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# Child Development Tracker: Mathematics From Age 3 to 4 (page 2)

### Operations on Numbers

• Throughout this year, some children will still be learning how 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." Also during this year, some children will be able to nonverbally and mentally determine sums up to "four" and their subtraction counterparts (e.g., "3 + 1," "4 - 1," "2 + 1," "3 - 2").
• Some children will be able to use informal knowledge gained from everyday experiences to nonverbally estimate sums up to "five" (e.g., for "3 + 2," puts out four to six items to estimate the answer) and their subtraction complements (e.g., for "5 - 2," puts out around three items to estimate the answer). The average child can do this during the second half of this year.
• During the first part of this year, the average child intuitively recognizes that if you change the size of a part of a collection, then you also change the size of the whole collection.
• Throughout this year, some three-year-olds will trade several small items for a larger one (e.g., trades four small candies for a candy bar).

### Geometry and Spatial Sense

• During the first half of this year, some three-year-olds may still be learning how to complete simple "insert" puzzles (e.g., completes a three-piece simple puzzle where pieces are whole objects). Also, some children may be learning how to remove a part from a toy (e.g., a wheel) and replace it.
• Throughout the year, children can complete increasingly complex puzzles (e.g., four-piece interlocking to eight- or ten-piece puzzles, to puzzles with smaller and up to 15 pieces) and progress in their abilities to put together and take apart shapes (e.g., understands that a whole object such as a pizza can be separated into parts). Children also build three-dimensional structures using one type of item (e.g., a cube) and/or multiple types of items (e.g., a rectangular prism, cube and arches).
• During the first half of this year, the average child creates pictures using one shape, but doesn't yet use shapes in combination.
• Throughout this year, a small number of three-year-olds will understand and use words representing physical relations or positions (e.g., "over," "under," "above," "on," "beside," "next to," "in front," "behind," "in," "inside," "outside," "between," "up," "down," top," "bottom," "front," "back," "near," "far," "left," "right").
• During this year, some children can use a model of a room or simple picture maps to locate where an object is hidden in a real room.
• Throughout this year, some three-year-olds can informally create two-dimensional shapes and three-dimensional buildings that have symmetry.

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