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# Child Development Tracker: Mathematics From Age 4 to 5 (page 3)

PBS Parents
Updated on Jul 9, 2010

### Geometry and Spatial Sense

• During the first half of this year, some children may still be learning to match shapes, first with same size and orientation, then with different sizes and orientation (e.g., matches simple shapes in form boards and puzzles, sorts simple shapes in a sorter box, etc.). At the same time, some children may be able to recognize and name some variations of a circle, square, triangle and rectangle. The average child can recognize and name these shapes during the second half of this year.
• During the first half of the year, some four-year-olds can build, copy and informally describe two-dimensional shapes. The average child can do this during the second half of the year. Throughout the year, some children will also be able to copy a shape from memory after seeing a model for several seconds.
• In the first half of this year, some four-year-olds will intuitively recognize congruence by matching shapes with other objects that have the same shape and size. The average child will be able to do this during the second half of this year. During the second half of this year, a few four-year-olds can explicitly define the term "congruent" as two shapes with the same size and shape.
• 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 multiple types of items (e.g., a rectangular prism, cube and arches). In the second half of the year, some children may create drawings that involve more than two geometric forms.
• In the first half of the year, some children may still create pictures using one shape, but won't yet use shapes in combination. Others may make a picture by combining shapes. By the second half of this year, the average four-year-old will be able to combine shapes to form a picture. Throughout this year, some children may also be able to cover an outline of a shape with other shapes without leaving gaps, first with trial-and-error, and then with foresight.
• Throughout the year, some four-year-olds can break apart simple two-dimensional shapes that have obvious clues for breaking them apart.
• Throughout the year, some children can find some shapes "hidden" in arrangements in which the shapes overlap each other, but are not embedded inside one another.
• Throughout this year, some four-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, the average child can use a model of a room or simple picture maps to locate where an object is hidden in a real room.
• During the first half of this year, some four-year-olds will be able to orient objects vertically or horizontally. The average child will be able to do this during the second half of the year.
• Throughout this year, some four-year-olds will informally recognize when a two-dimensional shape has been turned, flipped or otherwise moved, and will also move such shapes in this way.
• During the first half of this year, the average child can informally create two-dimensional shapes and three-dimensional buildings that have symmetry.

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