At about what age can children development specific mathematics concepts? This chart outlines what children are capable of understanding at 3, 4, and 5 years of age.

Verbal Counting. Learning the standard sequences of number words.Count 1 to 10Count one to 30, with emphasis on counting patterns; for instance, knowing that "twenty- one, twenty- two..." is parallel to "one, two ..."Count one to 100, with emphasis on patterns (e.g., "60, 70, "parallel "six, seven"; and "14" to "19" parallel "four" to "nine")
Object Counting. Creating a one-to-one correspondence between a number word and an item.Count one to four items, maintaining one-to-one correspondenceCount one to 10 items, knowing that the last counting word tells "how many"Count one to 20 items
"Seeing" Numbers. Instantly "seeing how many" supports counting, comparing, and adding.See groups of one to threeSee groups of one to fiveSee groups of one to six; regular patterns up to 10
Comparing Numbers. Comparing and ordering build on nonverbal knowledge and experience with real collections.Identify whether collections are the "same" number or which is "more" visuallyUse counting or matching to compare two collections one to five, despite distracting appearancesUse counting to compare two collections one to 10, using words "equal," "more," "less," and "fewer"
Adding and Subtracting.
Solving problems using informal strategies is critical in learning arithmetic.
Use nonverbal adding and subtracting with very small numbers of objectsSolve and make word problems using concrete modeling with sums to fivePose and solve word problems using counting-based strategies such as counting on, sums to 10
Shapes. Geometric shapes can be used to represent and understand objects in the world around us.Match shapes, first with same size and orientation, then with different sizes and orientationRecognize and name some variations of the circle, square, triangle, rectangleRecognize and name circle, square, triangle, rectangle, in any size or orientation (varying shapes for triangles and rectangles)
Putting Together Shapes. Shapes can be decomposed and composed into other shapes and structures.Use shapes in isolation to make a picture
Cover an outline with shapes without leaving gaps by trial-and-errorCover an outline with shapes without leaving gaps with foresight
Makes a picture by combining shapes
Locations, Directions, and Coordinates. Mathematics can precisely specify directions, routes, and locations in the world.Understand and use ideas such as over , under , above , on , beside , next to , between Learn a simple route from a map placed in direct relation to the spacePlace toy objects in correct relative position to make a map of the classroom
Symmetry. Symmetry can be used to analyze, understand, and create shapes in geometry and art.Show awareness of symmetry in block buildingsInformally create 2-D shapes and 3-D buildings that have symmetryIdentify and create shapes that have line or rotational symmetry
Measurement. Measuring can be used to specify and compare "how much."Develop language such as bigger , longer , and taller Discuss and compare attributes informally, including comparing gross differencesCompare length using another object. Measure with multiple copies of a unit (such as block)
Patterns. Patterns weave through all other topics in mathematics.Notice simple repeating
patterns, such as a wall of blocks with
long, short, long, short, long ...
Copy simple repeating patternsNotice and discusses patterns in arithmetic (such as adding one to any number results in the next "counting number")