Suppose you have the following counting board with two different kind of pebbles places as illustrated. Let the solid black pebble represent a dog and the striped pebble represent a cat.
How many dogs are being represented?
How many cats are represented on this board?
There are two black pebbles in the outer square regions – these represent [latex]2[/latex] dogs. There are three black pebbles in the larger (white) rectangular compartments – these represent [latex]6[/latex] dogs. There is one black pebble in the middle region – this represents [latex]3[/latex] dogs. There are three black pebbles on the second level – these represent [latex]18[/latex] dogs. Finally, there is one black pebble on the highest corner level – this represents [latex]12[/latex] dogs. We then have a total of [latex]2+6+3+18+12 = 41[/latex] dogs.
There is one striped pebble in the outer square regions – these represent [latex]1[/latex] cat. There are [latex]6[/latex] striped pebbles in the middle region – this represents [latex]18[/latex] dogs. There are three striped pebbles on the second level – these represent [latex]18[/latex] cats. Finally, there are two striped pebbles on the highest corner level – this represents [latex]24[/latex] cats.We then have a total of [latex]1+18+18+24 = 61[/latex] cats.