Your child’s developmental process is unique. To guide you, education experts have mapped a few basic Pre-K & kindergarten math skills to help you track your child’s development in different mathematical areas. See the Child Development Tracker for more information.

**Choose a topic:** Numbers | Geometry | Measurement | Patterns, Reasoning & Algebra | Statistics & Probability

### Numbers

During their third year, many children can tell their age and hold up that many fingers to demonstrate.

During the fourth year, many can accurately count up to five items, some can count up to 10, and a few can count to 20.

Many four-year-olds can tell what number comes after a given number in a sequence up to 10. For example, if asked “What comes after 1-2-3-4-5-6?” many four-year-olds can answer “7,” and so forth.

Given two numbers between one and 10, many five-year-olds can tell which of the two is larger.

### Geometry: Shapes & Space

During the third, fourth and fifth years, children physically explore and gain understanding of the directional words “up,” “down,” “front,” “back,” “over,” “under,” “above,” “on,” “beside,” “next to,” “in front,” “behind,” “inside,” “outside,” “between,” “left,” “right,” etc. By the fifth year, they can accurately use the words in a sentence.

During the fourth year, many children can recognize and name shapes with different sizes and orientations (for example, circles, squares, rectangles, and triangles).

Many four-year-olds will naturally make shapes that show symmetry without necessarily understanding the concept. For example, they might make a structure with blocks where one side of the structure is identical to the other because it appeals to them.

When asked, some four- and five-year-olds can copy a shape from memory after looking at it for several seconds.

Some four- and many five-year-olds can use a simple, two-dimensional picture map to find an object hidden in an actual, three-dimensional room.

### Measurement

During the third and fourth years, many children figure out how to compare two different objects. They might take two pencils and put them side by side and then tell you which is longer.

During their fourth year, many children will be able to compare objects using words such as “bigger” and “smaller,” “longer” and “shorter,” “heavier” and “lighter,” and “faster” and “slower.”

During the second half of the fourth year, most children will understand that, when given a group of items (like a handful of cookies), if they give one away, they will have less. Or, if you give them another item, they will have more.

During the second half of their fourth year, many children will understand different time concepts, such as morning, afternoon, night, earlier, later, and soon. Some children can name the days of the week, and some can name the months and the seasons.

By the end of their fourth year, some children may figure out how to measure an object (like a book) by using a number of identical smaller objects, such as paper clips lined up end to end. For example, they might measure and describe their favorite picture book as 35 paper clips long.

By the fifth year, most children will be able to look at different-sized containers of the same shape and tell which holds more or less.

### Patterns, Reasoning & Algebra

During the third year, some children figure out how to follow a simple sequence of familiar events. For example, they can describe the steps they follow in taking a bath. “First we plug the drain, then we run the water, and finally we take the bath.”

During the fourth year, many children can follow, and make their own, simple patterns that repeat. For example, if shown a color pattern like red-blue, red-blue, children will know that another red-blue comes next. Children may also be able to follow and make their own sound patterns, such as clap-stomp-clap-stomp.

By the fourth year, most children can place a small group of objects in order from biggest to smallest and talk about what they are doing using the words “big,” “bigger,” and “biggest.”

Four- and five-year-olds can sort a group of items by one or more characteristics. For example, given a bag of socks (or even a basket of laundry), children can sort them by color, and perhaps by size as well. Or they can sort forks, knives, and spoons and be able to explain how they sorted the objects.

### Statistics & Probability

Between the ages of three and five, children can begin to organize items into different categories and compare the results to answer a question, such as which group has more. For example, children might put all the brown socks in one pile, all the white socks in another, and all the black socks in a third pile. By age five, many can look at the size of the piles they made to answer the question: Which color sock is most common in our family?

During the fourth year, many children figure out that some things can only be answered or understood after they test it themselves. For example, if a child is told that the cloth ball just picked up won’t really bounce, the child is most likely to try bouncing it several times to see if this is true.

Throughout the fourth year, children are figuring out the meanings of words such as “certain,” “sure,” “uncertain,” “unsure,” “likely,” “probable,” “unlikely,” “improbable,” “maybe,” “possible,” and “impossible.”

Many children this age begin to understand the likelihood or chance of an event happening. For instance, they will know that it is unlikely that it will snow in summer, or that it is unlikely that they will catch a ball every time it is thrown to them.

When guided by an adult, many five-year-olds can understand simple graphs and use the information to answer questions. So by looking at a bar graph showing what pets their friends own, they can tell which animal is the most popular pet. They can also figure out information from pictures, such as looking at animal families of different sizes and declaring which family has more babies.