Balance Scale As A Mathematical Model

Balance Scale As A Mathematical Model

Which Coin Is Counterfeit?

Opening

Which Coin Is Counterfeit?

Suppose you have 12 coins, and one of the coins is counterfeit. You know that the counterfeit coin weighs less than the other coins.

  1. Can you use a balance scale to find the counterfeit coin?
  2. Turn and talk to your partner about this question. Share an idea about how you might approach the problem, but do not try to find the solution yet.

Hint:

  • Counterfeit means fake ; a counterfeit coin looks like a real coin issued by the government but is actually an imitation.
  • A counterfeit coin is made from cheaper metals, so it weighs less than a real coin.

Math Mission

Opening

Develop a strategy for consistently finding the counterfeit coin in a group of real coins using a balance scale.

Develop a Strategy

Work Time

Develop a Strategy

Think back to the problem you just discussed:

Suppose you have 12 coins, and one of the coins is counterfeit. You have a balance scale, and you know that the counterfeit coin weighs less than the other coins.

  • Using the Balance Scale Game interactive, develop a strategy for finding the counterfeit coin.

Challenge Problem

In another group of 12 coins, there are 2 counterfeit coins that are lighter than the rest.

  • How will you have to adjust your strategy to find the 2 counterfeit coins?
  • Use the Balance Scale interactive to find the 2 counterfeit coins.

INTERACTIVE: Balance Scale Game

Hint:

Suppose you have 6 coins on each side of the balance scale and the left side is heavier. What does this situation tell you?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the different strategies your classmates used for finding the counterfeit coin(s).

Hint:

As your classmates present, ask questions such as:

  • For one counterfeit coin: How do you know which side of the balance scale the counterfeit coin is on?
  • For two counterfeit coins: How can you be sure that both of the counterfeit coins are on that side of the balance scale?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

The strategy I like best for identifying the counterfeit coin is ___ because …