**Ideas for virtual instruction are included at the end of this post.**
When I look for children’s books to use during math class, I first look for books that are good pieces of literature. Good literature can provide children with intriguing characters, rich language, playful patterns, engaging plotlines, colorful illustrations, and interesting settings. Literature can also serve as real world or imaginary contexts or springboards for solving math problems. One of my favorite stories to start off the school year is Beasts of Burden by Malba Tahan that sets the stage for thinking about fractions, division, and remainders. The other is Rooster’s Off to See the World by Eric Carle, a book that invites young children to engage in problem solving.
The Tale of the 35 Camels: A Perplexing Fraction Problem from Ancient Iraq
Children love stories, especially ones that are mysterious and puzzling. “Beasts of Burden” is one of these tales. Set in ancient Iraq, “Beasts of Burden” is about Hanak Tade Maia and his adventures with the mathematician Beremiz Samir. It’s a story that involves a riddle worth exploring with fourth or fifth graders and is a wonderful way to bring the mysteries of mathematics to students.
Written in the style of the Arabian Nights, Brazilian scholar Breno de Alencar Bianco’s (aka Malba Tahan) “Beasts of Burden” is one in a series of stories in his book, The Man Who Counted (Norton & Company, 1993). It begins with Beremiz and his companion riding on their camel from Samarra to Baghdad when, close to an abandoned inn, they saw three men arguing beside a herd of camels.
The men were three brothers who had been given an inheritance from their father that included 35 camels. In the inheritance, their father had stipulated that each son would receive a fraction of the herd: one-half, one-third, and one-ninth. The brothers couldn’t figure out how to do the math so that the inheritance would come out even. After finding out why the brothers were quarreling, Beremiz offered a solution:
“Let me add to the inheritance of 35 camels this splendid beast that brought us here at such an opportune moment.”
Hanak was beside himself. How could Beremiz give away their camel?! How would they be able to continue on their journey if they were left without a camel? And how would giving the brothers a camel, solve the inheritance problem?
Reading (or telling) the Story and Posing the Problem to Fifth Graders
“What do you think of when I say the word, Iraq?” This is the first thing I ask fifth graders before I begin the tale. I am always curious about what they know, and I often wonder if students have any references other than war and conflict. Asking them about Iraq is a nice way to tap their knowledge of history, culture, and geography. After a brief discussion, I begin reading the story from the book, or telling the tale from notes.
I stop reading (or storytelling) when I get to the part where the brothers are quarreling and can’t figure out how to equally divide their inheritance. I have partners talk about what they think the problem is, and then call the class back together for what is usually a short discussion. Most students realize that figuring one-half of 35, one-third of 35, and one-ninth of 35 is problematic because the result of each gives you a remainder, and you can’t have a part of a camel!
Once we decide what the brothers’ problem is, I ask the class to predict what Beremiz might do to help them solve the problem. Fifth graders can have the most creative imaginations and they come up with a variety of solutions. “Beremiz could take one camel, and then there would be only thirty-four, and thirty-four is an even number so it can be divided in half,” one student suggests. “If there were some babies in the group, they could make two babies equal one adult camel,” another suggests. “It’s hard ‘cause you can’t split a camel in half!” says someone else.
Finally, I continue with the story and reveal Beremiz’ solution: to give the brothers their camel so that there is a total of thirty-six. At this point, I ask the students to explain, using words, numbers, and pictures, why Beremiz’ solution makes sense. Following are two examples of how students have thought about the problem.
This student explains why Beremiz’ solution works.
This student shows how they figured half of 36, one-third of 36, and one-ninth of 36.
After students finish their work, we convene for a final discussion, listening to ideas and reflecting on the problem. Students are always amazed when they find out that by giving the brothers their camel, Beremiz and his friend get two camels back in return, while the three brothers come out ahead in the end as well! Kids love the problem’s perplexing nature and begin to see mathematics as something we use to figure out interesting dilemmas.
Rooster’s Off to See the World
Rooster’s Off to See the World is a time-honored tale by Eric Carle about an adventurous rooster who goes off to see the world. On his way, he meets two cats, three frogs, four turtles, and five fish who join the rooster on his travels. Midway through the story, the animals decide, for one reason or another, to leave the group and head back home. Rooster’s Off to See the World provides a perfect context for young children to identify patterns, observe the actions of addition and subtraction, and engage in problem solving and represent their mathematical thinking.
The problem that I pose after reading the story is, “How many animals went off to see the world altogether?” It’s a pretty straight forward problem that asks students to find the sum of a string of numbers: 1+2+3+4+5. What’s interesting is how many different ways students go about finding the answer, organizing their work, and representing their thinking. While observing children work, or when examining their work samples, I keep several questions in mind. Are students able to model their thinking using numbers and equations? If students count to find the total, how do they count? Do they count by ones, or do they use grouping to figure the total? What tools do students make use of? Do they use number lines, ten frames, pictures, or number charts? Are their strategies for solving the problem efficient?
The rooster problem is a great assessment question to revisit throughout the year to find out how students are progressing in their problem solving and math reasoning skills. Following are some examples of student work from a first-grade class midway through the school year.
This student shows the story of their thinking: 5+4 is 9; 9+1 is 10; 10+2 is 12; and 12+3 is 15.
This student also shows the story of their thinking, explaining how they got to 15.
This first grader saw three fives.
Integrating Math and Literature using Virtual Platforms
The Common Core Standards encourage students to solve problems that are embedded in real world contexts. Whether students are figuring out how many animals went off to see the world, or explaining the solution to an inheritance dilemma, we can see how a good story has the power to motivate, engage, and bring meaning to mathematics. Starting a lesson with a good read is one of the best ways to hook students and pique their interest. But what are the best ways to do this when teaching online?
Desmos: Synchronous and Asynchronous
One way to approach using literature as a springboard for teaching mathematics remotely is by using platforms such as Desmos. Desmos is designed to be an in-class tool for building interaction and discussion which you can still fully utilize in synchronous sessions. However, it also works asynchronously. The following link takes you the Beasts of Burden task which we adapted using Desmos’ activity builder with asynchronous instruction in mind. You will notice the questions in the Desmos version we built are slightly different than those discussed above because in asynchronous instruction, the teacher is not present to facilitate the discussion. In an asynchronous task, we strive to scaffold the task and to prompt thinking through questions students can consider on their own. As students work on the task either at home or at school, they will see each other’s responses and have the advantage of learning from the thinking of peers even if they are not side by side in the classroom. Within Desmos tasks, you have the opportunity to provide feedback to students which is a powerful way to boost student engagement (be sure to check that box when you set-up your account). If you want to use this Desmos version with your students, be sure to set-up a free account at https://teacher.desmos.com/ and make a copy for yourself. Building an activity with Desmos is pretty easy! You should give it a try!
If you choose to utilize the online platforms to launch math and literature tasks, consider sharing books with your students using online videos if you don’t have a copy at home. Just google Rooster’s Off to See the World and you’ll find several different videos of people reading the book aloud. If your budget allows, I recommend purchasing the book for your classroom library.
What are your favorite children’s books to use for teaching mathematics?