Which potato chip is healthiest: regular, baked, or sour cream and onion? This problem, like so many in our data-drenched society, requires critical and numerical skills in order to read and compare nutrition labels. The question has applications in mathematics and science classrooms but also in teachers' lounges and school cafeterias. It is a problem that addresses the five process standards from the NCTM Principles and Standards for School Mathematics of problem solving, reasoning and proof, communication, connections, and representation, and it presents the perfect opportunity for a library lesson collaboratively planned with fourth grade teachers.
MATH IN THE MEDIA CENTER
The school library is the perfect place to explore mathematical problems. As Mardis (2007) said about science, “For some students learning how to respond to an inquiry-based, active environment is not part of their early classroom experience. The types of hands-on, multi-modal learning that can take place in the elementary media center during group activities can build the creative, open thinking required to thrive in inquiry-based situations.” My journey to infuse the library into mathematics instruction in my school began with the encouragement of my principal and a mathematics workshop I attended with my teachers where the presenter suggested that students write word problems using the familiar literary elements of character, setting, and problem. Suddenly I realized that I could construct a word problem to go with just about any story. Just use the characters and setting and construct a mathematical problem.
USING LITERATURE TO BUILD MATHEMATICAL THINKING
Several of my lessons followed a template of identifying the mathematical objective, choosing a book, writing a word problem on large chart paper, and sending that problem to the classroom for students to work on before they came to the library. Students excitedly brought the problem, their work, and their answers to the library. Together we explored various means of getting to the solution, often including the use of manipulatrves. Talk led by questioning was rich in examples and allowed us to think of problems in novel ways and untangle the thinking that led to wrong answers. And somehow, there was always a piece of literature included.
McKinney & Hinton (2010) promote the inclusion of literature in mathematics because it
- Connects mathematics to the real world
- Stimulates mathematical discourse among students
- Provides an avenue for mathematical problem solving investigations
- Provides illustrations that represent different mathematical concepts
One of these word problems was created for a third grade classroom studying elapsed time close to the Thanksgiving holiday. This was the problem they received:
The old lady is invited for Thanksgiving dinner that will include turkey, bread, salad, squash, and pie. Everything needs to be ready at 530. The bread was prepared ahead of time. The turkey will take four and a half hours. The squash will take 20 minutes. The pie will take 45 minutes and the salad will take 15 minutes to prepare. What time will you need to start cooking each item for it to be finished at 5:30?
This problem came from the book I Know an Old Lady Who Swallowed a Pie. An old lady swallows everything, gets bigger and bigger, and finally becomes a giant balloon in a Thanksgiving Day parade.
If you have ever prepared a large meal, the timing problem may be familiar. I always told my students, if you sit down for dinner and everything is ready and on the table, then someone had to have solved a similar problem. In this case, when students came to the library they found practice clocks at the tables and worked together to use the clocks to check their work. The solution generally involved creating a table for each item with the start time, elapsed time, and end time. Organizing data is an important information literacy skill, necessary in solving many complex mathematical problems.
HOW BIG IS AN INCH, PETER RABBIT?
I have created several lessons that involved measurement or area and perimeter. One year teachers were concerned that their students were not going to the next grade level with a concept of how big an inch was. I read Little Dog Poems and gave each student a 1x1” square sticker and colored pencils with directions to draw a picture showing the little dog from the book. These stickers were then stuck together to create a little dog quilt. I talked again and again about the dimensions of the stickers, and by the time students had drawn their masterpieces, I suspect most had a strong feel for how big an inch was. This lesson could be adapted to any story you choose to share.
Whenever I think of area and perimeter, I think of garden problems. How much fencing do you need? What square footage can you plant? Gardens remind me of Beatrix Potter, Mr. McGregor, and Peter Rabbit. Other garden books could be used as well to frame problems of area and perimeter.
Sometimes a book itself is a great mathematical problem. How Many Seeds in a Pumpkin? by Margaret McNamara features the well-loved primary lesson involving predicting, estimating, and counting the number of seeds in a pumpkin. Illustrations show how groups of students used different types of grouping (by 2s, by 5s, or by 10s) to count. The story includes the common misconception that the larger number of groups (not just how many are in a group) represents the larger quantity. I opened up the pumpkin at home, extracted, washed, and baked the seeds ahead of time. There were between three and four hundred seeds in one pumpkin. I divided them up into five baggies. When students came to the library I had the pumpkin with the lid carefully replaced and asked them how many seeds they thought would be in it before revealing that they would count them. Then we read the story together and they went in groups to five tables where they worked together to estimate, group, and count the seeds from their bag. Everyone's totals were combined for a grand total that was later displayed in the library for everyone to count.
PROBABILITY AND SOME LITTLE PIGS
Occasionally teachers presented me with a math concept where I struggled to find an obvious literature connection. One year I was asked to teach probability to fourth graders. I began to look in the 700s for games involving chance and found one called PIG. Players roll a die to get numbers to draw body parts of a pig. The first one to draw a complete pig wins. A player must first roll a six to draw the pig's body; other numbers are assigned to other body parts. For example, 1 is a head, 2 is a leg, 3 is an arm, 4 is the tail, and 5 is an ear. The word problem involved determining the probability that a player would roll a 6 when it was his turn, or would roll a 1,2, or 3 in one of the other turns, and so on. I chose to read The Three Little Wolves and the Big Bad Pig by Eugene Trivizas, but any pig story might be chosen, and, of course, students should have the chance to play the game.
COWS, GRAPHS, AND POTATO CHIPS
Graphs are an obvious feature of many reference books. In particular an almanac is full of graphs, tables, and charts. Dare I say the possibilities to create word problems that involve using the index to locate and read graphs seem endless? One year a fourth grade teacher and I created problems that we put together as a challenge center for her students. A lesson using Bubba the Cowboy Prince involved sending a graph of top cow populations by state to a class with several graph-reading questions. When the students came to the library we talked about the state with the most cows, Texas. Then I moved into how a fractured fairy tale might take a familiar story and put it in a new setting with new characters. Features of the setting, for example that Texas has lots of cows, might then determine how the tale will be fractured. In this case the Cinderella character is a cowboy and the fairy godmother is a cow.
The potato chip lesson involved graphing nutritional information from three kinds of potato chips: regular, baked, and sour cream and onion. Students came to the library made predictions based on their observations, including taste, and then used labels to gather information about calories, sodium, sugar, carbohydrates, fat, and calcium content of the chips. While they ate the chips, I read George Crum and the Saratoga Chips, a true story about the invention of the potato chip. Students took their data back to class and created graphs. These graphs were posted in our teacher's lounge, near the snack machine. The results provided information about the comparative nutritional value of different kinds of potato chips that was not obvious to consumers.
The potato chip lesson is perhaps one of the best illustrations of the importance of connecting mathematics to the Standards for the 21st-century Learner. Students created new knowledge that was valuable to the greater school community and their findings were shared with an authentic and interested audience. Their work had real-world value and involved them in a lifelong skill of reading nutrition labels and critically thinking about the comparative nutritional value of various chips. They found that the question of which chip was healthier depended on your need. The baked chips, for instance, were lower in fat but had more sodium and sugars. Of course, it didn't hurt public relations for the school library to have this work displayed in a spot frequented by administrators as well as teachers.
SPREAD THE WORD: THE SCHOOL LIBRARY IS THE MATH PLACE!
We occupy a space in the school rich in numbers and numeracy where questions abound. School librarians have long been familiar with integrating curriculum. Who is in a better position to broker connections with mathematics and literature, with data and critical thinking, and with mathematical questions across the curriculum and throughout the school? We need to spread the word to mathematics educators that we will be strong partners in inquiry learning.