Analysis, Lesson 1

Change Has a Shape

Run a journey and watch every moment draw its own graph.

How does a graph remember motion?

Predict a journey, then scrub one clock through the road, table, and graph.

Linked motion laboratory

Predict before the graph appears

Which pattern will make the graph become steeper?

Choose the pattern you think will bend upward.

0 m10 m

One clock: t = 0.0 s

Five equal time windowsEach window is exactly 2 seconds long.

The same 2 seconds adds the same 2 metres every time.

Same clock, numerical view
t	distance	gain

time0.0 s

distance from start0.0 m

average speed since startNot yet

Move the clock and watch all four representations change together.

Practice

Read motion from equal time windows

Answer all five before the graphs and motion stories are explained.

Walk. Stop. Then walk again.

Choose the shape that carries the story.

Practice

Complete the five motion stories before viewing the full explanations.

Watch an average line settle toward the instant at t = 5.

Time window Δt = 4.0

average slope1.40approaches 1.00

Smaller windows reveal more local change.

Practice

Submit all five answers together, then study each secant and tangent explanation.

Algebra 2 turns a single unknown into a moving variable and an input-output rule.