“It's about ducks!” Nelson exclaimed after my introduction. “Ducks go quack,” he added.
“Let's find out,” I responded. I opened to the first spread and read, “Seven ducklings in a row. Count those ducklings as they go.” The children counted along with me as I pointed to each of the ducklings.
I asked the children to count as I read the next rhyme — first the six ducklings on the left and then the one duckling on the right.
“How many ducklings do you think there are all together?” I asked. Some of the children knew that there were seven, while others weren't so sure. Together we counted all of them to verify that there were indeed seven!
I continued reading the rest of the book aloud and asking questions in this same way. On each page, we counted. We then had a class discussion of the book, talking about all the things the ducklings did.
For the second reading, I turned the focus to recording equations that would show our work. As I read, I wrote number sentences on chart paper to keep track of the ducklings. For example, as the children counted the six ducks on the left and one on the right, I recorded:
7 = 6 + 1
I had the children read the number sentence aloud as I pointed to the symbols. Then I invited them to help me write equations for the rest of the story. A nice feature of this story is that the illustrations near the end of the book encourage thinking about seven with more than two addends. When we finished the rereading, the chart looked like this:
7 = 6 + 1
7 = 2 + 5
7 = 5 + 2
7 = 1 + 6
7 = 4 + 3
7 = 2 + 3 + 2
7 = 3 + 4
7 = 2 + 2 + 2 + 1
I then gave the children seven Unifix cubes each and had them show the combinations by representing each addend with a “train” of cubes.
Lastly, I gave the children an independent assignment. Each child chose one of the number sentences from the chart, copied it, and illustrated it. “You can draw ducklings or any other shapes,” I told them. The result: artful number sentences from ducks to diamonds! Children ready to take on an additional challenge also wrote and illustrated their own equations, with combinations of more than two numbers that added up to seven.
After reading the story together, the children and I launched into a measurement lesson. We used a one-inch square tile to measure the length of the inchworm in the book.
Then I put down the book and asked the children, “I wonder if any things in our classroom measure about one inch long.” We tested various items — the width of a chalkboard eraser, the length of a pencil, the spines of several books. None was close. Then I held up an envelope with a postage stamp on it. Several of the children clapped when they saw that a side of the stamp was just about one inch long. Then we measured a quarter and discovered that it was one inch across.
On a sheet of chart paper, I wrote One Inch and underneath recorded stamp and quarter. With the One-Inch Challenge underway, the children moved about the classroom with their one-inch tile “worms” in search of objects to measure. As they called out items, I listed them on the chart. After about 10 minutes, I called the children back to the rug and we reviewed the items on our list, from crayon stubs to barrettes.
Next we moved on to measuring longer lengths, starting with our index fingers. I traced my index finger on the board and showed them how I could measure its length in two ways-using tiles and also using a 12-inch ruler. We next measured a pencil and the height of a tissue box using the same two ways. I showed the children that there are three possible ways to record our measurements, as shown below:
Finger: 3 inches, 3 in., 3"
Pencil: 7 inches, 7 in., 7"
Tissue Box: 4 inches, 4 in., 4"
Armed with a tile and a ruler, each child set off to measure at least five objects and record their findings in the three ways.
After about five minutes, I stopped the children to ask what we could do when a measurement wasn't an exact number of tiles, or fell between two numbers on a ruler. We talked about choosing the number that was closest (rounding) or, if they couldn't tell, adding half of an inch to the measurement.
A few weeks later, we repeated the activity again. First, we reread the book, savoring the story and the illustrations. Then the children again set off on a measurement quest, this time recording an estimate for each item before measuring. Afterwards we compared our estimates and the actual measurements. The children charted their results on posterboard.
When the math lesson ended, the children had the chance to take the book and their measuring tools home to share the story and their new skills with their families.
Knowing that I typically come to her third-grade class to teach a math lesson, Areli raised her hand and said, “I bet we get to figure out how many people came to the party.”
“You're exactly right,” I said, and reread the passage describing the guests: 2 sons, 3 daughters, 14 grandchildren, 35 great-grandchildren, 1 great-great-grandchild, and 47 other friends.
“Can we use paper to figure it out?” Brittany wanted to know.
“Let's try adding in our heads,” I suggested. I wanted to give the children valuable and much-needed practice with mental calculation. “Then we'll check our answer with paper and pencil,” I added.
The children attacked the problem using a variety of strategies, and we recorded each one. For example, after we had determined that 19 people had arrived (adding the 2 sons, 3 daughters, and 14 grandchildren), I asked, “How many would there be when we add on the 35 great-grandchildren?” I wrote on the board: 19 + 35.
Assia offered her strategy first:
19 + 10 = 29
39 + 10 = 49
29 + 10 = 39
49 + 5 = 54
Kevin used a different method:
35 + 10 = 45
45 + 5 = 50
50 + 4 = 54
Working together and sharing strategies, we finally figured out that 102 people attended Lily Laceby's party. The children then turned to paper and pencil to check our work.
This Night Noises lesson illustrates several important benefits of using children's books for teaching math. It connects a basic skill — mental addition — to a “real-life” example and encourages different ways to arrive at answers. It supports communication in math class by asking students to explain their thinking. Lastly, recording their strategies helps children make the connection between their reasoning and mathematical symbols.
Marilyn Burns is the founder of Math Solutions Professional Development, dedicated to improving K–8 math instruction. Ideas for using these and other books appear in her Math, Literature, and Nonfiction series. For information, visit www.mathsolutions.com. This article was originally published in the April 2005 issue of Instructor.