Hop the Hopping-Rabbit

Hop is a cream-and-grey rabbit-kid with strong back legs and soft long ears. She lives in the math-garden’s hopping-meadow — a long open meadow with a soft grass-path that has little dotted-line jump-arcs drawn on it. Calc Jr brings the kid here to visit Hop.

Hop’s hops are all exactly the same size. Every. Single. One. Hop. Hop. Hop. Hop. As she hops, the soft dotted arcs glow underneath her — each arc the same length as the others. When she’s done hopping, she looks back at the line of glowing arcs and says: “Same hop. Every time.”

That is Hop’s whole gentle teaching.

Same hop. Every time.

If Hop has hopped 3 times, she has gone 3 same-sized hops worth of distance. If she hops 4 times, she has gone 4 same-sized hops worth. Counting hops is counting equal jumps. This is the seed of early addition: equal-sized groups stacked up tell you how many of THAT-SIZED-THING you have.

When kids first hop, they sometimes hop big-then-small-then-big. That’s fine for play. But for counting-hops, Hop wants each one the same size as the others. She practices. She gets it right. She hops very slowly and very carefully — checking that each hop is the same as the last one.

The skill is the same-ness.

Calc Jr says to the kid: “Watch Hop hop. Then YOU hop. Count each hop. Same hop, every time. Count how many hops you took. That’s the answer.”

A grown-up can hop along too! The grown-up can clap; the kid can hop; they can count the hops together. Hopping is for play + thinking together, not racing.

Hop never says too short or too big. She just says “Let’s hop again. Same hop. Every time.” If a hop comes out the wrong size, you just hop again. There is no scolding in the hopping-meadow.

Sometimes Hop hops on the grass-path. Sometimes she hops over small stones. Sometimes she hops between Tappa’s pebble-groves. Each time, the hops are the same size as the others. Counting THEM is counting same-sized jumps.

When Hop hops 2 times, then 2 more times, she has hopped 2 + 2 = 4 same-sized hops. That’s the seed of adding. She doesn’t have to know the symbol *+ * yet. She just knows: some hops, plus some more hops, is more hops.

Calc Jr is always with the kid when they visit Hop. Hop is Calc Jr’s friend. Calc Jr brings the kid to visit. Together, all three hop carefully: same hop, every time.

“Same hop. Every time.” That’s Hop.

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