Real terms. Stable notation. Never dumbed down.

How much did it change? The gap between then and now.

1. Spot what changed between two pictures.
2. Make the change bigger or smaller on purpose.
3. Say the delta out loud: “it grew by three.”

How fast is it changing — change over time.

1. Which marble is getting faster?
2. Change the slope so it speeds up more.
3. Judge a rate: “that one’s faster.”

How steep a line is — the tilt of the hill.

1. Steeper hill, faster roll.
2. Tilt the ramp and predict.
3. Point to the steepest slope.

Getting closer and closer — almost touching.

1. Halfway, then half again — where does it land?
2. Add more steps; watch it settle.
3. Name where it’s heading.

The rate right now, at this exact instant.

1. How fast at this very moment?
2. Find the instant it’s fastest.
3. Say dee-y dee-x — the rate right here.

Adding it all up — the whole area underneath.

1. Fill the shape drip by drip.
2. Bigger shape, more to add up.
3. Name the total you filled — the integral.

A push or pull; mass times how fast it speeds up.

Everything falls at the same pull.

Distance covered over time.

How quickly speed changes.

How hard something is to stop.

The energy of moving.

The grip that slows things down.

Force squeezed into an area.

How much stuff is packed in.

Force moved across a distance.

How fast work gets done.

Wiggles that carry energy along.

The moon falls, and keeps missing the ground.

A long arm turns a small push into a big lift.

Push the water aside and it pushes back.

The same stuff wears three coats.

Heat and cold change the coat.

Stir together, then pull apart.

Where did the sugar go?

Two things make a brand-new thing.

Sour lemons, slippery soap.

Tiny pieces snap together.

Sugar grows into neat little shapes.