What does a student learn in
California, Pre-Kindergarten, Mathematics ?

Recite numbers in order from one to ten or higher with no more than a few errors.

Recite numbers in order from one to thirty with no more than a few errors. Count forward from a number other than one.

Count five objects or more using one-to-one correspondence (one object for each number word).

Count ten objects or more using one-to-one correspondence (one object for each number word).

Answer the question "How many?" by counting. May repeat the last number word in the number list after counting but is still developing an understanding that the number name of the last object counted represents the total number of objects in the group.

Consistently demonstrate understanding when counting that the number name of the last object counted represents the total number of objects in the group.

Identify without counting the number of objects in a small collection (for example, one to four objects).

Identify without counting the number of objects in a collection of one to five objects.

Recognize and name a few written numerals under 10.

Recognize and name all written numerals through 10.

Compare (with or without counting) two groups of objects that are clearly equal or different in size and communicate, "same" or "more."

Compare two groups of objects by counting and communicating, "more," "same," "less," or "fewer."

Demonstrate understanding that adding or taking away one or more objects from a group will increase or decrease the number of objects in the group.

Demonstrate understanding that adding one or taking away one object changes the number in a small group of objects by exactly one.

Demonstrate understanding that a set of objects is made up of smaller parts and that the whole set is bigger than its parts.

Decompose a set of objects into two small sets in more than one way (for example, decompose 5 into sets of 3 and 2, or 1 and 4). Combine two small sets to create a larger set (for example, 3 and 2 to make a set of 5).

Solve addition and subtraction problems with a very small number of objects in the context of everyday situations.

Solve addition and subtraction problems with a larger number of objects (sums up to 10) in the context of everyday situations.

Share a small number of objects (for example, four or six objects) equally between two recipients.

Share a slightly larger number of objects equally between two or more recipients (for example, nine objects among three recipients).

Notice similarities and differences in the attributes of objects. Sort and classify objects by one attribute into two or more groups.

Sort and classify objects by one or more attributes into two or more groups with accuracy and flexibility. When sorting by two attributes, a child may first sort by one attribute and then by the second attribute.

Notice and explore patterns in their environment and, with adult support, duplicate simple repeating patterns (for example, ABAB).

Explore, extend, and duplicate a variety of repeating patterns (for example, AABBAABB, ABCABC) with adult support. Describe the repeating part of a pattern (pattern unit).

Create, with adult support, a simple repeating pattern (for example, ABAB).

Create a variety of repeating patterns (for example, AABBAABB, ABCABC) or recreate existing patterns using different objects.

Demonstrate awareness that objects can be compared by length, weight, or capacity by noticing differences in objects and communicating about their comparison.

Compare two objects by length, weight, or capacity (for example, putting objects side by side) and communicate about their comparison.

Order a few objects (for example, three) by length or other attributes (for example, height, capacity).

Order a slightly larger number of objects (for example, four or five) by length or other attributes (for example, height, capacity).

Measure length using concrete objects laid end to end, sometimes needing adult support.

Use objects, tally marks, or pictographs to represent data in two groups, with adult support.

Use objects, tally marks, or pictographs to represent data in two or more groups. Demonstrate understanding that each object, tally mark, or picture represents one data point.

Notice, with adult support, differences in the data of two groups and describe which one has more or less.

Describe and compare, with adult support, the number of data points in two or more groups. Determine which group has more or less.

Identify familiar two-dimensional shapes such as circle, square, triangle, and rectangle.

Identify, describe, and construct different shapes including variations of circle, square, triangle, rectangle, and other shapes. Use informal language to describe defining properties of a shape (for example, sides, corners, round).

Occasionally identify a few familiar three-dimensional shapes using informal names (for example, saying "ball" when referring to a sphere).

Identify a few familiar three-dimensional shapes such as sphere, cube, and cylinder.

Compare two-dimensional shapes of different sizes and orientations to determine whether they are the same shape.

Compare two-dimensional shapes of different sizes and orientations to determine whether they are the same shape. Identify similarities and differences in the properties (number of sides or vertices) of two different shapes.

Use two- or three-dimensional shapes to represent different elements of a picture or design (for example, adding a circle in a corner to represent the sun).

Combine different two- or three-dimensional shapes to create a picture or design (for example, make a house with two blocks shaped like rectangular prisms and one shaped like a triangular prism).

Identify some positions of objects and people in space such as in/on, under/over, up/down, and inside/outside.

Identify positions of objects and people in space including in/on, under/over, up/down, inside/outside, near/far, next to, beside/between, and in front of/behind.

Rely on trial and error to determine how objects move in space and fit in different locations (for example, try to fit an object into a hole by rotating, flipping, or sliding the piece in different orientations until it fits).

Rotate, flip, or slide objects to solve a problem without relying as much on physical trial and error (for example, rotate an object before fitting it into a hole).