Reasoning · Grade 2-2 Conditions and Numbers
Problem
The odd numbers 1 to 39 are 20, so 20 open first.
Counting the odd numbers up to 40 is just skip-counting by 2s starting at 1 — half of 40 is 20.
2.NBT.A.2Identify SubproblemsNumbers with a 3 are 3, 13, 23 and the thirties: 13.
A digit 3 appears either as the ones digit (3, 13, 23, 33) or as the tens digit (all of 30-39), so listing both groups catches every one.
2.NBT.A.1Make A Systematic ListOf those, 8 odd ones close and 5 even ones open.
Toggling helps only the closed (even) lockers and hurts the open (odd) ones, so sorting Mia's list by odd/even tells the whole story.
2.OA.C.3Make A Systematic ListSorting Mia's lockers into odd and even settles everything, because a toggle opens a closed even locker but shuts an open odd one.
A locker is either odd or even and never both, so Mia's list splits cleanly into two groups whose effects can be counted apart.
One toggle changes a locker's state to the other one, so whether it ends open depends only on how many times it was touched.
So 20 − 8 + 5 = 17 stay open.
Instead of redrawing all 40 lockers, just bookkeep the changes: subtract the ones turned off, add the ones turned on.
2.OA.A.1Change Focus Count The ComplementDon't redraw all 40 doors — just notice Mia's flip closes the 8 open ones with a 3 and opens the 5 closed ones with a 3, so 20 − 8 + 5 = 17!