Administering & Scoring the Puzzle Tanks Test

As you may notice, the printout of the test contains six boxes, all of which contain a diagram of the tanks and the truck. On each, the size of the two limited tanks is indicated. The top tank is full, and the truck begins empty, as do the two finite tanks.

Begin by reading through the instructions with the child. Then work a few steps of the sample problems to show the child how the game works.
The child should be given a blue pencil and the proctor will have a red one.
For each move, the child will select an arrow on the diagram on the left to show how he/she wants to transfer juice from one tank to another. The child should then write in each of the tanks and the truck how much juice each contains.
The proctor will then use the red pencil to indicate, on the diagram on the right, how much juice each tank really would contain after the child's move. The game will thus continue until the tank contains the correct amount, or until the child has performed 18 moves without getting the right amount in the tank.

We are suggesting the following guidelines for scoring:

Problem 1: The most efficient solution takes four steps: (1) circle the arrow from the upper tank to the 6-unit tank, (2) circle the arrow from the 6-unit tank to the truck, (3) circle the arrow from the upper tank to the 5-unit tank, and (4) circle the arrow from the 5-unit tank to the truck. The order of the steps can be rearranged in several ways to produce the same effect. The overall pattern is simple addition: 6 + 5 = 11.

Problem 2: The most efficient solution takes three steps: (1) circle the arrow from the upper tank to the 5-unit tank, (2) circle the arrow from the 5-unit tank to the 1-unit tank, and (3) circle the arrow from the 5-unit tank to the truck. The overall pattern is simple subtraction: 5 - 1 = 4. A less sophisticated strategy is based on repeated addition: 1 + 1 + 1 + 1 = 4.

Problem 3: The most efficient solution takes five steps: (1) circle the arrow from the upper tank to the 7-unit tank, (2) circle the arrow from the 7-unit tank to the truck, (3) circle the arrow from the upper tank to the 7-unit tank, (4) circle the arrow from the 7-unit tank to the 2-unit tank, and (5) circle the arrow from the 7-unit tank to the truck. The overall pattern is a combination of addition and subtraction: 7 + (7 - 2) = 12. The less sophisticated approach is based on repeated addition: 2 + 2 + 2 + 2 + 2 + 2 = 12.

Scoring can be based on adding up the number of correct solutions within 18 trials, yielding a score ranging from 0 to 3. Scoring can be based on the total number of moves (with a maximum of 18 per problem), yielding scores ranging from a perfect score of 12 to a maximum score of 54. Scoring of the second two problems can be based on the strategy used to solve the problem: the sophisticated strategy which involves subtraction (i.e., circling the arrow from the 5-unit tank to the 1-unit tank in problem 2, or circling the arrow from the 7-unit tank to the 2-unit tank in problem 3) whereas the less sophisticated strategy involves only addition (i.e., not circling the arrow between tanks). A strategy score ranging from 0 to 2 is computed giving students one point for using the sophisticated strategy on problem 2 and one point for using it on problem 3.



		Directions for Administering & Scoring the Puzzle Tanks Test
		Click Here to Download the PDF file for this Page. As you may notice, the printout of the test contains six boxes, all of which contain a diagram of the tanks and the truck. On each, the size of the two limited tanks is indicated. The top tank is full, and the truck begins empty, as do the two finite tanks. Begin by reading through the instructions with the child. Then work a few steps of the sample problems to show the child how the game works. The child should be given a blue pencil and the proctor will have a red one. For each move, the child will select an arrow on the diagram on the left to show how he/she wants to transfer juice from one tank to another. The child should then write in each of the tanks and the truck how much juice each contains. The proctor will then use the red pencil to indicate, on the diagram on the right, how much juice each tank really would contain after the child's move. The game will thus continue until the tank contains the correct amount, or until the child has performed 18 moves without getting the right amount in the tank. The test itself consists of three problems to be solved in this manner. We are suggesting the following guidelines for scoring: Problem 1: The most efficient solution takes four steps: (1) circle the arrow from the upper tank to the 6-unit tank, (2) circle the arrow from the 6-unit tank to the truck, (3) circle the arrow from the upper tank to the 5-unit tank, and (4) circle the arrow from the 5-unit tank to the truck. The order of the steps can be rearranged in several ways to produce the same effect. The overall pattern is simple addition: 6 + 5 = 11. Problem 2: The most efficient solution takes three steps: (1) circle the arrow from the upper tank to the 5-unit tank, (2) circle the arrow from the 5-unit tank to the 1-unit tank, and (3) circle the arrow from the 5-unit tank to the truck. The overall pattern is simple subtraction: 5 - 1 = 4. A less sophisticated strategy is based on repeated addition: 1 + 1 + 1 + 1 = 4. Problem 3: The most efficient solution takes five steps: (1) circle the arrow from the upper tank to the 7-unit tank, (2) circle the arrow from the 7-unit tank to the truck, (3) circle the arrow from the upper tank to the 7-unit tank, (4) circle the arrow from the 7-unit tank to the 2-unit tank, and (5) circle the arrow from the 7-unit tank to the truck. The overall pattern is a combination of addition and subtraction: 7 + (7 - 2) = 12. The less sophisticated approach is based on repeated addition: 2 + 2 + 2 + 2 + 2 + 2 = 12. Scoring can be based on adding up the number of correct solutions within 18 trials, yielding a score ranging from 0 to 3. Scoring can be based on the total number of moves (with a maximum of 18 per problem), yielding scores ranging from a perfect score of 12 to a maximum score of 54. Scoring of the second two problems can be based on the strategy used to solve the problem: the sophisticated strategy which involves subtraction (i.e., circling the arrow from the 5-unit tank to the 1-unit tank in problem 2, or circling the arrow from the 7-unit tank to the 2-unit tank in problem 3) whereas the less sophisticated strategy involves only addition (i.e., not circling the arrow between tanks). A strategy score ranging from 0 to 2 is computed giving students one point for using the sophisticated strategy on problem 2 and one point for using it on problem 3. Top Return to Puzzle Tanks Test Home Page Back to Home Page