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.
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.
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.)
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 ForumPart I:
The setting is given:Part II: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:
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.
At this point, students have investigated the problem using manipulatives (containers) and technology (the ESCOT Runner simulation).
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