Marilyn Burns: Simple Ways to Assess Math Sense

Written by Rusty Bresser and Stephanie Sheffield
Edited by Marilyn Burns

Take it from us — assessing what students know in mathematics can be a real challenge. What number concepts are children comfortable with? Struggling to grasp? On the verge of understanding? We found fertile ground for evaluating students in straightforward activities that we based on two captivating children's books. While the moral of the books may be that things aren't necessarily the way they seem, the moral for us is this: Teachers don't have to look any further than everyday activities for rich assessment opportunities. Choose from:

Stephanie's Primary Lesson

Marc Harshman poetically begins his book Only One (Cobblehill, 1993), "There may be a million stars, but there is only one sky. There may be 50,000 bees, but there is only one hive." Each page of this beautifully illustrated countdown book contrasts a collection of things with a single object, sending the message to children that while something may belong to a group, it can, nevertheless, be unique.

Step 1

After reading the book aloud to my first graders, I ask students to think about how the pages are alike or different. Some may notice that the numbers at the beginning of the book are very large, diminish by leaps, and finally end up decreasing by ones. Others may point out that each page contains the words only one.

Step 2

I reread the pages that state, "There may be 11 cows, but there is only one herd. There may be 10 cents, but there is only one dime." Then I ask: Why must the page about dimes feature the number 10, while the page about the herds doesn't have to be about 11? I have children discuss why some words are specific to a particular number and why others could work for a variety of numbers.

Step 3

On the blackboard or a sheet of chart paper I make two columns, one labeled Dime and the other, Herd. Then I review the book with students, asking children to classify the object or animal featured on each page as a member of the dime or herd category. As students decide, I add the word to our class chart in the appropriate column. Some of the pages, I've discovered, require a bit of discussion. For instance, my students felt that the page that reads, "There may be 9 players..." was open to interpretation. The illustration shows a baseball team that has a set number of positions, but students decided to include team in the herd category. The word, they reasoned, doesn't necessarily imply a specific number of players.

Step 4

I have my class create our own Only One books. To get the publication process rolling, I ask students to brainstorm ideas for our book and record their suggestions on the board under either the Dime or Herd heading.

Step 5

Once we have a dozen or so examples (including larger numbers as well as several from which to count down by ones), students decide which number to use to kick off our book and which number to use to start counting down by ones.

Rusty's Intermediate Lesson

A Million Fish...More or Less by Patricia C. McKissack (Knopf, 1992) is a tale of adventure and one-upmanship set in a Louisiana bayou. Hugh Thomas doesn't know what to make of the whopper stories his friends Papa-Daddy and Elder Abbajon tell him. Are his friends telling the truth? Before Hugh has the chance to figure it out, he finds himself alone in the middle of a bayou where he catches three small fish, and then . . .a million more! To match the tales that Papa-Daddy and Elder Abbajon have been telling, Hugh conjures up an action-packed story complete with tangles with alligators and raccoon bandits.

Step 1

After reading the book to my fifth/sixth graders, I return to the part of the story where Hugh throws half of his catch back. To check students' number sense, I ask: If Hugh really had a million fish and threw half back, how many fish would he be left with? I give students time to talk in small groups and then ask for volunteers to give and explain their answers.

Step 2

For students who aren't comfortable thinking about halving one million, I have them look for patterns: "What is half of 10?" I record the answer on the board and then we continue incrementally as follows:

number | half
10 | 5
100 | 50
1,000 | 500
10,000 | 5,000
100,000 | 50,000
1,000,000 | 500,000

Step 3

I return to the part of the story where Hugh offers Mosley half of the fish he has left. I ask: How much is half of 500,000? I give children time to figure this out and have volunteers explain their solutions.

Step 4

I build the next part of the lesson on the exaggerations in the story, using several examples. First, I reread: "Take the time back in '03 me and Elder here caught a wild turkey weighed five hundred pounds!" I say to students: Five hundred couldn't be the number of pounds a turkey weighs, but it could be . . . I leave the last part of the sentence for students to complete, writing down several suggestions. Next, I reread the part of the story in which Hugh jumped 5,553 times in a jump-rope contest. I say: Maybe 5,000 isn't the number of times a person jumps rope, but it could be . . . Again, I leave the sentence for students to finish.

Step 5

I write on the board: " _ could not be the number of _, but it could be the number of _." and ask students to suggest numbers we could use to begin the sentence. (Students have suggested numbers ranging from 3 to 1,000,000.) Then I have children pick a number, use it to complete the sentence, and illustrate their work.

Step 6

After students share their completed sentences — explaining why the number they chose is reasonable for some things but unreasonable for others — we bind their papers into a class book.

Stephanie Sheffield (Math), a first-grade teacher in Houston, Texas, and Rusty Bresser (Math), a fifth/sixth-grade teacher in San Diego, California, are the authors of Math and Literature books, published by Math Solutions Publications from Marilyn Burns Education Associates. The books are available from Cuisenaire.

Marilyn Burns (Math), a household name to elementary teachers across the country, is the creator of Math Solutions, inservice workshops offered nationwide. She is also the author of numerous books and articles.

 


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