Last fall results from national math exams stirred up a tempest in a standardized test. It turns out math scores rose more quickly before No Child Left Behind was implemented, and fourth-grade math scores haven’t improved since 2007. As reported in the New York Times, the achievement gap remains a chasm between the haves and the have-nots.

What does this mean for your child? While pundits and politicians battle over the big issues, it’s up to parents to stay on top of the little ones: their own kids’ academic development. Keep tabs on what your third grader should learn in math this year with our grade-based milestones. Of course, math curricula still vary widely from state to state as school districts grapple with how to implement the Common Core Standards, so these are merely guidelines. For a better sense of how your child’s schoolwork compares, look up your state’s math standards, see what the National Council of Teachers of Mathematics recommends for preschool through high school, or read through the Common Core Standards for math.

In the classroom

What math concepts will your third grader learn?

“Every math concept your child is introduced to will form the basis for all future math studies,” says Linda Eisinger, the 2005 Missouri Teacher of the Year.

Third graders move from addition and subtraction to multiplication and division. At this stage, teachers will introduce the concepts behind those math operations using pictures and objects.

Because many kids at this age have a keen interest in how things are put together, your child may develop an interest in rules and logic. As a whole, third graders tend to be full of enthusiasm but lack patience: They may give up easily on more difficult assignments but respond well when a project is broken down into smaller, more manageable chunks. While they may need help from the teacher on getting organized and tackling challenges, they can be productive in small groups.

Mastering math operations

Third graders should be comfortable with the basics of arithmetic — addition, subtraction, multiplication, and division — and using them in computation exercises and problem solving. Fact families help your child think about the relationship between multiplication and division. For example, if 3 x 4 = 12 and 4 x 3 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3.

“In third grade the emphasis is on the recall of facts,” Eisinger explains. “This helps greatly when trying to introduce new concepts like regrouping and multiplication.”

From fractions and geometry

Third graders are introduced to fractions via measuring and weighing objects. They may also work with angles and perimeters, creating geometric patterns with pencil and paper.

Knowing numbers

In third grade your child will learn to count by 100s up to 1,000 and beyond. He or she will also learn about place value and how to read and write four-digit numbers.

Time, money, and graphs

Third graders should become more familiar with telling time, learning to tell time to the minute quickly. A typical exercise would be: “It’s 2:45. How much time has passed since 2:15?”

Though they may be more familiar with pocket change, third graders will get a chance to work with $5, $10, and $20 bills. They should also learn how to make change — and for this type of learning, leading questions can be beneficial: “How much change should Alex get if he gives the clerk a $20 bill and his groceries cost $18.25?”

Third-graders also continue to work with graphs, learning about line graphs and more sophisticated types of bar graphs.

Calculators: Tool or crutch?

How much should elementary school students rely on calculators? The issue has been debated by math teachers, university professors, and parents, but there is general agreement that calculators shouldn’t be a substitute for learning basic arithmetic skills. Talk to your child’s teacher about how they are used in his or her classroom. For a discussion on the pros and cons of calculators, check out Education World’s article “Educators Battle Over Calculator Use: Both Sides Claim Casualties.”