A method is easy to describe and hard to prove. What sits underneath 6i Lens is a catalogue of 13,243 items spanning Grade 3 through Algebra II, tagged to 550 standards, with a named error for each way students actually come apart on them. Of those, 2,516 are real released New York State questions and 2,116 are constructed response, which is where the gap on this page shows up. It took thirteen years to build and it is the reason a diagnosis here names a misconception instead of a score band.
An error pattern is not a wrong answer. It is a documented way of thinking, with the reason behind it and the cost of leaving it alone. Two real entries, exactly as they sit in the bank:
Student writes addition for a "groups of" situation.
Why Sees two numbers, defaults to addition. Has not internalized "each" and "per" and "groups of" as multiplicative markers.
What it costs later Forerunner of TT-E1 in Grade 6. The same trap, a multiplicative-language failure, recurring through Grade 7 percent and Grade 8 functions.
Student writes an additive equation for a multiplicative relationship. $5.95 per sandwich becomes 5.95 + x = 71.40.
Why Hears "per" or "each" and grabs addition. Does not encode either as a multiplicative marker.
What it costs later Sets up the wrong equation on every rate word problem. The most common 6.EE.7 trap, and it appears every test year.
Read those two together. They are the same error three years apart, and the bank says so in writing: the Grade 3 entry names the Grade 6 one as what it becomes. That is what the storybook shows one page at a time, and it is why the gap on 6.EE.7 is a structural finding rather than a bad week. Follow it across eleven pages →