.
What’s the gold-to-dirt ratio?
What’s the gold-to-total ratio?”

Display this slide. Give students a minute to calculate, then solicit answers. Emphasize simplifying ratios.

Gold Panning Exploration

  1. Grab a panning tray and a mix of colored counters (gold, silver, copper, “dirt”).
  2. Sort and count your gold vs. dirt pieces.
  3. Record your counts and calculate your ratios.

Explain the hands-on portion. Demonstrate how to pan and sort counters. Remind students to record counts carefully.

Practice with Your Pan

• Pan, count, and record:
– Gold pieces = ___
– Dirt pieces = ___
• Calculate and simplify:
– Gold : Dirt = ___
– Gold : Total = ___

Circulate as students work. Guide them to express ratios correctly and simplify. Check for understanding.

Worksheet Practice

Complete selected problems on your Gold Rush Worksheet:
• If gold : dirt must be 1:4 and gold = x, find x when dirt = 20.
• Solve proportions based on your pan data.

Introduce the worksheet. Remind students to set up proportions and simple equations when needed.

Cool-Down & Reflection

  1. Which strategy helped you simplify ratios or solve for x?
  2. Share one real-world example where you see ratios or proportions.
  3. What will you remember most from today’s Gold Rush?

Lead a brief whole-class discussion. Highlight student strategies and real-world applications.

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Worksheet

Gold Rush Worksheet

Gold Rush Worksheet
Name: ____________________ Date: ____________

A. Simplify the Ratios

  1. You pan 15 gold pieces and 45 dirt pieces.
    a) Gold : Dirt = _______
    b) Gold : Total = _______



  2. You pan 8 gold pieces and 24 dirt pieces.
    a) Gold : Dirt = _______
    b) Gold : Total = _______



B. Solve the Proportions

  1. If the ratio gold : dirt must be 1 : 4 and you have 28 dirt pieces, how many gold pieces (x) do you need?
    Set up the proportion and solve for x.






  2. If the ratio gold : total pieces must be 2 : 5 and the total pieces you collected is 35, find the number of gold pieces.
    Show your work.






C. Set Up and Solve Equations

  1. Let x be the number of gold pieces and you have 5 dirt pieces.
    If gold : dirt = 3 : 7, write an equation for x : 5 = 3 : 7 and solve for x.







  2. You collected a total of y pieces (gold + dirt).
    If the ratio gold : total is 1 : 3 and the dirt pieces count is 24, write an equation and find y.







D. Word Problem

  1. You combine two pans of gold mining results:
    • Pan A has 12 gold pieces and 36 dirt pieces
    • Pan B has 9 gold pieces and 21 dirt pieces
      a) What is the combined gold : dirt ratio?
      b) Simplify your answer.











Show all your work and remember to simplify each ratio!

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Answer Key

Gold Rush Answer Key

(This answer key corresponds to the Gold Rush Worksheet)

A. Simplify the Ratios

  1. You pan 15 gold pieces and 45 dirt pieces.

    a) Gold : Dirt
    • Start with 15 : 45.
    • Divide both numbers by their greatest common factor (15): 15 ÷ 15 = 1, 45 ÷ 15 = 3.
    Answer: 1 : 3

    b) Gold : Total
    • Total pieces = 15 + 45 = 60.
    • Ratio = 15 : 60.
    • Simplify by dividing both by 15: 15 ÷ 15 = 1, 60 ÷ 15 = 4.
    Answer: 1 : 4

  2. You pan 8 gold pieces and 24 dirt pieces.

    a) Gold : Dirt
    • Start with 8 : 24.
    • GCF = 8 → 8 ÷ 8 = 1, 24 ÷ 8 = 3.
    Answer: 1 : 3

    b) Gold : Total
    • Total pieces = 8 + 24 = 32.
    • Ratio = 8 : 32.
    • Simplify by dividing both by 8: 8 ÷ 8 = 1, 32 ÷ 8 = 4.
    Answer: 1 : 4

B. Solve the Proportions

  1. If the ratio gold : dirt must be 1 : 4 and you have 28 dirt pieces, how many gold pieces (x) do you need?

    Step 1: Write the proportion:
    (1/4 = x/28)

    Step 2: Cross-multiply:
    (4 \times x = 1 \times 28)
    (4x = 28)

    Step 3: Solve for x:
    (x = 28 ÷ 4 = 7)

    Answer: 7 gold pieces

  2. If the ratio gold : total pieces must be 2 : 5 and the total pieces you collected is 35, find the number of gold pieces.

    Step 1: Set up the proportion:
    (2/5 = x/35)

    Step 2: Cross-multiply:
    (5x = 2 \times 35 = 70)

    Step 3: Solve for x:
    (x = 70 ÷ 5 = 14)

    Answer: 14 gold pieces

C. Set Up and Solve Equations

  1. Let x be the number of gold pieces and you have 5 dirt pieces.
    If gold : dirt = 3 : 7, write an equation for x : 5 = 3 : 7 and solve for x.

    Step 1: Write the proportion:
    (x/5 = 3/7)

    Step 2: Cross-multiply:
    (7x = 5 \times 3 = 15)

    Step 3: Solve for x:
    (x = 15/7)
    (Approximately 2.14 if a decimal is needed.)

    Answer: (x = \tfrac{15}{7})

  2. You collected a total of y pieces (gold + dirt).
    If the ratio gold : total is 1 : 3 and the dirt pieces count is 24, write an equation and find y.

    Step 1: Let g = number of gold pieces.
    Then total = g + 24.

    Step 2: Write the ratio equation:
    (g/(g+24) = 1/3)

    Step 3: Cross-multiply:
    (3g = 1 \times (g+24))
    (3g = g + 24)

    Step 4: Solve for g:
    (3g - g = 24)
    (2g = 24)
    (g = 12)

    Step 5: Find total y:
    (y = g + 24 = 12 + 24 = 36)

    Answer: Total pieces (y = 36)

D. Word Problem

  1. You combine two pans of gold mining results:

    • Pan A: 12 gold, 36 dirt
    • Pan B: 9 gold, 21 dirt

    a) What is the combined gold : dirt ratio?
    b) Simplify your answer.

    Step 1: Add counts from both pans:
    • Gold_total = 12 + 9 = 21
    • Dirt_total = 36 + 21 = 57

    Step 2: Write the combined ratio:
    21 : 57

    Step 3: Simplify by GCF (3):
    21 ÷ 3 = 7, 57 ÷ 3 = 19

    Answer:
    a) 21 : 57
    b) Simplified → 7 : 19

End of Answer Key

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Warm Up

Gold Rush Warm-Up (5 minutes)

Think–Pair–Share:
Your goal: Quickly compare two pans to see which is “richer” in gold.

Pan A: 6 gold pieces and 18 dirt pieces
Pan B: 8 gold pieces and 40 dirt pieces

  1. Calculate each pan’s gold : dirt ratio.
    Pan A → ________
    Pan B → ________



  2. Which pan has a higher gold : dirt ratio? Explain your reasoning in one sentence.








3. Be ready to share your answer with a partner, then with the class!

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Cool Down

Gold Rush Cool-Down (Exit Ticket)

Name: _______________________ Date: ____________

  1. Describe one strategy you used today to simplify a ratio or solve for x.






  2. Provide your own real-world example (not mentioned in class) where you might use ratios or proportions. Explain why it’s useful.












  3. Quick Check: You pan 9 gold pieces and 27 dirt pieces.
    Simplify the gold : dirt ratio.
    Answer: __________



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Golden Gold Rush Math • Lenny Learning