1. Buy or build several geoboards so children can work together.
2. Make a collection of drawings of basic shapes. Place the shapes and rubber bands in a small basket or other storage container.
3. Encourage the children to pick a shape card and reproduce the shape pattern using rubber bands on the geoboard.

To make a geoboard: Cut plywood scraps into 14-inch squares. Sand the edges and coat with water-based varnish. Use a ruler and marker to make a grid 12 points across and 12 points down. Hammer a finishing nail into each point on the grid.

1. Indicate a building area such as a sand table indoors or a sandbox outdoors.
2. Introduce the activity by inviting children to explore a brick. Offer a magnifying glass and ask questions about weight, texture, and color. Talk with the children about how bricks are made from clay and minerals. Brickmakers mold the clay into standard rectangles and dry the clay in a hot oven or kiln.
3. Invite the children to make bricks by filling containers with wet sand, tamping it down, and turning it out as a brick.
4. Help children line up the bricks end to end. Ask questions that encourage the children to estimate how many bricks they’ll need to make a wall between two points.

1. Use a permanent marker and straight edge to draw basic shapes on cardboard squares.
2. Punch holes along the sides of the shapes.
3. Introduce the activity with instructions on how to thread and hold a sewing needle to stitch along the shape outline. A double, knotted length of yarn is easiest for children to use.
4. Show the children how to undo their sewing for other children to use. Clip off the knot and gently pull the yarn out of the cardboard one hole at a time.

Variation: Use 12-inch squares of pegboard (2-foot by 4-foot sheets are usually available at home supply stores). Cut to size and sand edges. Use a permanent marker to draw basic shapes on the board. Encourage children to place golf tees in the holes following the outline.

Spatial sense—essential to developing mathematical skills—is reinforced in art, music, science, construction, movement, vocabulary, reading, and writing activities. Skilled teachers find ways to help children bridge the informal knowledge learned from playing with shapes and formal numeracy and mathematical skills.

1. Cut hundreds of 2-inch squares from colored construction paper. Place in a basket or other storage container.
2. Talk with children about squares. Encourage clear definitions: A square is a rectangle (four-sided shape) with equal sides. A square can be of any size but each of the four sides must be the same length.
3. Show the 2-inch squares. Encourage the children to measure them.
4. Use the ruler and draw a 4-inch square on the paper. Encourage the children to observe and determine (hypothesize) how many 2-inch squares are needed to fill the 4-inch square. Invite children to glue the construction paper squares into place. It takes four 2-inch squares to fill the 4-inch square.
5. Repeat the activity with 8-, 16-, and 32-inch outlines.
6. Encourage children to build their own squares. Observe and reinforce four equal sides, counting squares as necessary.

Here’s what you need:
tangram sets (see construction directions below)
flat work surface
shape patterns

1. Introduce tangrams by first exploring the pieces: two large triangles, one medium triangle, two small triangles, one square, and one quadrilateral. Encourage the children to sort, combine, and stack the seven pieces.
2. Give each child in the group a tangram set. Explain that children will work at copying a construction shape you create. Ask them to stack their seven pieces and place their hands on their tummies until you give three signals: Observe, create, and repair.
3. Use two pieces (the square and a large triangle, for example) to make a shape. Give the observe signal and allow a couple of seconds for children to study the design. Cover the shape with a sheet of paper.
4. Give the create signal. Watch the children recreate the shape. Give the children about 30 seconds to work on their shapes. Some will be successful, others not.
5. Uncover your shape and give the repair signal.
6. Repeat with increasingly challenging designs. Remember to have conversations with the children about what they have recreated, how hard the puzzles can be, and what trial-and-error steps they’ve taken. Remember the repair part of the activity builds as many skills as the create one.

Variation: Copy tangram patterns from Google™ images—there are many links to simple designs. Challenge children to copy the design but remember to give lots of time to concentrate, experiment, and create.

Build a tangram: You can use either heavy cardboard or thin (¼ inch) plywood for the puzzle, but it’s essential that the measurements be precise and cuts accurate. Cut the puzzle material 6-inches square. With a ruler and light pencil line, mark a grid on the square dividing the surface into 16 squares of 1 ½ inches each. Use the diagram below as a guide and cut along the heavy lines to make the seven tans. If you’re using wood, lightly sand and varnish the pieces. Store the pieces in a cloth bag.

1. Introduce the activity with definitions. Symmetry divides a figure into two parts that are mirror images of each other. Share examples and ask children to suggest other objects.
2. Invite the children to explore symmetry by drawing half of a picture—a person, flower, or butterfly, for example.
3. Show how to hold the completed drawing at a right angle on a mirror to see the complete image.

Variation: Find large, simple images in magazines—animals, houses, or trees, for example. Cut the image up the middle and tape one half to the edge of a sheet of paper. Challenge children to complete the other half of the picture using paint, crayons, markers, or watercolors.

1. Gather pictures from old magazines. Place each picture in a plastic sheet protector.
2. Challenge children to identify the unique shapes that make up the whole picture. Show a few examples—a circle clock, a cube ottoman, or french fry rectangles, for instance.
3. Encourage the children to use a marker to outline each distinct shape.
4. Ask that the plastic sleeves be wiped clean with a damp paper towel to prepare the activity for another child.

1. Prepare for the activity by gluing graph paper to sheets of cardboard to strengthen the paper and provide a working surface for the children’s art. Let dry thoroughly.
2. Introduce Mondrian’s art to the children. Engage the children in conversation about what they see and feel in the pictures. Encourage questions and observations about color and geometric shapes.
3. Encourage the children to imitate Mondrian’s geometric art with tape and color.
4. Show how to use the lines on the graph paper as a guide for placing tape around the perimeter of the paper and then in different sized rectangles and squares.
5. Invite the children to choose colors to fill in some of the geometric areas.