Reasoning · Grade 4-1 Overlapping, Folding, and Cutting Paper
Problem
At each crossing note that the unbroken one is above.
At a single crossing the comparison is easy -- one pencil is drawn whole and the other is interrupted -- so eight tangled pencils become twenty-one simple two-at-a-time comparisons.
K.MD.A.2Visualize Spatial RelationshipsThe 'above' relation carries along a chain.
This is the same indirect comparison you use to order sticks by length: if the red stick beats the blue one and the blue one beats the green one, you already know the red beats the green without measuring them together.
1.MD.A.1Visualize Spatial RelationshipsBeing above carries along a chain, so verdicts read off separate crossings link into one stacking order.
If red lies above blue and blue above green, red must lie above green, so no crossing between them has to be looked at.
At each crossing exactly one pencil is drawn whole and the other is interrupted, so every crossing gives one clear verdict.
Nothing covers bright yellow, so it is 1st.
Instead of comparing all eight at once, ask one narrow question -- who is never covered -- and only one colour can answer it.
1.MD.A.1Eliminate PossibilitiesPeel the pile one pencil at a time to fix each place.
Taking the pile apart from the top is exactly how you would undo it in real life, and each removal makes the next choice easier because fewer pencils are left to cover anything.
1.MD.A.1Eliminate PossibilitiesEvery neighbouring pair matches the picture, so the order is unique.
A chain in which each link is directly observed leaves no room for choice, which is what turns a plausible order into the order.
1.MD.A.1Make A Systematic ListCounting down, 6th is lavender.
Counting the same position from both ends is a quick self-check, because with 8 pencils the 6th from the top has to be the 3rd from the bottom.
1.MD.A.1Make A Systematic ListWrite down who is on top at each crossing, then peel the pile from the top -- the pencil nobody covers goes first, and the same question answers itself all the way down.