Spread out 5 Lima beans. Spray paint one side blue.
Give the child a cup with the five Lima beans inside, several index cards, a pencil and a blue crayon.
Tell the child to toss the beans on the table. Some will be white side up, others blue side up.
Hand him one index card. Ask him to count and draw the blue beans first. Next he counts and draws the white beans.
Continue the process with each new toss. The child records his results on a separate card each time. Ask him how many different combinations he thinks are possible. Proceed until he believes he has every possible combination of blue and white beans. Instruct a more mature kindergarten student to write the addition problem beneath each illustration, for example "3 blue + 2 white = 5 total beans."
Set up patterns with small snacks similar in shape and size, but differing in color, such as jelly beans or mixed cereals. Start with a simple repeating pattern. For example place a blue, then a green, another blue and another green.
Challenge the child to replicate the pattern and then extend it.
Ask, "Why did you start with blue?" or, "How did you know that was the next color?" Let the child explain in his own words why he made his selections.
Allow the child to eat the patterns when you are done.
Show the child how to fill an outlined shape with tangrams. Demonstrate that the geometric shapes can be placed in a variety of configurations on the paper. Teach him to keep the tiles within the outline. Remind him that he can turn or flip a tile to align it with another piece, creating a different effect. Show him that two triangles turned in opposite directions make a square, or a parallelogram takes fewer tiles than a square and two triangles. Explain that the puzzle is complete once the entire outline is filled in and no tangrams overhang the outline.
Provide the child with tangrams and an outlined shape of his own to fill.
Ask him why he chose this piece, or that combination of pieces. Encourage him to fill the outline with the fewest pieces, or the most possible, causing him to reason through the puzzle and understand the relationship of the different shapes to one another.