Teacher Lesson Plan

Using Manipulatives

    Simulating the activity:

1. Use the following materials:
   • one 6 unit container
   • one 10 unit container
   • dried beans or small cubes (something to represent the diamonds)
   • paper to record method

2. You are given the following scenario:

   The pirate ship has just landed, loaded with diamonds. You've been sent to buy 8 lbs. of diamonds but you only have 10-lb. and 6-lb. measuring containers.

3. How can you make the purchase?

   Remember that there are various problem solving techniques which you can choose from including:

   Choose the Operation
   Evaluate Information
   Find the Pattern
   Guess and Check
   Make a Table
   Plan and Reason
   Work Backward
   Write an Equation
   

Using Technology

Specific instructions for using the ESCOT Runner software to interact with the Pirate Diamond Activity can be viewed here.

The Pirate Diamond Activity can be downloaded from:

ESCOT Problem of the Week hosted by the Math Forum

The setting is given:

The pirate ship has just landed, loaded with diamonds. You've been sent to buy 8 lbs. of diamonds but you only have one 10-lb. and one 6-lb. measuring container.

You will be asked to respond to this question:

How can you make the purchase?

Can you measure 1 lb. of diamonds using only one 10-lb. and one 6-lb. measuring container? How about 2 lbs.? Consider the amounts between 1 lb. and 16 lbs. What conclusion can you make about the amounts of diamonds that can be purchased using only one 10-lb. and one 6-lb. measuring container?

You now have a choice of five pairs of containers to use for measuring. For each pair of containers, can you make the purchase of 8 lbs. of diamonds? For those pairs that work, how can you make the purchase?

There is a counter which keeps track of the number of times you have emptied a container. You may have noticed that you end up emptying the containers quite often, which seems like a waste of time. Also, the pirate is liable to make you walk the plank if you empty the containers too often because you are handling his diamonds too much.

Which pair of containers should you choose to minimize the number of steps (Fill, Empty, Pour) it takes you to measure 8 lbs. of diamonds?

At this point, you have investigated the problem using manipulatives (containers) and technology (the ESCOT Runner simulation).

Select one of the container problems (6 and 10 to 8; 6 and 10 to 2; 6 and 10 to 4; 6 and 10 to 12, etc.) and explain in writing how to reach the desired amount using the two given containers. Draw diagrams to accompany your explanation.