Problem
Length of the loop in the 30 cm direction
One loop crosses the top, down a side, under the bottom, up the other side: two 30 cm edges and two 40 cm heights make 140 cm.
Wrapping a loop around the box traces a rectangle, so it uses each edge of that rectangle twice.
3.MD.D.8Identify SubproblemsThe ribbon loop that wraps the box in the 30 cm direction measures 140 cm, because it covers the 30 cm edge twice and the 40 cm height twice (30 + 40 + 30 + 40).
Why?
Wrapped once around, the ribbon traces an upright rectangle whose top and bottom are the 30 cm edge and whose two sides are the 40 cm height.
Why?
A rectangle's opposite sides are always the same length, so the loop has two 30 cm sides and two 40 cm sides.
Why?
The whole loop's length is just its four straight pieces added together.
Why?
The four pieces meet end to end with no gaps or overlaps, so their lengths add back to make the whole loop.
Length of the loop in the 35 cm direction
The other loop uses two 35 cm edges and two 40 cm heights: 150 cm.
Same loop idea, now around the 35 cm cross-section of the box.
3.MD.D.8Identify SubproblemsAdd both loops and the bow
Add the two loops and the 45 cm bow to get 335 cm in all.
Total ribbon is all wrapping plus the extra for the bow; 335 cm regroups into 3 m and 35 cm.
2.MD.B.5Draw A DiagramEach ribbon wrap is just a rectangle's perimeter — add both loops and the bow, plain Grade 3 length work!
- Length of the loop in the 30 cm direction
- Length of the loop in the 35 cm direction
- Add both loops and the bow