evaluate the effectiveness of a particular diet or food supplement. Counting the number of cars passing the front of the school over a period oi time, children can predict how the new road construction will affect traffic in the school zone. Describing and analyzing changes in various contexts helps children develop their algebraic thinking.
Providing a mathematics-rich environment
Many of the materials mentioned in Chapter 4 (focusing on number and operations) also help children learn about pattern, and recognizing and working with patterns help children understand more about numbers.
Even the youngest children begin to notice the patterns in routines that are repeated—put on coats, go outside, come in, take coats off—and anticipate the next action. Stories and poetrv for young children are filled with patterns. Songs, of course, follow a pattern. Toys, furnishings, and children's own clothing often display bright, colorful patterns. Pattern scavenger hunts help children become more aware of patterns in their own classroom. Search-ing for patterns at home and bringing back information about these discov-eries serve to connect home and school.
Many of the manipulatives used for number and geometry are useful also for considering pattern. In addition, pattern blocks (the color¬ful geometric shapes) are especially helpful. Children love to use them to cover large spaces. Because they fit together nicely and because of their regular shapes, the growing patterns created almost occur naturally. Other useful manipulatives include shape cutouts, Unifix cubes, base-lOJblocks, plastic counters in a variety of animal shapes, and large beads.
The calendar is one staple in the environment that offers many opportunities to consider pat¬tern. In addition to the 7 pattern that Tommy noticed in the Tuesday column of the class calendar (pp. 88-89), other natural calendar patterns include days of the week and months of the year. Even weather conditions and holidays can be described in terms of patterns. Creating a linear number line (like the one in Chapter 4, p. 63) to count the days of school yields many place-value patterns.
Children's errors often tell us what they understand about pattern. The child who predicts that 39 comes after 35 has little understanding of the pattern established with the order of the numbers 1 through 9. In contrast, the child who believes that 9010 ("ninety ten") comes after 99 seems to un-derstand the pattern of counting and simply needs help with the conven¬tional symbolic form.
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