AMC 10 · 2012 · #1
Grade 6 arithmeticPick an answer.
The bug moves along positions on a number line, so the natural first move is Tool #1: sketch the line and mark -2, -6, and 5. The picture instantly shows the trip has two straight legs in opposite directions. Tool #7 then splits the whole crawl into those two subproblems — leg one from -2 to -6, leg two from -6 to 5 — each an easy distance on its own. Tool #8 keeps the focus on "units of distance," reminding us that a distance is always the positive gap between two points (never a negative), so the two legs simply add up.
Draw the number line
Marking the three stops makes both legs visible.
Seeing the points on the line makes the two separate crawls obvious at a glance.
6.NS.C.6Draw A DiagramLength of leg one
The first leg is 4 units.
From -2 to -6 you step across 4 tick marks, so that leg is 4 units long.
6.NS.C.7Identify SubproblemsLength of leg two
The second leg is 11 units.
Crossing 0 from -6 up to 5 covers 6 units to reach 0 and 5 more after it, which is 11 units.
6.NS.C.7Identify SubproblemsAdd the two legs
Adding gives 15, choice (E).
Total distance is just the first leg plus the second leg, so the bug crawls 15 units in all.
The total distance crawled is just the first leg plus the second leg.
▸ Why?
The trip is exactly its two legs laid end to end, so their lengths add.
▸ Why?
Each leg's length is the gap between its two endpoints, no matter where on the line they sit.
Distance is always the positive gap between two points, so when something turns around you add each leg separately: 4 + 11 = 15 units.
- Draw the number line
- Length of leg one
- Length of leg two
- Add the two legs