b
Number and Operation Concepts: The student
uses and understands the inverse relationships between addition
and subtraction, multiplication and division…; uses the inverse
operation to determine unknown quantities in equations.
The student
used transitivity and inverse operations to determine that g=3.
A possible solution was inadvertently lost when the student decided
to “divide each side by g,” because division by zero is
undefined. She should have been aware, though, that g=0 also satisfies
=3g.
As in the second step, this possibility would have been dismissed
because “e is already 0.”
d
Number and Operation Concepts: The student
is familiar with characteristics of numbers…and with properties
of operations….
The student
recognized the additive identity, 0.
The student
recognized the multiplicative identity, 1. She realized the effect
of multiplication by zero. The latter was dismissed as a possibility
because zero was used elsewhere.

d
Function and Algebra Concepts: The student
finds solutions for unknown quantities in simple equations.
b
Problem Solving and Mathematical Reasoning:
Implementation. The student…
• invokes problem solving strategies…
The student paused to review what she had done and what remained.
Understanding and solving the remaining clues was easier after eliminating
the digits already used once.
• solves for unknown or undecided quantities….
c
Problem Solving and Mathematical Reasoning:
Conclusion. The student…verifies… results with respect
to the original problem situation….
d
Problem Solving and Mathematical Reasoning:
Mathematical reasoning. The student…makes justified, logical
statements.
The “process
of elimination” applies.
