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## Mathematics

### Bath Math

Fill and empty containers of varying sizes to introduce the concept of volume.

As one-year olds play, they start to recognize patterns and understand shapes. They begin to sort familiar objects by one characteristic, such as whether they are "hard" or "soft." They may enjoy filling and emptying containers. They notice that night is followed by day, and that socks go on feet before shoes. They know that when an object is hidden, it is still there. Many can also do simple insert puzzles when the puzzle pieces show whole objects.

### Numbers

• Between 18-24 months, some children will begin to use a few number words without understanding quantity (e.g., imitates a simple counting rhyme). Some children may also begin to understand the words "one" and "two" (e.g., distinguishes "one" or "two" from many; identifies pairs of items as "two;" identifies three or more items as "many" rather than as "one" or "two;" asks for "one" or "two" of something; knows age; responds appropriately to the request, "Take just one," or "Give me two.").

### Operations on Numbers

• Between 18-24 months, a few children will begin to nonverbally and mentally determine that one item added to another makes "two," and that one item taken away or subtracted from "two" makes "one."

### Geometry and Spatial Sense

• Between 12 and 18 months, the average child understands that when an object is completely hidden, it is still there ("object permanence"), and can be recovered. (Some children may understand this between 18-24 months.)

• During the first half of this year, some children will even be able to recover an object that has been hidden in one place, and then visibly moved to a second position and re-hidden. (The average child will establish such "object permanence" during the second half of this year.) During the first half of this year, the average child will also be able to recover an object that has been covered with one item, and then covered with something else while remaining in the same position

• Between 18 and 24 months, some children will informally identify and play with solid objects (e.g., picks out a familiar object by touch when that object is placed in a bag with two other objects).

• Between 12-24 months, children are typically able to work simple "insert" puzzles (e.g., completes a three-piece simple puzzle where pieces are whole objects). Also, children can remove a part from a toy (e.g., a wheel) and replace it. Finally, children can build three-dimensional structures using one type of item (e.g., a cube).

### Measurement

• Between 12-18 months, children adjust their reach based on the distance and size of an object (e.g., accurately reaches and closes hand around an item instead of missing the object or closing hand before contact). Children also adjust their grasp of an object based on its weight (i.e., no longer grasps all items tightly or allows arm to drop when given heavy items).

• Some children at 12-18 months believe that a cracker broken into many pieces is more food than the same type of cracker that is whole. (The average child believes this between 18-24 months.)

• Some children during the second half of this year will explore objects by filling and emptying containers (e.g., with sand or water).

• During the second half of this year, a few children begin to develop a sense of time through participation in routine daily activities (e.g., knows about when it is time to eat, nap time, etc.). Children's sense of time develops gradually over the next several years.

### Patterns, Reasoning, and Algebra

• Between 12-18 months, some children recognize that there is an order to the day (e.g., Mommy comes to get me after storytime). The average child sees daily patterns by the second half of this year. In the second half of the year, some children show a greater understanding of daily time sequence (e.g., time to eat, nap time, etc.).

• During the second half of the year, some children notice patterns in the environment (e.g., day follows night, patterns in carpeting or clothing, etc.). They also use the terms, "tomorrow," and "yesterday."

• In the second half of this year, some children show interest in patterns or sequence (e.g., attempts to follow patterns with stringing beads, magnetic shapes, peg boards).

• Between 18-24 months, some children can classify, label and sort familiar objects by a known group (e.g., hard v. soft, large v. small, heavy v. light).

• During the second half of this year, some children can pick up blocks in the order of size.

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