Math Skills – Shapes and Spatial Relationships

Shapes and Spatial Relationships

This skill involves an understanding of 2 dimensional and 3 dimensional shapes, relative sizes, position (above, below, behind), direction (left, right, up, down) and movement (toward, away from).

Spatial awareness and spatial relations allow children to locate objects and navigate successfully in their environments; and using spatial language enables children to express their needs and concerns (“Oh no, Mama! Teddy under bed!”) and describe and discuss the world around them (“If you put the triangles together, they make a square!”). (Source)

The more physical interaction kids have with the more kinds of physical objects and activities, the better they understand these concepts. It is much harder to learn about shapes from pictures in books that you can’t manipulate, or to learn about movement from the flight of Angry Birds on a screen.

Developmental Stages

  • Can match shapes: this circle matches this same size circle. (~1 – 2 years)
  • Can stack three or more blocks, Can start simple puzzles. Can understand directional words, especially with gestures. Can do puzzles. (2 – 3)
  • Around 3 years, children can tell a circle from a square and a sphere from a cube. But they couldn’t tell you that squares have four sides. They can tell what’s alike and different, but often don’t get all the nuances. This figure appears at, which says “a three-year-old might say that the shapes in Figure 3 are the same because they both have ‘pointy tops.’ … If the adult asks whether the shapes are at all different, the child might say that one has three sides and the other four, but they are the same because they each have that ‘pointy top.'”early math shapes same top
  • Can demonstrate positional words like above, below, behind; can recognize and name shapes (even if they’re different sizes, and turned around in different directions). May build or draw symmetrical things, but can’t describe what symmetry means. (3 – 5 years)
  • Accurately use directional words when talking; can copy a shape from memory after looking at it for a few seconds, can use a simple 2 dimensional map to find an object hidden in a room. (5 years)
  • Can combine two shapes to make a new shape. Can notice shapes in objects: books are rectangles, a cup lid is a circle, and so on. (6 – 7)
  • Can compose and de-compose shapes – put two squares together to form a rectangle, or divide a square into two triangles. If shown a 3 dimensional shape, they can re-create it (e.g. a play-dough cube) from memory. (7 – 8)

How to Help them Practice / Learn Skills:

  • Notice shapes in the world around you – “your cereal is round, my cracker is square, that sign is a triangle.”
  • Shape Matching Toys: These are self-correcting toys that have a right answer – one way you can put them together that will work well. These start with nesting cups and shape sorters and shape connecting toys for babies and toddlers. Then advance up to wooden puzzles (choose a number puzzle to combine shape learning with representation, or circle fractions). Then jigsaw puzzles, starting with around 12 pieces, then 25, 50, 100, 500….
  • Free Play Shapes:  TangramsPattern Blocks, PentominoesMagna-Tiles and Pattern Play blocks are just some ways to play with shapes and mix and match them together to form pictures or patterns.
  • Block play: A classic set of blocks with rectangles, squares, triangles, arches, and semi circles allows for tons of fun building freely, and exploring which items stack on which other ones – which fit inside others, composing and de-composing.
  • Make shapes: with play-dough, pipe cleaners, cookie cutters, Wiki Stix, paint, crayons. Cut shapes into pieces – a circle into wedges, a square into two rectangles.
  • Games with spatial commands: “can you put the ball under the chair?” “can you run around the couch?”
  • Give positional clues in hide and seek or egg-hunt games: “Try looking between two books” or “it’s above your sock drawer.”
  • Play the symmetry game with blocks or other building materials.
  • Set up a big motor game with shapes taped out on the floor: hop on the circle, jump on the square.
  • Teach how to read a map. Then how to make a map. Start with a simple map of a room, and go up from there.

Click here to read more about teaching math to kids.


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