Skipper the Frog

Skipper is a cheerful, bright-green frog with big friendly eyes and springy legs. Skipper does not like to walk one slow step at a time. Skipper likes to hop - and every hop is exactly the same size. And that is Skipper’s whole happy idea: “When the rows are equal, hop and count by the row.”

One sunny day the animals lay out a garden in tidy rows. Each row has three little lots. And there are four rows, one under the other, all exactly the same. A snail starts to count the lots one… by… one… “One, two, three, four, five…” and by lot number seven he is already muddled.

Skipper hops over, grinning. “You don’t have to count them ONE at a time,” Skipper says. “The rows are all equal - three lots in every single row. So hop by three.”

And Skipper hops along, landing lightly on each row. “Three!” - the first row. Hop. “Six!” - the second row is three more. Hop. “Nine!” - three more again. Hop. “Twelve!” - the last row. Four equal rows of three, skip-counted: three, six, nine, twelve. Twelve lots, and Skipper barely broke a sweat.

“See?” says Skipper, catching his breath happily. “Equal rows, hop and count by the row. Three, six, nine, twelve. That’s it. That’s what multiplying really is - the same equal group, counted again and again.”

That is Skipper’s whole springy idea.

Equal rows, hop and count - three, six, nine, twelve.

The snail tries it himself, slow but steady - three, six, nine, twelve - and lands on twelve without getting muddled once. “I skip-counted!” he says, amazed. “And I multiplied!”

A grown-up can play too! Lay out equal rows of tiles or buttons - say three in each row, and make four rows. Then skip-count down the rows together, one row per hop: “three… six… nine… twelve.” Give a little hop or a clap on each number if you like! Feel how the same equal group, counted again and again, gets you to the answer fast. Try different rows - two in a row, or five in a row - and hear the skip-count change.

That is equal rows, skip-counted. An array is just the same equal row over and over; hop along counting by the size of one row, and you have multiplied without counting every single tile.

When the snail skip-counts to twelve all on his own, Skipper feels a bright, bouncy joy - the zingy happy feeling of a friend catching the rhythm. Skipper does one big proud hop. “Equal rows!” he sings. “Hop and count! Three, six, nine, twelve!”