Innovative ways to add math into daily activities!
Close your eyes. Think about the steps you go through to group students for an activity. How do you determine the number of groups and the number of students in each group? What mental math skills do you use to figure it out? Verbalizing vour solution process — or sharing your thoughts with students so that they can effectively crawl inside your brain — is what´s known as a "think-aloud." Jeffrey Wilhelm writes, "Think-alouds make invisible mental processes visible to children." (See "Think-Alouds Boost Reading Comprehension," Instructor, Nov./Dec. 2001, page 26.)
Math think-alouds engage students and help them make their way step-by-step through a solution process, reasoning right along with you. Best of all, math think-alouds can be used quite effectively both in school and at home. Research has proved that young children can comprehend spoken words and ideas before their speech is fully developed. Similarly, your students can understand a more complex or difficult solution process than they can execute independently. By thinking aloud, you share a thought process that may be too sophisticated for them to come up with on their own, but one which they are able to comprehend by hearing.
Once such a solution is learned and practiced by children, they can begin to apply it independently to other math problems they encounter.
THINK ALOUDS IN SCHOOL
Here are several math think-alouds that you can share with your students during the course of the school day.
Find Elapsed Time
Think aloud about how many minutes until the class needs to be ready for their next class, a special activity such as an assembly or guest speaker, or lunch. Even if your students have not yet learned how to calculate elapsed time, they should be familiar with the concept of time and the terms used to measure it. (If you are teaching primary grades, limit the elapsed time think-alouds to either hours or minutes, rather than both, so that your thought processes are within students' reach.)
You might say, "I know lunchtime is at 12:00. It's 11:40 now. I can count by fives to see how many minutes until lunchtime: 11:45, 11:50, 11:55, 12:00. I counted by five minutes four times, so that's 20 minutes in all. Lunch is in 20 minutes."
Other elapsed time think-alouds include finding:
- The number of minutes or hours since the school day began
- The number of minutes in a class
- The total number of hours spent at school in a day
After several elapsed-time think alouds, some students will begin to pick up the process. Ask: How does such a skill help us? How often might we use it?
Work With Money
Think aloud about how much money will be I collected if seven cartons of milk are ordered for 50 cents each. You may begin by saying, "One carton of milk is 50 cents. If I skip-count by 50 cents seven times, I can find the total cost: 50 cents, $1.00, $1.50, $2.00, $2.50, $3.00, $3.50. So 7 cartons of milk at 50 cents each is $3.50." You may wish to emphasize that there is more than one way to arrive at the total cost by adding, "Let me check to make sure that's right. I'll use a different strategy this time. If one carton of milk costs 50 cents, then two cartons cost $1.00. I have three groups of two cartons, that's $3.00. And 50 cents more for the seventh carton would make a total of $3.50." Invite students to offer additional strategies, perhaps involving multiplication, repeated addition, or other mental math.
Older students may benefit from hearing you think aloud about how to arrange their papers in a bulletin board display. You may say, "We want to display your work on the bulletin board. Each paper is about 9 inches wide and 12 inches long. We will also need space between each paper. The bulletin board is about 80 inches wide. I can fit 7 papers in a row — that's 63 inches — with plenty of space between each paper. The board is about 60 inches tall, so I can make 4 rows (48 inches) with space in between. That means I can display 4 rows of 7, or 28 papers on the board."
Other math think-aloud topics that fit naturally into your day involve data analysis of daily occurrences. Think aloud about how to compare the number of sunny days with cloudy ones, how many more days until the end of the month, or how many more students buy than bring lunch one day. To highlight estimation, think aloud about how to estimate the numher of tiles on the floor, or about how many buttons are worn in the classroom on one day.
THINK-ALOUDS AT HOME
Math think-clouds need not be limited to the classroom-parents can also think aloud about their daily math routines! Here are several think-clouds that parents can use to heighten children's awareness of math at home. Send the ideas home in a newsletter or e-mail, or share them during parent-teacher conference night.
Car Pool & Practice
Suggest that parents think aloud about how they determine when to leave their home to pick up students in a car pool and arrive at soccer practice on time, for example. They might say, "Practice starts at 4:00 p.m. We're about 15 minutes from the ball field, and we need about another 10 minutes to pick up Jackie and Keisha. That's 25 minutes in all. So if we leave 25 minutes before 4:00, or at 3:35, we should arrive on time."
Preparing a Meal
Parents can also think aloud about the math they use when preparing a meal. Younger children can learn about how an ingredient is measured: "I need onehalf cup of oil. I'll pour oil into this measuring cup until it reaches the mark that shows one-half cup." Older children can find out how ingredients are measured to make the appropriate number of servings: "I need about five ounces of chicken for each person. There are four of us. Four times five ounces is 20 ounces. Since there are 16 ounces in one pound, I need about one pound four ounces, or one and onefourth (one quarter) pounds."
Cost of Groceries
Most of us have estimated the total cost of our groceries as we place them on the check-out counter. Parents can share their strategies for doing this simply by thinking aloud as they estimate. As they do, their children will hear how rounding, mental math, and number sense are used in a real-life setting. Children might hear, "Cereal is $3.99, that´s about $4.00. The milk is $1.79, that´s about $2.00. Four plus two is six, so that´s $6.00 so far. We have bananas for $1.59 and bread for $2.49 — another $4.00. Added to the $6.00, that´s $10.00. Plus two candy bars at 49 cents each, that´s $1.00; so this will cost about $11.00 in all."
Other math think-alouds parents can do include calculating when to begin to prepare dinner for a specific serving time, doubling or halving a known recipe, estimating the cost of a special event, calculating a tip, and estimating the time needed to get ready for school. Math think-alouds help your students to become more aware of mathematics in everyday life. Several ideas for implementing math think-alouds have been offered here, but there are many more. By sharing mental solution strategies aloud at school (with parents doing the same at home), your students are exposed to how math concepts are used and applied. Children will soon develop their own solution strategies — ones they will use daily for the rest of their lives. Best of all, they will truly understand the usefulness and importance of what they learn during math class.
Robyn Silbey is a school-based math specialist in Montgomery County, Maryland.