Making "cents" of decimals: expert advice on using pocket change to teach a tough topic.

Third-grade teacher Kristina Shultz has a math-class challenge many upper-elementary teachers share. "My kids have trouble with decimals," she says. "They just don't seem to understand tenths, hundredths, and numbers smaller than one. They also have trouble transferring this knowledge to money. They'll write $3.5 for three dollars and five cents."

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Sure enough, decimals can be a tough concept for students who are used to dealing largely with whole numbers. Over the years I've learned that the most effective way to introduce decimals (or any new material) is a two-pronged approach: Build on students' knowledge and give them concrete experiences with the new ideas. Once students have a base of understanding, I help make the connection to mathematical symbolism and vocabulary. Here are the steps I go through in order to teach decimals.

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STEP 1: SHOW THEM THE MONEY

When introducing decimals, I find it useful to rely on what children know about money--specifically pennies, dimes, and dollars--and to provide them the concrete tools of pennies and dimes (real or play) and replicas of dollar bills. First I make sure that the children understand the relationships between pennies, dimes, and dollars--that, for example, 10 pennies are equivalent to one dime, and 100 pennies are equivalent to $1.00, and 10 dimes are also equivalent to $1.00. I also check that students can represent these amounts symbolically. I usually find that while students use the dollar sign to show one dollar (writing $1, for example), they rely on the cents sign to show amounts less than one dollar (23 cents instead of $0.23).

STEP 2: PLAY "RACE FOR $1.00"

"Race for $1.00" is a great game to build number sense and lay the foundation for introducing decimal notation. Students play in pairs. Each pair needs a 1-6 number cube, a supply of about 20 dimes and 20 pennies, and two $1.00 "bills." Each player makes a recording sheet like this.

Students take turns rolling. When players roll the cube, they take either that many pennies or that many dimes and write their choice on their recording sheet. After six turns, they each figure out how much money they have and record their total. They check each other's figuring and see who got closer to $1.00. Can they trade in their coins for one of the bills? If so, are there still coins left over? How much money is it? If they don't have enough to make $1.00, how much more money do they need?

When first teaching the game, don't focus on the notation. Just let students become familiar with the game. When rolling a three and taking three dimes, for example, some children may write 3 in the dimes column, others may write 30 cents, and a few might even write $0.30--it doesn't matter for now. Once students have played a round or two, you can introduce the concept of decimal notation for money. Here's where you establish that each type of coin has its own place in the number. Have them practice reading and writing different amounts using the dollar sign notation--$0.35, $0.71, $0.05, and so on. Then have them play "Race for $1.00" again, this time using a new recording sheet that has them use this notation.

To change the game, have students play "Race for $2.00." The rules stay exactly the same but the new goal of $2.00 will require them to change their numerical strategy.

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STEP 3: TALK ABOUT PLACE VALUE

As the children become more confident, you can add in information about the values of the places and the relationship of these decimal numbers to the whole numbers. Place value is one of the biggest concepts children need to grasp at this stage of their math careers, and they need many experiences to help cement their understanding. We've traditionally asked students to demonstrate place value knowledge by identifying the place a digit in a particular number holds. For example, we might ask students, "How many hundreds are there in 3,412?" Or, "What place does the four hold in 3,142?" A correct response indicates that the student knows where the hundreds place is. But it does not necessarily mean that the student understands the meaning of the four, that it represents four groups of one hundred. This sort of understanding develops from children exploring how to group objects, seeing that when they have 132 objects, they can make one group of 100, three groups of ten, and have two extras.

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STEP 4: EXTEND THE LEARNING

Money can also be helpful for giving students experience with adding and subtracting decimals. For example: If you buy an apple for $0.39 and raisins for $0.25, how much money do you need? First ask the students to estimate if they need more or less than $1.00. (Playing "Race for $1.00" should have helped them think about estimates.) Then have them figure, using coins if needed. Finally, connect their reasoning to the correct terminology and record the equation horizontally and vertically.

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For more practice, try the "Books for Teaching Decimals" on this page. Students will enjoy these stories, and grow more confident in their abilities.

* WIN * More help from Marilyn. See p. 59.

RACE FOR $1.00

       DIMES  PENNIES

   1)  -      -
   2)  -      -
   3)  -      -
   4)  -      -
   5)  -      -
   6)  -      -

TOTAL  -      -

RELATED ARTICLE: Books for Teaching Decimals

* PIGS WILL BE PIGS by Amy Axelrod (Aladdin, 1997). This story is about the Pig family's search for money to go out to their favorite restaurant. Ask students to listen as you read and estimate the total amount of money the pig family finds. When you finish, ask students to report their estimates. Then reread, this time asking a volunteer to record the amounts found. Compare the actual amount ($34.67) with the children's guesses.

* ALEXANDER, WHO USED TO BE RICH LAST SUNDAY by Judith Viorst (Aladdin, 1987). When Alexander receives a dollar, he feels rich--but the feeling doesn't last! He finds so much to buy that soon he has only bus tokens. First read the book aloud in its entirety. Then reread it, stopping each time Alexander spends some of his dollar. Ask your students to figure out how much he has left. Have the students figure mentally or give them coins to use, but either way, have them explain their reasoning.

IDEAS ADAPTED FROM MARILYN BURNS CLASSROOM MATH LIBRARIES, TO ORDER, CALL 1-800-SCHOLASTIC OR GO ONLINE TO HTTP://TEACHER.SCHOLASTIC.COM.

ASK THE EXPERT

Marilyn Burns

Marilyn Burns is the founder of Math Solutions Professional Development (www.mathsolutions.com) and the author of 13 books for children and 23 books on teaching math. Have a question for her? E-mail [e-mail].