L2 · Same length, different units
“I can explain why the same length gives different counts in different units: the bigger the unit, the fewer copies I need.”
We measure the same desk two ways. Step 1 - LONG PENCILS: the desk is 4 long pencils long. Step 2 - SHORT CRAYONS: the same desk is 8 short crayons long. Step 3 - COMPARE: the desk did not change. The unit changed. Each long pencil covers more length, so fewer pencils are needed. Each crayon covers less, so more are needed. Say it plainly: for the same length, a bigger unit gives a smaller count, and a smaller unit gives a bigger count.
The desk is 4 pencils long and 8 crayons long. Why are the counts different?
A shelf is 5 big books long. The same shelf is 10 little books long. Which book is the bigger unit? -> the big books (fewer copies needed)
"A rope is 3 arm lengths long and 12 clips long. The ___ unit is bigger, because it needs fewer copies." -> arm length
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.