Math in Numbers — and Words

Today’s 4th graders must not only come up with the right answer — they must explain their reasoning, too.

Fourth grade is a pivotal year in math. Although there aren’t many new subjects introduced, your child will explore several topics, especially long division and fractions, in greater depth. Being able to compute quickly and accurately becomes more vital, and those who can do calculations with ease may be grouped separately from those who need more time.

In 4th grade, your child will be expected to:

Have a solid grasp of number facts
Be able to do more difficult long-division problems
Have a conceptual understanding of fractions
Be able to explain in words how a math problem was solved

It’s natural for kids to arrive at school in September rusty in their multiplication skills. Most teachers start the year reviewing and evaluating their students. My daughter’s teacher would break up the monotony of repetition with games such as “Around the World,” where kids take turns circling the classroom answering math facts to see who can get the farthest. Kids also have to answer a flash card correctly to get in and out of the classroom. A game called “Connect 24,” where students try to create different equations that amount to 24, is also popular in 4th grade classrooms. This is a fun way to hone the important skill of “mental math,” where students become comfortable calculating in their heads by taking apart and recreating numbers in various combinations. Education experts applaud these methods. “Kids have to know their number facts cold,” says Susan Sclafani, Ph.D., assistant secretary of education and a leader of the U.S. Department of Education’s math and science initiative. “That fluency comes from lots of engaging ways of learning math facts.”

Long Division and Fractions
Tracking Begins
Solve It, Explain It

Long Division and Fractions
Confidence with calculations comes in handy when students tackle long division with double-digit divisors. “There are many steps involved in long division,” says Lauren Fernicola, 4th grade teacher at Brookdale Avenue School in Verona, New Jersey. “The better children are at multiplication, the better they are at long division.” Good number sense and estimation skills also help, since long division requires kids to make educated guesses about how many times a certain double-digit number, say 34, might go into 395.

Much time is also spent in 4th grade on fractions. In the past, fractions were treated superficially — students were given a set of rules that covered computing with fractions. But if they missed or forgot a rule, they were lost. “Fear of fractions has been a tripping point for many adults with math anxiety,” says Cathy Seeley, president of the National Council of Teachers of Mathematics. “Modern classrooms put an emphasis on giving fractions a deeper, longer treatment so kids really understand them.” In addition to understanding conceptually the relationship of a fraction to the whole, and of fractions to each other, 4th grade students learn how decimals and fractions relate to each other.

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Tracking Begins
Differences in math ability become more evident in the 4th grade. Some kids can do a string of calculations in their heads, others struggle to add 8 plus 6. Children who rely on counting on their fingers or on other crutches may begin to fall behind. Many schools begin some sort of tracking now, either by dividing a class informally into small groups that can work at the same pace, or by having different teachers for different math levels.

Whatever level a child is at, teachers work hard to help students enjoy math and boost their skills. Educators know, however, that the more abstract a concept is, the more kids struggle. That’s why the best teachers try to relate math to everyday life, and come up with a range of activities to keep kids engaged. For example, a teacher might ask students to add up their own spelling grades and divide to find the average. Cooking is another great activity to boost math sense. In my daughter's 4th grade class, the kids spent an afternoon making muffins. They gained a better understanding of what fractions mean, along with a hands-on lesson in proportions and the relative size of cups, pints, quarts, and other units of measure. They even practiced converting to the metric system, since the teacher asked them to convert cups into the metric equivalents using their knowledge of decimals and multiplication skills.

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Solve It, Explain It
Problem-solving, an ever-important math skill, ties together the important concepts of number sense, data analysis, and basic computation skills. Students in my daughter's 4th grade class start the day working on and then discussing the “problem of the day.” Teachers stress that there are usually several ways to approach a problem; in the end the children must show their mathematical reasoning in words as well as numbers.

In many school districts, practice in solving open-ended questions is extra-important, since these problems are a new feature of the standardized tests administered to most 4th graders in the spring. These exams, mandated by the No Child Left Behind testing signed into law in 2002 but administered by individual states, aim to judge whether the district’s children are meeting performance standards set by the states. They usually include multiple choice tests as well as open-ended math problems. Children are graded on their mathematical reasoning along with their answer.

Julia Martin Langan, a freelance writer and the mother of three school-age children, lives in Verona, New Jersey.

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