Fractions & Skills Math From Grades 3 to 5
To prepare for algebra, experts say, elementary students must learn how to work with fractions
math education, with a report on development of crucial analytic and computational skills.
Redskins Give an Assist
Football fans in Ellen Harrison's class had no time to grieve after the Washington Redskins lost the season opener. There was math to do.
Harrison, a math teacher at Judith A. Resnik Elementary School in Gaithersburg, gave fourth-grade students a worksheet as they walked into class: "There were 79,742 fans at the stadium who watched the Redskins lose." Students were told to write the number in expanded notation (showing the value of each digit), then in words. Later, they puzzled over how to read numbers that stretch into the hundreds of thousands or millions.
As third-graders, students learned to plot whole numbers and simple fractions on a number line and compare numbers up to 10,000. This year, the work gets harder. By year's end, the fourth-graders should have a grasp of multiplication and division. They'll tackle addition and subtraction of some fractions and decimals. And they'll learn to solve for an unknown in a simple equation. All that prepares them to solve problems with fractions, decimals and percents in fifth grade.
Harrison, a former Rand Corp. analyst and math major, said her students are learning fundamentals. Any skill they fail to grasp will snowball into later problems.
"For long division, you need to be able to add, subtract, multiply and estimate," she said. "If you miss any one of those concepts, you can make a mistake along the way."
The Fifth-Grade Factor
Vern Williams knows what happens when students get to middle school and don't know how to add 2/3 and 7/8 .
"Trouble," he said. "Big trouble."
It turns out that fractions -- those little numbers kids learn to manipulate in third, fourth and fifth grades -- are a big stumbling block for many students.
Educators and policymakers who fret about global competitiveness often point to algebra as a gateway to higher math. But teachers say that for many kids who struggle with algebra, the problem starts much earlier.
"Teachers will tell you if you don't get a good foundation by the fifth grade you are in tremendous trouble," said Williams, a math teacher at Longfellow Middle School in Falls Church who was a member of the presidential National Mathematics Advisory Panel. "You don't have to know how to do an algebraic equation before we get you. But please know how to add, subtract, multiply and divide fractions."
So what's so intimidating about decimals and fractions? For many elementary students, Williams said, working with such numbers demands a little more brainpower. Practice and effort, he said, pay off.
"If you have 1/5 plus 1/7 , you want it to be 2/12 . That would be so simple," Williams said. "But then you run into these nasty things called common denominators. And then you have to add them. And then the teacher is going to get upset if they're not simplified. It's 'I have to do five steps just to get an answer.' "
(Which in this case is 12/35 .)