|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 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 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 repeating|
patterns, such as a wall of blocks with
long, 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")|
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.