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In Times Past
an eBook on CD
by Carol Hurst and Rebecca Otis

Integrating US History with Literature in Grades 3-8.

Enliven your US History curriculum!

Teach US History using great kids books.

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Computation and Picture Books

This is a sample chapter from Picturing Math by Carol Otis Hurst and Rebecca Otis (Order through Amazon.com. SRA/McGraw-Hill, 1996. ISBN 0-02-687367-2)

According to The Role of Routine Procedures in the Development of Mathematical Competence, the 1990 Yearbook of the National Council of Teachers of Mathematics, "If we want students to remember procedures, we should ask them to step back and think about the procedures they are using rather than practicing more exercises."

It turns out that solid skills with computation come not so much from repeated drills of methods taught by a teacher, but from the students' ability to create their own methods of completing computations, and the deeper understanding provides the computation process itself. Flexibility and the ability to recognize more than one way of completing the task actually create a stronger math sense and, eventually, greater skill in manipulating numbers.

This type of computational ability develops when students are encouraged to work together to solve a problem, when a wide range of approaches to a calculation are solicited by the teacher, and when students are not penalized for doing things in unconventional ways. When the focus is on developing a method for solving a computation and on describing that process to others, students are forced to think more about what they did and why they did it than about whether they got the right answer. Students still want to get the right answer, of course, but they no longer cease thinking about the process when they discover whether their answer was right or wrong.

For more information on creating students with strong computation skills see Appendix B: Professional Resources (See the print version of Picturing Math, page 144.) for books on the topic.

We are also including in this computation chapter work with estimation (which could have easily been placed in the numeration chapter) because it is intertwined with computation skills. The chapters on Measurement (See the print version of Picturing Math, page 91), Money (page 99), Data Gathering & Analyzing (page 102), and Fractions & Proportion (page 115) all list many books and activities that involve computation.

Developmental Stages

In PreK, the groundwork for computation ability includes free exploration of materials and development of communication skills about attributes and classification.

On the kindergarten level, groundwork for later computation ability includes developing a strong number sense. (See the print version of Picturing Math, Numeration, page 81.) In particular, the ability to arrange a certain number of objects in various subgroups underlies computation. Kindergartners are able to see that groups can be composed of subgroups.

First-grade students begin combining and separating groups of objects for addition and subtraction. Addition and subtraction facts can be searched for patterns. Students learn to describe the process they used in adding and subtracting and to listen to the processes used by others.

At the second-grade level, adding and subtracting abilities extend to larger numbers and more complex methods of computing an answer. The focus is on flexibility of methods. Multiplication and division processes develop as students continue to manipulate numbers.

Using Picture Books for Computation

Some picture books contain obvious math computations, and these stories can be used as models for students to write their own math stories. When students write math stories or their own word problems, this writing serves multiple purposes. The students get to experiment with another kind of writing and think through their ideas about numbers. Also, their writing often offers a window into their process so you can evaluate where they are in their work with numbers.

Other picture books introduce us to areas of interest where further exploration can involve computation as students attempt to answer their own questions about the subject.

Computation Activities

Grades 1-2
Often a book with numerous characters can be used to estimate how many more would be needed to have ten, a hundred, or even a thousand in all.

Grades 1-2
Many books introduce particular foods that the class can prepare. The recipe you use provides a wealth of computation material. How large is a serving? How many servings do we need? Should the recipe be doubled? Tripled? Rewrite the recipe, substituting the new amounts.

Grade 2
Using a meal from the story, calculate it's nutritional value. Estimate serving size and look up the nutritional contents. Find the recommended daily allowance for a nutrient and determine how many servings the characters would have to eat to meet the requirement.

Grades 1-2
When you come across a number in a book, use computation to look for ways to better understand its value. If it's a weight, compute how many students it would take to equal that weight. If it's a distance, compute how long it would take a car to drive it or a person to walk it. Look for other ways to convert amounts to familiar quantities.

Grades 1-2
Subtraction is most commonly modeled as taking away. (There were ten cookies and Cindy ate three. How many cookies are left?) Look for instances in picture books of other models of subtraction, such as finding the difference between the number of boys and girls; determining subsets; and finding a missing amount.

Look at the activities in Data Gathering & Analyzing (in the print version of Picturing Math, Numeration, page 102) and Measurement (page 91) to find more activities that naturally include computations.

Picture Books for Computation

Anno, Mitsumasa. Anno's Counting Book. HarperCollins, 1977. ISBN 0-690-01288-8
Against a barren landscape, Anno presents sets of numbers and their numerals, the months and seasons, and even builds us a village. There is so much to count and examine here that one look through is not enough.

Anno, Mitsumasa. Anno's Math Games I, II, and III. Putnam, 1991.
These are three separate picture books in which various functions of math are required in order to solve the puzzles or play the games. Many primary children will be confused or frustrated with these three math games books, but those who can follow the games should find them delightful. The puzzles increase in difficulty throughout each book.

Anno, Mitsumasa. Anno's Mysterious Multiplying Jar. Putnam, 1983. ISBN 0-399-20951-4
Anno explores the factors of ten, but he does so in a playful way that tends to delight and instruct rather than frustrate the young reader.

Barry, David. The Rajah's Rice. Illustrated by Donna Perrone. Freeman, 1994. ISBN 0-7167-6568-3
Subtitled "A Mathematical Folktale from India," this book is just that. A young girl gets the Rajah to promise her rice as calculated on a chess board, doubling the previous amount on each square of the board.

Brisson, Pat. Benny's Pennies. Illustrated by Bob Barner. Doubleday, 1993. ISBN 0-385-41602-4
Benny has five new pennies, but he's got lots of family members telling him what they want him to buy with the money. When he returns from his shopping trip, he discovers that he has satisfied them all. Furthermore, his purchases make sense and could conceivably be bought with the money. (See the print version of Picturing Math, page 9.)

Cleveland, David. The April Rabbits. Illustrated by Nurit Karlin. Scholastic, 1986. ISBN 0-590-42369-X
Each day of April, David discovers that number of rabbits in his life. This is a good counting book because the story is funny and it combines ordinal and cardinal numbers.

de Regniers, Beatrice Schenk. So Many Cats! Illustrated by Ellen Weiss. Houghton, 1985. ISBN 0-89919-700-0
They started with one lone and rather lonely cat and then there were more. They come singly and in groups. (See the print version of Picturing Math, page 17.)

Fox, Mem. Shoes from Grandpa. Illustrated by Patricia Mullins. Orchard, 1990. ISBN 0-531-08448-5
In this cumulative tale, each of Jessie's relatives buys her clothing to go with the shoes her Grandpa bought her. Illustrated with cut-paper collage, the book is light and playful as Jessie's costume becomes more and more elaborate. (See the print version of Picturing Math, page 21.)

Giganti, Paul. Each Orange Had 8 Slices: A Counting Book. Illustrated by Donald Crews. Morrow, 1992. ISBN 0-688-10429-0
Children can count or multiply with this book of sets and numbers.

Giganti, Paul. How Many Snails? Illustrated by Donald Crews. Morrow, 1988. ISBN 0-688-06370-5
As we view different sites, we are asked to count a variety of items. Then we count subsets.

Hill, Elizabeth Starr. Evan's Corner. Illustrated by Sandra Speidel. Penguin USA, 1991. ISBN 0-670-82830-0
In the apartment where Evan lives with his family, there are only two rooms for eight people. Evan longs for a place of his own and is given a corner. (See the print version of Picturing Math, page 29.)

Hirst, Robin and Hirst, Sally. My Place in Space. Illustrated by Roland Harvey and Joe Levine. Orchard Books, 1990. ISBN 0-531-08459-0
Henry gives his address as 12 Main Street, Gumbridge, Australia, Southern Hemisphere, Earth, solar system, solar neighborhood, Orion Arm, Milky Way Galaxy, local group of galaxies, Virgo Supercluster, the universe. Computation can be used to create scale models of the address as well as to convert many of the measurements to familiar forms of reference. (See the print version of Picturing Math, page 30.)

Hoban, Tana. Twenty-Six Letters and Ninety-Nine Cents. Morrow, 1987. ISBN 0-688-06362-4
Photographs show us letters, which seem to be the plastic raised letters on magnets commonly used on refrigerators, and coins. The book is divided into two parts to show the letters and money separately. As a nice touch, an amount of money is shown in two or three combinations of coins.

Hutchins, Pat. The Doorbell Rang. Morrow, 1986. ISBN 0-688-05252-5
Llaman a la puerta. Spanish from Lectorum.
A brother and sister sit down to share a plate of cookies. Every time the doorbell rings, however, there are more friends to share the cookies with. How many cookies will they each get now? How many more friends can come before they run out of cookies? (See the print version of Picturing Math, page 33.)

Lillegard, Dee. Sitting in My Box. Illustrated by Jon Agee. Penguin USA, 1989. ISBN 0-525-44528-5
A little boy is sitting in a big cardboard box when someone knocks. It's a giraffe who is followed by an elephant, a baboon, a lion, a hippopotamus, and a flea. (See the print version of Picturing Math, page 38.)

O'Keefe, Susan Heyboer. One Hungry Monster: A Counting Book in Rhyme. Illustrated by Lynn Munsinger. Little, 1989. ISBN 0-316-63385-2
Not only is this house infested with monsters, they are rude, boisterous, and noisy monsters. More importantly, they are hungry and after they are assembled, the boy gets the food for them.

Pinczes, Elinor. One Hundred Hungry Ants. Houghton, 1993. ISBN 0-395-63116-5
One hundred ants are rushing off to a picnic. Unfortunately, there's one ant who insists on regrouping them.

Pulver, Robin. Mrs. Toggle's Zipper. Illustrated by Robert W. Alley. Simon and Schuster, 1990. ISBN 0-02-775451-0
Mrs. Toggle, the teacher, got a new winter jacket for Christmas. She puts it on one cold winter morning and can't get it off because the zipper's stuck. Not only that, but the thing-a-ma-jig that you use to open the zipper is missing. Everybody at school gets into the act of trying to extricate Mrs. Toggle, but it's the custodian who finally does it (See the print version of Picturing Math, page 44.)

Rylant, Cynthia. The Relatives Came. Illustrated by Stephen Gammell. Simon and Schuster, 1986. ISBN 0-02-777210-1
Vinieron los parients. SRA, 1995. Available in Big Book and Small Book formats.
Here is a beautiful book about an old-fashioned family reunion in which the relatives come from far across the mountains and pile into and around the house with love and exuberance. (See the print version of Picturing Math, page 46.)

Schwartz, David M. How Much Is a Million? Illustrated by Steven Kellogg. Morrow, 1985. ISBN 0-688-04049-7
Not only a million, but a billion and a trillion are shown in graphic ways that help children understand these difficult concepts.

Schwartz, David M. If You Made a Million. Morrow, 1989. ISBN 0-688-07018-3
Starting with one dollar and proceeding to a million, this is a wonderful book involving much more than counting.

Sloat, Teri. From One to One Hundred. Dutton, 1991. ISBN 0-525-44764-4
In this book, we count sets. The pages are crowded and, at times, confusing, but the target sets are placed in isolation at the bottom of the page.

Stevenson, James. The Mud Flat Olympics. Morrow, 1994. ISBN 0-688-12823-4
The animals are having their own Olympic games and, in four short chapters plus a preface and epilogue, Stevenson presents their efforts and results in a mock serious tone Many of the math activities in this delightful book are obvious and they should be kept at the same level of enjoyment as the book projects. (See the print version of Picturing Math, page 47.)

Viorst, Judith. Alexander, Who Used to Be Rich Last Sunday. Illustrated by Ray Cruz. Simon and Schuster, 1978. ISBN 0-689-30602-4
Alexander, Que ere rico el dominogo pasado. Simon and Schuster, 1989. ISBN 0-689-31590-2
Alexander and his two older brothers get a dollar each from their grandparents on Sunday. Alexander falls victim to temptation and accidents and we watch him as his money goes. (See the print version of Picturing Math, page 50.)

To order Picturing Math call 1-800-843-8855. Or order through Amazon.com. Item no. 0-02-687367-2.