Distance and displacement · 4:14
Sketchnote in the works
status captions saved · analysis package pending
Unit 05 · Forces & Motion arc · 7th grade
It's all
relative.
Is the beetle fast? Compared to what — the tile, the classroom, the garden snail? Motion only makes sense against a reference point, and "fast" only makes sense with a graph. Five frames, one dash, and the slope that tells the truth.
position → velocity
6 manipulatives
12 flashcards
1 beetle
the 10-cm dash · one frame per second
t = 0 s0 cm
t = 1 s3 cm
sniff!
t = 2 s4 cm
t = 3 s8 cm
t = 4 s10 cm
same beetle, same dash — uneven frames. was he fast?
The phenomenon · five frames, one question
The 10-Centimeter Dash
One frame per second, start to finish. Look at the spacing: frames 1–2 barely moved (he stopped to sniff — it's what he does), frame 3 covered four times that ground. So: was he fast?
3 cm/s
frame 0 → 1 · cruising
0 cm/s
frame 1 → 2 · sniff break
4 cm/s
frame 2 → 3 · scurrying
2 cm/s
frame 3 → 4 · cruising home
"Was he fast?" is really two questions.
On average: 10 cm in 4 s = 2.5 cm/s — one number for the whole trip. Second by second: 3, 0, 4, 2 — a different story in every frame. The average is honest but quiet; the graph remembers everything. Keep both habits for the rest of the year.
Watch · Khan Academy
The odometer's side of the story
Unit context only. This saved-caption video teaches distance and displacement. It is not exact support for the worksheet's speed, acceleration, unit-rate, or graph-segment Parts, so it is not promoted into those Learn How routes.
Read · Eleo explains
The beetle's commentary track
A motion article remains source-gated until its exact companion video and investigation hand-off are settled.
Sketch · sketchnotes
Map the journey two ways
The exact distance/displacement captions are saved. Printable sheets stay pending until the full analysis package is ready.
Investigate · evidence first
Predict the graph before it moves
The page's race, odometer, speed, and graph tools remain the working lab. A standalone print-first investigation is still in review.
Investigation in the works
Use the existing page models now; a prediction, data, and revision record will land here when authored.
in the worksManipulative 01 · where, compared to what?
The odometer vs. the ruler
Every position needs a reference point — a "compared to here." Walk the beetle around the track and watch two honest instruments disagree: the odometer counts every step (distance), the ruler only cares where you started and where you stand (displacement).
0odometer · distance (cm)
+0ruler · displacement (cm)
012345
678910 cm
walk around. watch the two numbers.
Manipulative 02 · distance ÷ time
The Speed Board
Average speed = total distance ÷ total time. That's the whole formula — the drama comes from the range. Pick a mover, pick a trip, and feel the difference between a snail and a sound wave.
2.8 min
the beetle gets there eventually. bring a book.
Read the units like a scientist
cm/s — beetle speeds, ant speeds, classroom speeds.
m/s — the science standard. 1 m/s ≈ a relaxed walk.
km/h — road speeds. 3.6 km/h = 1 m/s exactly.
Speed is a ratio — distance per time. That's the crosscutting concept Scale, Proportion, and Quantity doing its job.
Manipulative 03 · the truth-teller
The slope remembers everything
Time on x, distance on y — the dash from the film strip, drawn as a line. The slope of that line IS the speed. Drag across the graph and read it like a scientist.
drag across the graph — read the race
steep faster speed — more ground per second
flat stopped — time passes, distance doesn't
downhill coming back toward the start
slope = rise ÷ run
Pick the scurry segment: the line rises 4 cm while time runs 1 s. 4 ÷ 1 = 4 cm/s. Do it anywhere on the graph — the slope and the speed are the same number wearing two outfits.
Manipulative 04 · match the story to the shape
Pick a race story, then file it under the graph that tells it.
steady climb
one slope, no drama
fast, then flat
steep, then stopped
flat, then fast
stopped, then steep
there and back
out, then home again
0 / 4 matched
Disciplinary Core Idea: PS2.A Forces and Motion — the motion of an object is described by its position, direction, and speed (NGSS Lead States, 2013). This unit carries the motion half; Forces (stop #06) brings the pushes, and together they feed MS-PS2-2. Crosscutting Concept: Scale, Proportion, and Quantity — speed is a ratio, and the graph makes it visible.
One more word · direction required
Velocity = speed + a compass
"6 cm/s" is a speed. "6 cm/s east" is a velocity. Direction is the upgrade — and it's why the round trip gets weird.
+5 cm/s
Outbound, heading east along the ruler. Positive direction, positive velocity.
−3 cm/s
Coming home, heading west. Same ruler, opposite sign. The minus is a direction, not a debt.
0 cm/s avg
Out and back to the exact start: zero displacement, zero average velocity — despite never standing still.
Myth-busters · tap to flip
Unlearn these three things
Manipulative 05 · Spaced repetition
Say it like a scientist
Twelve words. Flip the card, grade yourself honestly, and the deck schedules your next review — hard words come back sooner. Come back tomorrow and it remembers you. (It lives in your browser, no account.)
–due now
–locked in
–seen so far
flip the card, then grade yourself
Practice · Math skills
Can a graph tell you who won?
The beetle's frames become a table, the table becomes speeds, and the speeds settle the argument. Unit rates, distance–time graphs, and the fastest human in intervals. Print it, solve it, check the key.
Exit ticket · 5 questions
Before you leave the track
No grade, no stakes — just proof the slope stuck. Answer all five to earn the stamp.
question 1 of 5