Quantity Without Counting

What do you see?

We frequently use numbers or quantity to describe the world around us. When we do, we’re using the math part of our brain.

How does it work? Do we count? Do we guess? Or do we just know? 

Recognizing Exact Quantities

See if you can determine the number of dots as they appear below. Press “Show” when ready. You’ll only have a second to identify the number in each set.

What was the largest set of dots you identified?

Usually, the most dots people recognize is between 5 and 7. Brain researchers have discovered that even infants can identify 1 to 3 objects, well before they know number names. 

Math educators call this ability to recognize small quantities at a glance, subitizing. Humans of all ages recognize sets of 1, 2, or 3 objects without counting or even thinking about it. Some people can easily recognize sets of 4 to 7 objects.

Can you recognize the number of dots on dice without counting? 

Comparing Quantities

Researchers have also discovered that we're born with a basic ability to compare quantities. Try out your comparison skills. Press the “Show” button below and compare the number of red versus black dots. Which color has more dots? Look quickly. You’ll only have a second to decide.

Were you able to tell which color group had more dots? Were you still counting when time ran out? When was it easy to recognize the larger set of dots and when was it challenging?

It’s easy to compare groups of objects when they're small in number, like groups of 2 & 3 or 3 & 5.

But quickly comparing larger groups can be challenging—when they're close in size, like 8 & 9 or even 24 & 27.

Yet when larger groups differ greatly in size, like 18 & 10 or 24 & 40, it's easier to compare them without counting.

Thinking about this from an evolutionary viewpoint, our natural ability to compare the size of groups can be quite helpful.

Would you rather ride in the subway car on the left or the right?

This natural number sense of knowing small amounts (like with dice) and comparing numbers of objects (like a few trees versus a forest)—without counting—are the foundations of our math abilities. From this starting point, we begin our individual journey as mathematicians. In the next chapter we take our first step, learning to count.