Physics · Unit 1: Kinematics ·  Activity 1-1-3

Sign Convention Scramble

➕➖ Activity
1 class day  ·  Work in pairs
Activity 1-1-3: Vectors as Signed Numbers

You've been walking number lines since Lesson 1-1-1 and reading rising and falling graphs since 1-1-2. Today the words "away" and "back" retire — from now on, direction is a sign, and you're going to prove to yourself that the sign is a choice you make, not a fact about the world.

🎯 Goals

🧰 Materials

🧻Number line from Activity 1-1-1 (reuse the same taped line if you still have it)
🃏Signed movement cards (e.g. “+4 m”, “−3 m”, “+2 m”)
📏Meter stick or tape measure
📓Physics notebook or the printed data sheet
Section 1 of 4

Pick Your Positive Direction

1
Re-tape or reuse your number line from Activity 1-1-1.
Mark a 0 m reference point somewhere in the middle so you have room to move in both directions.
2
As a group, choose which direction counts as positive.
Draw an arrow on a sticky note or index card and place it at one end of the line pointing in your chosen positive direction. Every card you draw from now on will use this convention.
⚠️ Whatever you pick, everyone in your group has to use the same convention for the whole activity — this is the one rule that can't bend.
Section 2 of 4

Walk the Signed Cards

3
Shuffle the signed movement cards and draw them one at a time.
Each card is a signed displacement, like +4 m or −3 m. A plus card means walk that many meters in your positive direction from wherever you currently are; a minus card means walk that many meters the other way.
4
After each card, record your new position on the ledger.
Your running position after each card is your previous position plus the signed value on the card — not a fresh measurement from zero each time.
5
Draw and walk 5 cards total, then find your total displacement and total distance.
Displacement is your final position minus your starting position — one subtraction. Distance is the sum of all five card magnitudes, ignoring every sign.
Card drawnRunning position (m)

In-class scratch ledger — copy your final values onto your printed data sheet to turn in.

📓 Physics Notebook
Which of your five cards, if any, worked against the net direction of your trip? How would your total displacement change if you swapped the sign on just that one card?
Section 3 of 4

Swap Conventions With Another Group

6
Trade your list of five cards (in order) with a group that chose the opposite positive direction.
Don't tell them your walk's results yet — just hand over the sequence of signed cards.
7
Walk their sequence using YOUR group's positive direction.
Track your own running position and find your own total displacement, exactly as before.
8
Compare final answers.
You should find that your total distance matches theirs exactly, but your total displacement comes out with the opposite sign — same physical trip, described from two different conventions.
⚠️ If your distances don't match, you and the other group aren't actually walking the same physical sequence — check that you copied the card values (not just the signs) correctly.
📓 Physics Notebook
Explain why distance matched between the two groups but displacement's sign flipped. What does this tell you about which of the two quantities depends on your choice of positive direction, and which one doesn't?
Section 4 of 4

Conclusion

Question 1
A classmate says, 'The object has a negative velocity, so it must be slowing down.' Explain what's wrong with that statement and what a negative velocity actually tells you.
Question 2
If you and a partner choose opposite positive directions for the exact same physical trip, which quantities from today's cards change sign, and which stay exactly the same no matter what?
Question 3
Describe a real situation (sports, driving, walking somewhere) where choosing a smart positive direction ahead of time would make the problem easier to reason about.
📤 Turn In
← Back to Activity 1-1-3 OverviewReview the Deep Dive →Next up: Project 1-1-4, Motion Detector Graph Match.