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Classroom activity Grade 7 Math

Contamination Odds: A Grade 7 Water-Sample Probability Game

A grade 7 card-draw game where student groups calculate experimental and theoretical probabilities of contamination for two fictional water systems.

Objectives

  1. Students will calculate experimental probability from repeated card draws and compare it to a stated theoretical probability.
  2. Students will compare probability values between 0 and 1 to decide which of two systems is more likely to show contamination.

Vocabulary

Key words: probability, experimental probability, theoretical probability, likelihood

Teacher overview

This is a small-group card-draw game for groups of 3 to 4 students. Each group receives two decks of 20 index cards representing water samples from two fictional systems, Sunset Hills and Fernwood: Sunset Hills' deck has 3 cards marked "Contaminant Detected" and 17 marked "Clear," while Fernwood's deck has 1 card marked "Contaminant Detected" and 19 marked "Clear." Groups draw cards with replacement, tally the results, and compare their experimental probability of drawing a "Contaminant Detected" card to each deck's known theoretical probability, turning an abstract 0-to-1 probability scale into something they generate with their own hands.

Activity Directions

  1. Before class, prepare two labeled decks of 20 index cards per group, representing the fictional systems Sunset Hills and Fernwood: Deck S (Sunset Hills), with 3 cards marked "Contaminant Detected" and 17 marked "Clear," and Deck F (Fernwood), with 1 card marked "Contaminant Detected" and 19 marked "Clear." Shuffle each deck.
  2. Explain that the theoretical probability of drawing a "Contaminant Detected" card equals the number of such cards divided by the total number of cards in the deck: 3/20 for Deck S and 1/20 for Deck F.
  3. Each group draws one card from Deck S, records whether it says "Contaminant Detected" or "Clear" on their tally sheet, returns the card to the deck, and reshuffles. Groups repeat this draw-record-return process 20 times for Deck S.
  4. Groups calculate their experimental probability for Deck S: the number of "Contaminant Detected" draws divided by 20 total draws.
  5. Groups repeat steps 3 and 4 with Deck F, drawing, recording, and returning cards 20 times, then calculating Deck F's experimental probability.
  6. Groups compare their two experimental probabilities to the theoretical probabilities (3/20 = 0.15 for Deck S, 1/20 = 0.05 for Deck F) and discuss whether their results ran higher, lower, or close to the theoretical values.
  7. End the game once every group has completed 20 draws from each deck and recorded both experimental probabilities on their tally sheet.
  8. Gather the class for a debrief. Ask each group to report their Deck S and Deck F experimental probabilities, then pose two questions: which system has the higher probability of contamination and should be prioritized for more testing, and why might a group's experimental probability differ from the theoretical probability even though every deck was built the same way.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 0.15.
    Deck S's theoretical probability is 3 "Contaminant Detected" cards divided by 20 total cards: 3/20 = 0.15, or 15 percent.
  2. Answer: 0.05.
    Deck F's theoretical probability is 1 "Contaminant Detected" card divided by 20 total cards: 1/20 = 0.05, or 5 percent.
  3. Answer: Sunset Hills (Deck S).
    This answers the first debrief question, on which system should be prioritized for more testing. Sunset Hills has a theoretical probability of 0.15, greater than Fernwood's 0.05, so a larger share of its samples are expected to show contamination.
  4. Answer: chance variation across only 20 draws.
    This answers the second debrief question, on why results can differ from the theoretical probability. With only 20 draws, chance variation means a group can draw more or fewer "Contaminant Detected" cards than the theoretical ratio predicts; theoretical probability describes the average outcome over many, many draws, not a guarantee for any one small set of draws.

Differentiation

Support (below grade level)

Keep both 20-card decks but reduce the number of draws per deck to 10, so the fractions and division stay simpler while the theoretical probabilities (0.15 and 0.05) and the comparison stay the same.

Extension (above grade level)

Ask groups to combine their class's total draws for Deck S (adding every group's tally together) and recalculate one combined experimental probability, then explain whether the combined class result lands closer to the theoretical value than any single group's individual result.

ELL supports

Use color-coded cards (one color for "Contaminant Detected," another for "Clear") in addition to the text labels, and provide a simple tally sheet with icons instead of only words. Allow groups to report their probabilities as fractions (such as "3 out of 20") before converting to decimals.

Extensions

Have groups design a third deck representing a system they believe falls between Sunset Hills and Fernwood in contamination risk, state its theoretical probability, and test it with 20 draws the same way.