Follow the Moon
With a large piece of colored construction paper, markers, scissors and white paper, you can create a guide to the phases of the moon. After folding the piece of construction paper in half lengthwise, cut seven lines, evenly spaced, horizontally along one side to create eight even strips. Each strip will be for one phase of the moon. Tape or glue a piece of white paper onto the uncut half of the paper; this will be the part on which you'll write about the moon phases. On the front of each strip, draw or color a phase of the moon. Inside, underneath the corresponding flap, write information about that phase of the moon.
Calendar
For a more complete view of the phases of the moon and how they progress through a month, purchase or create a monthly calendar. Using a "Farmer's Almanac," draw a picture on each day of what the moon will look like that night. Alternatively, you could view the moon each night of any month and then draw its appearance on your calendar so you can see, once the month's over, what the moon's phases were that month.
Planting by the Moon
You could perform an experiment to see how the phases of the moon affect certain plants. Find a plant or herb that can be planted in a certain season; during that season, plant half of your seeds when the moon is full the following night and the other half when the moon is new that night. As the plants grow, make note of the plants' growth rate and growth habits. See if you can discern any differences in the plants you planted during the full-moon period.
Demonstrating Moon Phases
For a more instructive moon phase craft, cut two circles out of paper, one black and one white. You can decorate the white circle like the moon if you want to. Place a magnetic strip on the back of each circle and keep both on your refrigerator. Each night, move the black circle over the white according to how the Earth's shadow is blotting out parts of the moon.