Games like Jumping on the Lily Pads help children develop a mental number line. In this game, children take turns rolling a dot cube and moving a “frog” along the game board. The goal is to be the first whose frog reaches its lily pad. There is advanced mathematics hiding within this game, making it a great way for children to stretch their math muscles. And parents and teachers can play an important role by asking questions, such as, “Who rolled more? How many more? Who is closer to the pond?” and “How many more spaces does the frog have to jump to get to the pond?” This game helps children build the idea that whole numbers are spaced equally along the number line.
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Formative Assessment: Preschool Math Look Fors
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Anno’s Counting Book by Mitsumasa Anno
This beautiful illustrated book invites children to look closely to find all the ways the illustrator has integrated number into the drawings. The first page is zero—an empty winter landscape—and nothing to count. The next page is 1—one tree, one bird, one house. The next page is 2—two buildings, two trucks, two children, two men, 2 trees, and the clock is at 2 o’clock. As you turn each page notice the clock tower marking the hours, the number of blocks on the side of the page, and how the seasons change. Each page also corresponds to the months 1 to 12. Children can find mathematical ideas from the very simple to the complex in this book and can look at the pictures over and over again. Your class could create their own bulletin board like a page in Anno’s Counting Book, making 5 of a variety of their favorite objects. There are more ideas about how to bring out the math in this book on the last page.
The Very Hungry Caterpillar by Eric Carle
This popular book is great for talking to children about ‘how many in all’ (cardinality) and comparing numbers. After you have read the book to the whole group, have book discussions in small groups. Ask the children questions such as “How many apples did he eat through? Pears? Plums? Strawberries?” See if they can name the total number rather than recount each time. Also notice if they are subitizing or counting one by one. Give the children practice comparing numbers by holding the book open to the pages that are cut out for each fruit. Ask children questions such as, “How many more pears did he eat than apples? How many more oranges than strawberries? How many more oranges than apples?”
Ten Black Dots by Donald Crews
Classic counting picture book: one black dot makes a sun, 2 black dots the eyes of a fox, and three black dots a snowman, etc. As you read, have the group count the dots on the page together. This book is a great compliment to the dot card games where kids are practicing one-to-one counting and subitizing. As an extension have kids put 1-10 circle stickers on a page and draw their own designs. You can use this book to extend the idea that numbers are composed of parts by finding the smaller numbers of dots that are part of the whole. For example, on the 6 dot page one hand holds 3 new marbles while the other hand holds 3 old marbles—3 and 3 are 6. The train has 4 pairs of 2 wheels that make 8 wheels (dots) total.
Fish Eyes: A Book You Can Count On by Lois Elhert
This counting book is a pleasure to read aloud with beautiful, vivid illustrations. The narrator imagines she has turned into fish and to “flip down rivers and splash in the sea.” One each page, children can count the fish 1 to 10. The little narrator fish includes a simple addition problem on each page such as, “4 striped fish plus me makes 5.” Children enjoy counting the fish or sometimes the fish eyes as you read the book. For a challenge, they can try the “plus one” problem on each page. At the art table, children would enjoy making their own illustration of fish to count. To make their fish, they could glue color bits of paper on to their page or use crayons, markers, or paint. Children enjoy narrating their own picture and having you write down what they say.
Five Little Monkeys Jumping on the Bed by Eileen Christelow
This fun book and song can be used to teach pattern, counting backwards, knowing one less, and understanding cardinality. For pattern, you can draw kids attention to the lines of the song that repeat each time and see if they know what changes—there is one less monkey jumping (rather than a growing pattern, it’s a shrinking pattern). You can ask children to act out the book by having five children pretend to be the monkeys and someone pretend to be the mama. They can see how the number of children (monkeys) jumping decreases by one each time the pattern (verse of the song) repeats. To practice the pairs that make 5, you can ask children how many monkeys are not jumping (if 3 are jumping, 2 are not jumping).
How Many Snails?: A counting book by Paul Giganti, Jr., illustrated by Donald Crews
Walking to the meadow, lake, library, park, bakery, toy store, and other stops, the author wonders ‘how many?’ about a variety of different objects and in different combinations; such as: “How many snails were there? How many snails had striped shells? How many snails had striped shells and stuck their heads out?” This is a fun counting book to use as a read aloud and then for children to browse on their own counting all the objects and sorting them into different groups.
Quack and Count by Keith Baker
The seven ducklings in the books split into all the whole number combinations that make seven. First children count all seven ducks, then the ducks slide, hide, chase, splash, and quack in the combinations 6 + 1; 5 + 2; 4 + 3; 3 + 4; 2 + 5; 1 + 6, and finally all seven fly. This book helps children understand that numbers are composed of smaller numbers. This is the same mathematical idea in the How Many Are Hiding game—numbers are composed of parts that make up the whole.
Seashells by the Seashore by Marianne Berkes
Children walk along the beach gathering up seashells one by one and adding them to the collection that gathers on one side of the page. After reading the book to the whole class, have book discussions in small groups. Turn to a page and ask children how many shells the children have collected. Hold the sidebars of two pages next to each other and ask children on which page have they collected more and how many more. The shells are in the same orientation on each page which makes it easier to count and compare.
The Baseball Counting Book by Barbara Barbieri McGrath
Similar to an alphabet book, this book has a page for each number 0 to 20. It starts with the score is zero to zero; then one ball, one bat, and one call; then two teams; and at the end nineteen ice-cream cones to celebrate; and twenty baseball cards. After reading the book to the whole class, have book discussions in small groups. Children can practice counting the objects on each page as well as noticing that some numbers are bigger than others (i.e., 20 is much bigger than 2).