Pirate Diamond Activity

Teacher Lesson Plan

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This activity is aligned to NCTM Standards - Grades 6-8: Geometry, Measurement, Problem Solving, Reasoning and Proof, and Communication and California Mathematics Standards Grade 7: Measurement and Geometry #1.1, Mathematical Reasoning #1.1, 1.3, 2.2, 2.4, 2.5, 2.8.

Students use problem-solving strategies and then justify their reasoning: they pour using containers (manipulatives) and also simulate pouring using the ESCOT Runner software (technology) to determine whether they can produce eight units using only a six-unit container and a ten-unit container. After working through the first problem students are asked to respond to similar problems. Students explain one of those problems step-by-step in a paper/pencil activity.

It is important to build a bridge between the technology representing the containers and the actual physical containers. Visiting the problem using both techniques addresses a variety of learning styles, brings the abstract into the concrete, and offers interaction with the computer as students investigate, discover, form hypotheses, draw conclusions, and benefit from the quick feedback and the interest a computer provides. Once students have had these experiences it is important to arrive at a synthesis by spending the time necessary to internalize the concepts. Manipulatives can provide space for group work, computers can afford individual explorations, and the synthesis can take place during a full-class discussion. Students can then demonstrate their individual understandings through the writing process.

 Using Manipulatives

Simulating the activity:

(Suggestion: Use 2 measuring cups with tape marking the 6 oz. line on one cup and the 10 oz. line on the other cup.)
1. Pass out the following materials for each group of four students:
• one 6 unit container
• one 10 unit container
• dried beans or small cubes (something to represent the diamonds)
• paper to record method

2. Provide the students with 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. Ask the question: How can you make the purchase?

Remind students of the various problem solving techniques which they 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.

ESCOT Problem of the Week hosted by the Math Forum

Part I:
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.
The students are asked to respond to this question:

How can you make the purchase?
Part II:
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?
Part III:
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?
Part IV:
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?

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

Ask the students to 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. Encourage them to draw diagrams to accompany their explanation.