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 fourth 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 fourth grader learn?

The math your fourth grader is learning might be a little different from what you learned in school: Now there’s more emphasis on real-world applications. “The purpose of math in the fourth grade is to help students make the connection between classroom concepts and real-world problem-solving,” says Wendy Miller, the 2006 North Carolina Teacher of the Year.

What’s real-world problem solving? Try: mapping a daily bus route or figuring out how much paper you’d need to plaster a café bulletin board with ads for yoga courses. Long story short, your kid may learn more than one way to solve a problem, focusing on the process — not just the solution. Typically students at this age work to develop an understanding of mathematics and engage in activities that require complex thought instead of just memorizing rules. Children may also work in groups to find solutions to tough math problems.

According to Kathy Rank, Ohio’s 2005 Teacher of the Year, “Having students work in groups is an extremely effective technique for getting them actively involved in doing math. It is important that students share solutions and explain their thinking and that they know their ideas will be valued.”

### Knowing numbers

Fourth graders should be able to read and write whole numbers and understand place value into the millions.

Students will also gain a deeper understanding of numbers in general, learning how they relate to each other as well as new ways to represent them. Continuing the work they started in previous years, fourth graders should hone their number skills, from mental computations to estimation to judging whether an answer seems reasonable.

In the classroom, fourth graders may rely on visual models and objects like base 10 blocks to develop their understanding of numbers. Kids may be asked to arrange whole numbers, decimals, and fractions on a number line. They may also learn to compare numbers using the symbols for greater than (>), less than (<), and equals (=).

### Mastering math facts

Because your child will be working with larger numbers, it’s important for them to be able to recall math facts quickly. They should know times tables up to 10. By the end of the year, they’ll typically be multiplying three-digit numbers by two-digit numbers (like 42 x 638) and dividing four-digit numbers by one-digit numbers and 10 (like 7,445 ÷ 4) with and without remainders. They’ll also be adding and subtracting five-digit numbers.

### Understanding the meaning of operations

Fourth-graders should understand the meaning of operations and be able to explain the relationships between addition, subtraction, multiplication, and division. Some teachers use word problems that involve addition, subtraction, multiplication, and division using whole numbers, fractions, and decimals.

For example: Four children ate two pizzas, each with eight slices. If each child ate the same number of slices, how many slices did each child one have? The answer: (2 x 8) ÷ 4 = 4 slices each.

### Working with fractions and decimals

Your child will be expected to add and subtract fractions with like denominators (the bottom number of the fraction). For example: 3/8 + 2/8 = 5/8.

Developing number sense, students learn to compare fractions and decide whether the fraction is closer to a half or a whole.

Teachers typically relate decimals to money, which provides a familiar context. By comparing fractions and decimals, students learn to equate them, recognizing, for example, that the decimal 0.5 represents the fraction 5/10 and the decimal 0.25 represents the fraction 25/100. They’ll learn to add and subtract decimals and arrange decimal numbers in order from smallest to largest. On top of that, they should know how to round decimals to the nearest hundredth, tenth, or whole number. For example, fourth-graders should be able to tell you 1.768 rounds to 1.77, the nearest hundredth, 1.8, the nearest tenth, and 2, the nearest whole number.

### Algebra

Algebra is the exploration of mathematical relations using letters, symbols, and numbers. Teachers will begin to help students understand these concepts using objects and visual aids. Students learn about area by using the formula area = length x width (a=lw) and by using blocks to build flat figures. Students might be asked to cover a surface with tile blocks and calculate its area by counting the blocks.

Fourth-graders will also start to solve equations using parentheses. For example, they should know that 5(4) is the same thing as 5 x 4. Students also learn the order of operations involving parentheses. In the problem (8+3) x 2, the parentheses tell the student that he or she should add 8+3 before multiplying the sum by 2.

They’ll learn that adding or multiplying the same number to both sides of an equation doesn’t change the equation. For example: If Y- 8 = 12, Y equals 20. If you add 5 to both sides of the equation, you have (Y- 8) + 5 = 12 + 5 and Y still equals 20. If you multiply 2 to both sides of the equation, you have (Y- 8) x 2 = 12 x 2 and Y still equals 20.

### Geometry

In geometry, students gain an understanding of space by studying points, lines, shapes, and figures. Children should learn that a point is a single location in space and that a line is a group of points that goes on in both directions and is endless. Students will learn about rays (lines that begin at a point and extend indefinitely) and angles — including right, obtuse, and acute angles. It’s equally important to be able to measure and draw perpendicular, parallel, and intersecting lines using a ruler.

“Geometry is a part of everyday life for many professionals,” says Miller. “Graphic designers, landscapers, and architects use geometry daily to express their creativity. Math is more than numbers. Math is a form of art when using geometry.”

### Learning about two- and three-dimensional figures

Fourth graders will be introduced to new vocabulary, using words like *faces *and *edges *to describe the characteristics of two- and three-dimensional figures. They’ll use the names of different polygons and closed figures, such as hexagons and octagons, and learn to draw and classify polygons with up to eight sides. Fourth graders should also know that two polygons are congruent if their angles and sides are equal and that the line of symmetry divides a polygon into two equal parts. In class, teachers often use geoboards — the crazy brainchild of Egyptian mathematician Caleb Gattegno — which let kids create many types of polygons with just a few rubber bands. Students can also learn about polygons by looking at examples from architecture.

### Tesselation escalation

In fourth grade, students make time for tessellations, repetitive patterns of shapes that cover an area without any gaps or overlaps — think M.C. Escher. In many classes children create tessellations and are asked to explore them in the natural world, where they occur in honeycombs and other structures.

Once students can identify a tessellation, they’re often surprised by just how many examples they can find in the world around them. Everyone from interior designers to architects uses them. As they explore tessellations through translation, rotation, and reflection, students draw on the geometric concepts of angles and symmetry.

### Grasping coordinate graphs

Your child will probably be asked to use graphs and coordinate systems to identify, locate, and plot ordered pairs of whole numbers. (A coordinate graph is a grid with four sections with a horizontal x-axis and a vertical y-axis.) They’ll need to plot x and y values on the graph, a skill important in developing algebraic logic. The coordinate plane is an important tool for solving equations with two variables, offering a way to present equations visually and make them easier to understand. Students will need to use this concept as they develop map-reading skills. (Hey, even a space shuttle uses a grid system to locate specific points and objects onboard, as it’s hard to keep track of things — you know, with the lack of gravity and all.)

### Measurement

Measurements help students develop an understanding of precision and accuracy. Kids should use both metric and standard units to measure length, weight, capacity, and temperature, using common tools like rulers, thermometers, measuring cups, and scales. They’ll be asked to select appropriate units of measure — inches, miles, pounds, or pints — and if asked to measure the length of a book, for example, they should know to use a ruler and provide the answer in inches or centimeters. By comparing temperatures in Fahrenheit and Celsius, students will learn the temperatures at which water freezes (0ºC and 32ºF) and boils (100ºC and 212ºF). Lastly students should learn to convert larger units of measure to smaller ones, such as meters to centimeters, minutes to seconds, and feet to inches.

### Data and probability

Charts and graphs are common accessories in many fourth-grade classrooms, where students are learning to interpret and display data on bar, circle, and line graphs. They’ll practice devising survey questions and learn to represent data in appropriately labeled charts or graphs. Moreover, students will learn new probability vocabulary: mode (the value that occurs most frequently), median (the midpoint), mean (the average), and range (the difference between the greatest and smallest values). They should learn about how data are collected and used in the working world.

Probability is about making predictions about what will happen next, and to learn about probability, fourth-graders typically record possible outcomes of simple experiments that might include a coin toss or dice throw. They should learn that when flipping a coin, the probability of it landing heads-up is 50%.

### Calculators

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.”

### State math tests

At the end of fourth grade, your child may be required to take a state math exam that measures student progress. To see if your state releases its test questions, search your state Department of Education’s website.