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• #### Credits 165-166

rod sizes used, or the way in which an individual span is constructed. For example, each span might have three upright support rods, and each horizontal piece might consist of two rods of the same color, one on top of the other. This is a setting in which children can invent their own styles of bridges and their own questions about them.

More generally, bridge-building with centimeter rods can be used to explore other mathematical topics — for example, in the area of primes and factors: "Can you build a bridge that is exactly 101 cm long, using spans of the same length?" or "Can you build two parallel bridges of the same length, one using 6-cm rods and the other using 8-cm rods; if so, how long might the bridges be?"

#### Protorubric

Characteristics of the high response:

The high response shows that the child can make a transition between the physical materials and the more abstract arithmetical ideas.

All questions are answered correctly. The rules described in question 5 of Parts 1 and 2 clearly describe a general case, that is, how one would find the total number of rods for any number of spans. This can be done through words or through symbols, or a combination of both. Some children may not explicitly mention the spans; for example, they might simply write "multiply by 3" for question 5 of Part 1.

The justifications in question 6 in both parts are detailed. For example, in Part 1, the explanation indicates that 185 was divided by 5, and that there are twice as many red rods as yellow rods. If a calculator is used in question 6 of Part 2, the decimal result is interpreted correctly.

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