Four Less One Is Three

"Counting is good," said Ronnie, "but let's not forget what we came here for. I am starving. Where's my apple?" And, with these words, he tossed the apple into his mouth.

"Wait!" squeaked MeeMee, "Wait!" But it was too late. "Mmm," Ronnie closed his eyes enjoying the juicy fruit.

"Hey, you, glutton. Couldn't you wait a second? I really wanted to count our snacks one more time," MeeMee said with tears in his voice. "What am I going to do now?"

Ronnie swallowed the remains of his apple. "Why? You can count what is left here. Surely, you can. Look here ..."

"No, no, wait," cried MeeMee. "Let me do that."

MeeMee began to count as before: "The sandwich is one, the apple is not here, banana is three, and orange is four... That's four snacks!"

"How can that be?" protested Gerri. "There are only three snacks. Ronnie has already gobbled his apple. Four less one is three. Only three snacks remain. Sandwich, banana and orange."

MeeMee was startled. "Oops. Did I do anything wrong?" And he began at great speed, "The sandwich is one, the apple is not here, banana is three, and orange is four... That's four snacks! Isn't that so?"

Gerri sighed, "Of course not! I am telling you: there are only three snacks."

"But, when we counted them before, banana was number three and orange number four. All I did was repeating my last count."

"Ah," said Gerri, "I see. You are simply confused. Count them in a different order. Don't you remember what we learned before: it does not matter how you count."

"Remember we once counted differently?" She scratched her head. "Banana is one, orange is two, apple is three, and sandwich is four."

"We could also make apple the last. See: banana is one, orange - two, sandwich - three, and apple - four."

"And what happens after Ronnie ate his apple? Banana is one, orange two, sandwich three, and there nothing left to count. There are only three snacks, you see?"

"I certainly do," said MeeMee peevishly. "But what is wrong with my first count? The sandwich is one, the apple is not here, the banana is three, and the orange is four... That's four snacks!"

Ronnie listened to this argument attentively for a while, and finally he broke his silence. "I'll tell you what is wrong with your first count, MeeMee. In fact, there are wrong things there," he with a sly smile on his face.

"First, you can start counting anywhere. One is where you point first. It could be anything: apple, banana, orange, or sandwich. One is not like a label or a name, it is simply the first thing to count."

Counting is not like giving names or attaching labels because it does not matter how you count.

"Four," he continued, "is the last thing to count, if there are four things of course. And when there are four, any one of them can be the last."

"Ah," said MeeMee, "I see. Now I know what else went wrong. I counted the apple as if it was there. It was number two before. However, after Ronnie chewed it up, I had to point the count two to another snack. This way I would have only counted only the snacks that were there."

"Oh, boy! This business of counting can surely make one hungry. Would you mind giving me my sandwich? Truth be told, the apple was yammy. We now know that numbers are not quite as names or labels, but a lunch is still a lunch. Let's move on."

Remember: Numbers are not the same as names or labels.

Everyone thought Ronnie was being very wise. Gerri picked her orange, MeeMee began to peel his banana, and Ronnie - Ronnie almost choked on his sandwich so hungry he was.

After the lunch the friends snoozed. MeeMee dreamed of dancing snacks. They danced in pairs and all four together in a circle. From time to time, they would line up one after another. Sometimes the apple was first and sometimes the orange but the order kept changing. He was awaken by a fly on his nose just when the sandwich managed to get first in line.

Related material

  • The Idea of Counting
  • Let Them Count
  • A Market Day
  • Finger Counting
  • Counting: The Beginning of Mathematics
  • The Basic Rules of Counting

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