You asked

How well should my two year old understand numbers?

Most preschoolers start to develop a rudimentary understanding of numbers as they near the age of three. This starts when they develop an understanding that there are single items (one) and many (more than one.)
The average two year old can count to two, and by three, most can count to three. Some children may memorise numbers up to as high as ten at this age, but it’s more a case of remembering the words than understanding the concept.

If you want to encourage numeracy, then the best way to do so is not to try and teach your child numbers by memory. It’s by using numbers to refer to everyday objects and sights.

Talk to your child about the three birds on a tree when you’re out on a walk, or help your child to count his candy. This helps to develop numeracy using a form of learning known as pre reading, where your child who cannot yet read learns to identify the name of something by seeing visual cues.

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