Illustration by Joyce Hesselberth.
Searching for something to get kids excited about math? Scrambling for a great resource to share with your colleagues or use in the library?
Consider picture books.
What I’ve learned over the years is that illustrated books can help dispel the myth that math is dull, unimaginative, and inaccessible. They can spark children’s mathematical imaginations in ways that textbooks and workbooks often don’t. Picture books can also help students who love to read—but think math isn’t their thing—experience the wonder of math in the same way they already enjoy the wonder of books. Plus, students whose first love is math will learn to look at books in a new way. If you’re an educator who doesn’t enjoy or feel comfortable teaching math, using picture books can build on your existing strengths in teaching reading and language arts, and help bolster your confidence and enthusiasm for teaching math.
To show you what I’m talking about, I’ll present a vignette of a first-grade math lesson. But keep in mind, picture books also work well as a springboard to math with older students in grades four, five, and six. (For some tips on selecting an appropriate picture book, see "Count on Me" below.)
One of my favorite books to share with young students is Keith Baker’s Quack and Count (Harcourt, 1999). After gathering the children on the rug, I show them the cover of the book and read the title and author’s name.
"What do you think this book is about?" I ask.
After children share their ideas, I say, "Let’s find out."
I open to the first spread and read: "Seven ducklings in a row. Count those ducklings as they go." After talking about "ducklings" being a word that describes baby ducks, I ask the students to count along with me as I point to each of the ducklings in the illustration.
Then I turn to the next spread and read the accompanying rhyme. Six ducklings are shown on the left page and one on the right page, and I have the kids first count the ducks on the left and then the one duck on the right. "And how many ducklings do you think there are altogether?" I ask. Some of the first graders know that there are seven, others aren’t so sure. Together we count all of them to make sure that six ducks plus one more are indeed seven.
The following spread shows five ducklings on the left page and two on the right. I read the rhyme and we count the ducks on the left first and then those on the right. After posing the same question about how many there are in all, we verify that there are seven by counting all of the ducks together.
I continue in this same way for the rest of the book. Then I talk with the children about the story, asking them to recall what the ducklings did, revisiting the illustrations, and repeating the addition sentences—seven equals six plus one, seven equals five plus two, and so on.
To extend this experience, I reread the book to the class, this time writing number sentences on chart paper to keep track of what happened and to model how to connect mathematical symbols to the story. For example, after rereading the spread with six ducks on the left and one on the right, I write:
7 = 6 + 1
I have the children read the number sentence aloud as I point to the symbols, and I invite them to help me write equations for the rest of the story. An especially nice feature of this book is that the illustrations near the end allow for thinking about seven with more than two addends. When we finish the rereading, the chart looks like this:
7 = 6 + 1
7 = 5 + 2
7 = 4 + 3
7 = 3 + 4
7 = 2 + 5
7 = 1 + 6
7 = 2 + 3 + 2
7 = 2 + 2 + 2 + 1
I then give each of the children seven interlocking cubes and have them show each of the combinations by using the cubes to represent each addend with a train. The students enjoy holding the trains up as if they were finger puppets.
For an individual assignment, I ask them each to choose one of the number sentences from the chart, copy it, and illustrate it. "You can draw ducklings or any other shapes," I tell them. For kids who finish quickly, I ask them to grab another sheet, fold it in fourths, and illustrate a different equation in each section. And, to differentiate the assignment further, I ask students who are ready for an additional challenge to write and illustrate their own equations, each with combinations of more than two numbers that add up to seven.
Often the same book is suitable for more than one grade level. I read Quack and Count to a class of kindergarteners, and it worked just fine. However, I limited the math part of the experience to focus only on the combinations of two addends, and I skipped the individual writing assignment.
To help you get started, here are some of my favorite titles for introducing or reinforcing a wide range of math concepts. For each title, I’ve listed the math concepts and skills they include, along with the appropriate grade levels. Following each brief story description, there’s also an idea for a math lesson. I hope these suggestions will inspire you to use picture books to teach math to your own students.
Burns, Marilyn. Spaghetti and Meatballs for All! Scholastic, 1997. Gr 4–6: AREA AND PERIMETER
For a family reunion, Mrs. Comfort arranges eight square tables, each with four chairs, so that all 32 guests will have a place to sit. But as guests arrive, they create havoc with their own seating plans.
Have students use square tiles or draw on squared paper to experiment with what happens to the seating when square tables are pushed together. Introduce the math vocabulary of area (one square unit for each tabletop) and perimeter (four units for each square table, one unit for each side).
Emberley, Ed. The Wing on a Flea. Little, Brown, 2001. K–Gr 2:
With brightly colored illustrations and simple rhymes, children learn how common geometric shapes—triangles, rectangles, and circles—are found in the world that surrounds them.
Prepare a sentence starter strip for each child:
A triangle could be a ___________.
Also, title chart paper with the sentence starter. As children share ideas, list them on the chart. Then each student writes a word to complete his or her own sentence starter strip, glues the strip to construction paper, and illustrates the idea with cutout shapes and drawings. On the next two days, repeat for two other sentence starters:
A rectangle could be a ___________.
A circle could be a ___________.
Compile their work into class books.
Florian, Douglas. A Pig Is Big. Greenwillow, 2000. K–Gr 1:
The book opens by asking, "What’s big?" and presents an exploration of things that are increasingly bigger and bigger—from a pig to a cow, car, truck, street, neighborhood, city, Earth, and finally the universe.
Give each student two pieces of paper and ask them to draw something that is bigger than a pig on one piece and something that is smaller than a pig on the other. Have children share their drawings and record what they drew (or record for them). Compile their work into two class books: What Is Bigger Than a Pig? and What Is Smaller Than a Pig?
Goldstone, Bruce. Ten Friends. Holt, 2001. Gr 1–2:
COMBINATIONS of 10
The book presents different combinations of guests that could come to tea; for example, eight trusty tailors with two proud plumbers, or seven salty sailors with three loud drummers. Ten combinations of 10 guests are suggested in all.
Present children the challenge of writing as many different addition equations as they can that show different combinations of numbers that add to 10. It may help some children to use interlocking cubes of different colors to build different combinations.
Hutchins, Hazel. A Second Is a Hiccup. Scholastic/Arthur A. Levin Bks., 2004. K–Gr 1:
This book explains units of time in ways that all children can recognize. Beginning with "How long is a second?" it goes on to addresses the length of a minute, hour, day, week, month, and year.
Revisit the spread that begins, "How long is a minute?" Tell the children that you’ll time one minute while they cover their eyes or put their heads down on their desks. When they think one minute has passed, they should raise their hand. They may have to wait until you say "One minute." Then have children think of things they do that take about one minute.
Krull, Kathleen. Wilma Unlimited. Harcourt, 1996. Gr 4–6:
This is the inspiring story of Wilma Rudolph, the first woman to win three gold medals in a single Olympics. A sickly child just over four pounds at birth who had a leg paralyzed by polio just before she turned five, Rudolph became an incredible athlete.
A few days before reading the book, ask students to find out how much they weighed at birth. List the information on chart paper. Then, after reading the story, have students work in pairs to create a graph of the data.
Lionni, Leo. Inch by Inch. HarperTrophy, 1995. K–Gr 3:
An inchworm is able to measure anything and proves it by measuring a robin’s tail, a flamingo’s neck, a toucan’s beak, and more. When confronted with either measuring a nightingale’s song or being eaten, the inchworm creatively solves the problem.
Model for the students how to use a one-inch tile to search for objects that measure one inch. (For older students, use a ruler.) Entitle a piece of chart paper "1 Inch" and list the items you find. Then have students search for things to add to the list.
Pinczes, Elinor J. A Remainder of One. Houghton, 2002. Gr 3–6:
Soldier Joe is in a squadron of 25 bug soldiers and is left to march alone when the troop assembles in two, three, or four lines. The Queen is displeased until finally the soldiers organize into five lines.
To reinforce or introduce the idea of remainders, write division equations for each arrangement of 25 bug soldiers—25 ÷ 2 = 12 R1, 25 ÷ 3 = 8 R1, 25 ÷ 4 = 6 R1, 25 ÷ 5 = 5 R0. Then give students clues and have them figure out the number between 1 and 25 that fits them all:
When you divide by 2, the remainder is 0.
When you divide by 3, the remainder is 1.
When you divide by 4, the remainder is 2.
When you divide by 5, the remainder is 0.
Students can make up their own sets of clues for other problems.
Ross, Tony. Centipede’s 100 Shoes. Holt, 2003. Gr 3–4:
MULTIPLICATION AND ADDITION
A little centipede buys 100 pairs of shoes at the shoe store and, the next morning, discovers that he bought too many. He only has 42 legs (which is typical for centipedes!) and, besides, the shoes hurt his feet. So he sells them along with the 42 socks his aunties knit for him.
List who bought the shoes and socks. The centipede sells shoes to all of them, and socks as well to the spiders and worms. Either include the number of legs each has or have the students research to find out.
4 beetles (6 legs each)
2 woodlice (14 legs each)
1 grasshopper (6 legs each)
5 spiders (8 legs each)
2 worms (1 leg each)
Then have them verify that the centipede really did sell all the shoes and socks.
Shulevitz, Uri. One Monday Morning. Farrar, 2003. K–Gr 1:
NUMBER SENSE, GRAPHING
This tale begins one Monday morning when a king, queen, and prince pay a visit to a little boy who isn’t home. They return each day of the week, each time with one more visitor, and finally find the boy at home on Sunday.
As children retell the story, use stacks of interlocking cubes to make a concrete graph that represents how many visitors arrived each day, using a different color for each character. Record for each day, writing two different equations from Wednesday on:
Tuesday 3 + 1 = 4
Wednesday 4 + 1 = 5, 3 + 1 + 1 = 5
Thursday 5 + 1 = 6, 3 + 1 + 1 + 1 = 6
and so on.
Appelt, Kathi. Bats on Parade. HarperCollins, 1999. Gr 3–4: addition, multiplication, square numbers
The Marching Bat Band parades past a grandstand of cheering animals, marching 2-by-2, 3-by-3, and so on until the sousaphone players, marching 10-by-10, bring up the rear. The parade ends with the entire band taking flight.
The books helps students see that square numbers—1, 4, 9, 16, 25, and so on—relate to the geometric interpretation of squares, as well as to the numerical interpretation of multiplying a number by itself. Before reading the last page which reveals that there are 385 band members, have the students figure out how many bats were on parade.
Axelrod, Amy. Pigs Will Be Pigs. S & S, 1994. Gr 2–4: money
There’s nothing to eat in the refrigerator, so the famished pig family decides to go out for dinner. But they don’t have enough money, which results in a search throughout the house for coins and bills. Finally, they pig out at their favorite restaurant, the Enchanted Enchilada.
Ask the students to estimate how much money the pigs turned up on their hunt. Then reread the book and have students take notes so they can figure out how much the pigs found. Have students compare their results in small groups, then share their answers and how they figured. Also have them figure out how much the pigs spent on dinner, and how much change they had left over.
Birch, David. The King’s Chessboard. Scott Foresman, 1993. Gr 4–6: doubling, addition
When the king wants to give a gift to his wise man, the man points to a chessboard and suggests one grain of rice on the first square the first day, two grains on the second square the second day, and so on, doubling each previous day’s gift for each of the 64 squares on the board. The king finally realizes that he can’t fulfill the agreement.
On the board or chart paper, write the number of grains of rice for the first five days—1, 2, 4, 8, 16. Ask students for the numbers for the next several days to be sure they all understand the doubling pattern. Then have students continue to find the numbers up to the 20th day (524,288 grains), or 30th day (536,870,912 grains). Students who are interested could continue, or do the addition required to figure the total amounts for different days. For a literacy lesson, have students compare the different versions of the story.
Some similar books for this same lesson:
Barry, David. The Rajah’s Rice. Freeman, 1994.
Pittman, Helena Clare. A Grain of Rice. Dell, 1996.
Demi. One Grain of Rice. Scholastic, 1997.
Burns, Marilyn. The Greedy Triangle. Scholastic, 1994. Gr 2–4: geometry
This story is about a dissatisfied triangle that always wishes for more—more sides and more angles. A shape shifter grants the wishes until the shape finally learns that it likes begin a triangle best after all.
Title a piece of chart paper Polygons. Revisit the book and list the names of polygons as they occur—Triangle, Quadrilateral, Pentagon, Hexagon, and so on. Be sure to include the names of different quadrilaterals—square rectangle, parallelogram, trapezoid, and rhombus. Have students present their theories about why, near the end of the story, the shape begins to roll.
Cave, Kathryn. Out for the Count. Frances Lincoln, 1991. Gr 1–2: place value
Tom finds it hard to sleep, and counting sheep is the beginning of a madcap dream adventure of counting pythons, pirates, penguins, vampire bats, and more.
To help students understand the tens and ones structure of our place value system, reread the book, again showing the students the illustrations. For each spread, have students practice counting the objects by 10s and adding on the extras.
Fox, Mem. Night Noises. Harcourt, 1989. Gr 2–4: addition
Almost 90 years old, Lily Laceby lives in a cottage with her dog, Butch Aggie. One night, as she doses off and dreams about her life, she is awakened suddenly by strange noises and finds her friends and family coming for a surprise birthday party.
Pose the problem of figuring out mentally how many guests came to Lily Laceby’s party. Then since she was ninety years old, and the book was published in 1992, have the children figure out in what year Lily Laceby was born.
Geringer, Laura. A Three Hat Day. HarperCollins, 1985. Gr 1–6: permutations
R. R. Pottle the Third has an extraordinary collection of hats, but he is lonely and dreams of meeting a perfect wife. One day, when R. R. Pottle goes out wearing three hats stacked to cheer himself up, his dream comes true.
The three hats R. R. Pottle wears are a bathing cap, fireman’s helmet, and sailor’s hat. Ask the students to figure out how many different ways the three hats could be stacked up. Young students can draw pictures; older students can choose to use symbols. Extend the problem by adding another hat—a top hat. For older students, extend the problem further with additional hats.
Hong, Lily Toy. Two of Everything: A Chinese Folktale. Albert Whitman, 1993. Gr 1–3: doubling numbers, algebraic thinking
When old Mr. Haktak digs up a huge pot in the garden and brings it home for Mrs. Haktak, they discover that it is a magic doubling pot. Their lives are changed all for the better until Mrs. Haktak slips and falls into the pot herself!
Have students think up things and how many of them might fall into the pot, and then figure out how many would come out. Keep a list on a chart with two columns labeled In and Out. Talk about their strategies for doubling. As a challenge, pose problems in reverse. For example, ask, “What would have to fall into the pot in order for five dollars (or 12 peaches or 30 socks) to come out?”
Hutchins, Pat. The Doorbell Rang. HarperCollins, 1986. Gr 2–3: division
The doorbell rings just as Sam and Victoria are about to share a dozen cookies, so they have to share the cookies with friends. But the doorbell rings again and again, until there are 12 hungry children. Luckily Grandma arrives with a tray full of more cookies.
Each time the doorbell rings, ask students to figure out how many of the dozen cookies each child gets. Then introduce or reinforce how to record each division; e.g., 12 ÷ 4 = 3. If appropriate, pose another problem: Grandma had baked 18 cookies. How many cookies are there altogether, and how can they share them equally among 12 children? (30 ÷ 12 = 2 R6 or 2½)
Mahy, Margaret. 17 Kings and 42 Elephants. Dial, 1987. Gr 2–4: division
With dreamlike jungle illustrations and rollicking verse, this is a story in verse about 17 kings going somewhere, never revealed, with 42 elephants. The language is rich and imaginative, and the book is exquisite.
Give students the problem of figuring out how 17 kings could share the responsibility equally of taking care of the 42 elephants.
McKissack, Patricia C. A Million Fish… More or Less. Knopf, 1992. Gr 4–6: number sense
In this tall tale set on a bayou in Louisiana, Hugh Thomas catches three small fish . . . and then a million more. This fish story sets the stage for students to relate numbers to real-world contexts and think about what numbers can and can’t represent.
Give students a beginning example: Five hundred could not be the number of pounds a turkey weighs, but it could be the number of _____________. Have them suggest ideas for completing the sentence. Then write an open prompt on the board for students to make up their own examples:
_____________ could not be the number of _______________,
but it could be the number of _______________.
Moore, Inga. Six-Dinner Sid. S & S, 1991. Gr 1–2: addition
Sid, a clever cat, has convinced six people on Aristotle Street that each is his owner so that he gets fed six different dinners every night. When the neighbors catch on, Sid moves to a new neighborhood.
Write on the board: Sid ate ___ dinners in a week. Be sure that children know you are talking about all seven days in a week. Allow children to use counters, draw, or rely on any other way that helps them solve the problem.
Mosel, Arlene. Tikki Tikki Tembo. Holt, Reinhart and Winston, 1968. Gr 4–6: data analysis
A boy, honored as the first-born son with a name that is 50 letters long (Tikki Tikki Tembo is a shortened version), fell into a well and nearly perished because it took so long for his brother to say his name. This retelling of a folk tale from China that explains why all children are now given short names.
Use the book to introduce or reinforce the vocabulary and concepts of data, range, mean, median,and mode. Give each student a sticky note on which write the number of letters in their first and middle names combined. Post them to make a class graph, and then figure out the mode, median, and mean for the data.
Myller, Rolf. How Big Is a Foot? Dell, 1962. Gr 2–3: measurement, ratio, and proportion
The king wants to give his queen a very special birthday present and decides on a bed. (Beds hadn’t even been invented yet.) He paces to measure that the bed needs to be three feet wide and six feet long, but the apprentice who makes the bed is a good deal smaller than the king.
Stop reading the story when the apprentice is sent to jail. Have the students share ideas about advice to give the apprentice and then have them each write the apprentice a letter. After students share their letters, finish reading the story.
Neuschwander, Cindy. Amanda Bean’s Amazing Dream. Scholastic, 1998. Gr 2–3: multiplication
Amanda Bean loves to count anything and everything, but she isn’t interested in multiplication. An amazing dream convinces here that multiplication is another—and faster—way of counting.
Revisit each page in the book and talk with students about different ways to count the objects shown. For example, the first page shows a building with six large windows, each with a 6-by-3 array of panes. Have children figure out how panes are in each window, and how many there are altogether in the building.
Pinczes, Elinor J. One Hundred Hungry Ants. Houghton, 1993. Gr 2–4: multiplication
One hundred ants are marching in single file to a nearby picnic. The littlest ant suggests that they hurry their progress by reorganizing into 2 equal lines of 50, 4 equal lines of 25, and in several other ways until they arrive at the picnic in 10 equal lines of 10… too late for the food.
Revisit how the ants reorganized and write a related multiplication equation for each. (For example, 2 lines of 50: 2 x 50 = 100). Then ask, “Why didn’t the littlest ant suggest that they get into three lines?” (It isn’t possible to organize 100 ants into three equal lines.) Investigate the different ways that 10 ants can reorganize into equal lines. Repeat with 12 ants.
|Marilyn Burns is the founder of Math Solutions, which helps schools improve K–8 math instruction through professional development and publications.|