One of the best ways to teach preschoolers about octagons and pentagons is to demonstrate how they exist in the real world. Show them a picture of a stop sign, for instance, as an example of the eight-sided octagon, or an aerial picture of the Pentagon in Washington as an example of the five-sided pentagon. Find other images and have them identify octagon and pentagon shapes in fruit, architecture and nature. Encourage them to count the sides of these objects to identify them as octagons and pentagons, since learning about these shapes is, in part, a lesson in counting, as well.
Flash cards are a great way to encourage instant recognition of shapes, including octagons and pentagons. Create flash cards with all kinds of shapes, with extra octagons and pentagons. Hold each shape up, one at a time, and have the children identity them. Children often learn the easier shapes first, so showing them some circles and squares and letting them get the right answers will make them feel confident. When they're faced with the more complicated octagons and pentagons, they can take their time, count the sides and understand what they're looking at. A fun twist on this activity is to help the children make their own flashcards by drawing the shapes on index cards and then coloring them in. Making their own flashcards will make them even more engaged with the project, and it will help them to learn about the shapes through interacting with them and creating them.
Preschoolers like matching games, and for this activity, cut out various sizes of octagons and pentagons from colored construction paper. Cut out two of each size, and give the child one set. Have the preschooler find the matching shape for each shape they hold in their hands. Two children can compete in this game, using two sets of shapes, to see who can get all the shapes matched up first. After all the shapes are gathered, have each child name the shapes they have in their hands, counting the five or eight sides as part of the identification process.
Preschoolers can use octagons and pentagons cut out of colorful construction paper to create artwork. Offer them an assortment of different sizes of these shapes, and encourage them to form whatever artwork they would like with them. Snowmen, animals, houses or whatever interests them can all be good topics for their artwork. They can experiment with putting the shapes next to each other to see what additional larger shapes can be created with these smaller components. After they lay out the shapes in the manner they choose, the children can glue them in place and add pencil, pen or crayon touches to the art.