Scalars and Vectors in One Dimension
Direction is the first thing physics asks you to track. A scalar is a one-number quantity like speed, distance, or mass. A vector adds direction, like velocity, displacement, or force. In one dimension, "direction" just means a sign. You pick which way is positive, and after that the signs have to stay consistent everywhere in the problem.
The misconceptions here aren't really about math. They're about whether you treat negative numbers as smaller (they aren't, they just point the opposite way) and whether you can keep one sign convention through a whole problem instead of swapping it halfway through.
The work
3 ways in · any order
Lesson
Scalars and Vectors
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Scalars carry size; vectors carry size and direction. The lesson sorts the eight ways students smear that line, then closes with a ten-scenario applet that asks you to label, sign, and add 1D vectors before the algebra runs.
Diagnostic
10-item topic check
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Ten items spanning the eight foundation U1 misconceptions: scalar/vector category, distance vs displacement, speed vs velocity, position vs displacement, the two natures of negative signs, sign-convention discipline, and arrow representation. Take it cold to surface the ones still tangled, or after the lesson to confirm they aren't.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.