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.

 NUMBER CONCEPT AT 3 YEARS CHILDREN MAY: AT 4 YEARS CHILDREN MAY: AT 5 YEARS CHILDREN MAY: Verbal Counting. Learning the standard sequences of number words. Count 1 to 10 Count 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 correspondence Count 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 three See groups of one to five See 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" visually Use counting or matching to compare two collections one to five, despite distracting appearances Use 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 objects Solve and make word problems using concrete modeling with sums to five Pose and solve word problems using counting-based strategies such as counting on, sums to 10 GEOMETRY AND MEASUREMENT 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 orientation Recognize and name some variations of the circle, square, triangle, rectangle Recognize 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-error Cover an outline with shapes without leaving gaps with foresightMakes 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 space Place 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 buildings Informally create 2-D shapes and 3-D buildings that have symmetry Identify 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 differences Compare 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 repeatingpatterns, such as a wall of blocks withlong, short, long, short, long ... Copy simple repeating patterns Notice and discusses patterns in arithmetic (such as adding one to any number results in the next "counting number")