In Your Child's Classroom Emphasis on Real-World Problem Solving The math your fourth-grader is learning may look different from the math that you learned in school. Today, for example, there is an emphasis on real-world math applications and problem solving.

Wendy Miller, North Carolina's 2006 Teacher of the Year, explains: "In the fourth grade classroom, lifelong skills should be embedded in the curriculum and in daily lessons. Students should develop skills such as reasoning and problem solving in order to be productive in a globally diverse society. The purpose of math in the fourth grade is to help students make the connection from classroom math concepts and processes to real-world problem solving."

Your child may map a bus route or determine how much paper is needed to cover a bulletin board. She may learn more than one way to solve a problem, focusing on the process and not just the solution. She works to develop an understanding of mathematics, rather than just memorizing rules, and engages in activities that require her to think about numbers and their relationships. She may work in groups to cooperatively find a solution to math problems.

Kathy Rank, Ohio's 2005 Teacher of the Year, explains: "Having students work in groups is an extremely effective technique for getting students 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."

Math Topics and Standards Math is separated into topics that are taught sequentially. The name and number of topics vary from state to state and textbook to textbook. The topics we are covering here are numbers and operations, algebra, geometry, measurement, and data and probability.

Academic standards in math describe what your child should be learning. You can look up your state's math standards and compare it with the work your child is doing to see if he is learning what your state's standardized tests will measure. But this is sometimes difficult because some state standards include long lists of expectations and no clear areas of emphasis for each grade.

The National Council of Teachers of Mathematics has released a listing of the three topics it considers most important for each grade from K-8. The NCTM's short list is an attempt to start a discussion about making the study of math more consistent and coherent, the group says. The "focal points" have already been the subject of many news stories and are certain to be discussed in your state and district.

Numbers and Operations Your child is expected to read and write whole numbers to the millions and understand number place value through the millions.

Your fourth-grader works to understand numbers — ways of representing them, relationships among them and number systems. Your child continues his work from previous years on "number sense." Number sense is the ability to understand numbers, and work with them in a variety of ways — from computing mentally, to estimating and judging whether an answer seems reasonable.

He may still use visual models and "manipulatives," such as base 10 blocks, to develop his understanding of numbers.

He might be asked to place whole numbers, decimals or fractions in order from largest to smallest on a number line. He learns to use the symbols for greater than (>), less than (<) and equals (=) symbols to compare numbers.

Mastering math facts Because your child will be computing with larger numbers in the fourth grade, it is important for her to recall her math facts quickly. She should know times tables up to 10. By the end of the year, she will typically be multiplying three-digit numbers by two-digit numbers (example: 42 x 638) and dividing four-digit numbers by one-digit numbers and by 10 (example: 7445 ÷ 4) with and without remainders. She will also be adding and subtracting five-digit numbers.

Learning the meaning of operations Your fourth-grader will understand meanings of operations and how they relate to one another, learning to explain the relationship between addition and subtraction, and the relationship between multiplication and division. Your child will solve word problems involving addition, subtraction, multiplication and division using whole numbers, fractions and decimals. He will be asked to select the appropriate computational and operational method to solve multi-step problems. For example:

Four children ate two pizzas. There were eight slices in each pizza. If each child ate the same number of slices how many slices did each child have? (2x8) ÷ 4 = 4 slices of pizza each.

Working with fractions and decimals Your child will add and subtract fractions with like denominators (the bottom number of the fraction). For example,

3/8 + 2/8 = 5/8

To develop their number sense, students learn to compare fractions to decide whether the fraction is closer to a half or a whole. Students typically relate decimals — also a type of fractional number — to money because this is a familiar context. She will compare fractions and decimals to learn, for example, that the decimal 0.5 represents the fraction 5/10 and the decimal 0.25 represents the fraction 25/100. She will add and subtract decimals, and place decimals in order from smallest to largest. Your child will also round decimals to the nearest tenth, hundredth or to the nearest whole number. She should be able to tell you that 1.768 rounds to 1.77 to the nearest hundredth, 1.8 is to the nearest tenth and 2 is to the nearest whole number.

Algebra In algebra, mathematical relations are explored by using letters or symbols to represent numbers. Students begin to understand the concepts by using "manipulatives" and visual models. Students learn about the area, which is the formula A=lw by using blocks to build flat figures. Students may also use tile blocks to cover a diagram and then count how many blocks cover the area.

In fourth grade your child begins to solve equations using parentheses. For example, your child should know that 5(4) is the same as 5 x 4. He will also learn the order of operations when parentheses are used. In the problem (8+3) x 2, the parentheses tell the student that she should add 8+3 together before multiplying the sum by 2.

Your child will learn that adding or multiplying the same number to both sides of an equation does not 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, studying points, lines, shapes and figures provides students with an understanding of the structure of space and spatial relations. Your child learns that a point is a single location in space and a line is a group of points that goes on forever in both directions. He learns about rays and how they form angles. He compares and measures right angles, obtuse angles and acute angles. He identifies and draws perpendicular, parallel and intersecting lines using a ruler.

Miller explains: "Geometry is a part of everyday life for many professionals. 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 to solve authentic problems."

Learning about two- and three-dimensional figures Your fourth-grader will use vocabulary, such as faces and edges, to describe that two- and three-dimensional figures have faces and edges. He uses the names of different polygons and closed figures, such as hexagons and octagons. He will draw and classify polygons having up to eight sides. He will learn 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. He also will measure the perimeter and area of polygons. He may use a geoboard to make different polygons, stretching rubber bands from one nail to another or construct polygons using toothpicks or straws. He may explore polygons in architecture or in the objects in the classroom.

Exploring tessallations Fourth-graders explore tessellations, which are a repetitive pattern of shapes that cover an area with no gaps and no overlaps. Your child will make tessellations and explore tessellations in the world around him such as in honeycombs and in art. Students will see how tessellations fit into the environment and will be surprised at how many examples they are able to find once they can identify a tessellation. Interior designers, quilt makers, graphic designers and architects all use tessellations. Students will investigate the geometric concept of angles and symmetry as they turn shapes by using translations, rotations and reflections to explore tessellations.

Learning about coordinate graphs Using graphs and coordinate systems your child will be asked 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.) Your child will be placing points on the graph with a horizontal and vertical value. This skill is needed to later develop algebraic logic. The coordinate plane is an important tool to use when working with equations that have two variables. It is a way to draw pictures of equations that makes them easier to understand. Students will also use this concept as they develop map reading skills including longitude, latitude and any other navigational systems. Even a space shuttle uses a grid system to locate specific points and objects on the shuttle as it is hard to keep track of things when there is no up or down because of the lack of gravity.

Measurement Through measurement, students develop an understanding of the importance of precision and accuracy. Your child will use both metric and standard units, measuring length, weight, capacity and temperature using common tools such as a ruler, a thermometer, a measuring cup and a scale. She will be asked to select appropriate units of measure such as inches, miles, pounds or pints. If she's asked to measure the length of a book, she should know to use a ruler and provide the answer in inches or centimeters. She will measure and compare temperatures in degrees Fahrenheit and Celsius, learning the temperatures when water freezes (0ºC and 32ºF) and boils (100ºC and 212ºF). She will 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 commonly displayed in a fourth-grade classroom. Your child learns to interpret and display data on bar, circle and line graphs. He will come up with survey questions and represent the data in an appropriately labeled chart or graph. He will also learn to find the mode (the value that occurs most frequently), median (the midpoint), mean (the average), and range (the difference between the greatest and smallest values) for a data set. He'll also begin to learn how data are collected and used in the real-world.

Probability is making predictions about what will happen next. Your child will make predictions for simple probability situations and record possible outcomes of a simple experiment such as a coin toss or dice throw. He'll learn that when flipping a coin the probability of it landing heads up is 50%.

State Math Tests Your child may take a state-level math test at the end of fourth-grade. To see if your state releases its test questions, search your state Department of Education Web site.

Calculators How much should elementary school students use calculators? The question has been debated by math teachers, university professors and parents. There is general agreement though that they should not be used as a substitute for learning basic arithmetic skills. Talk to your child's teacher about how calculators are used in your classroom. The pros and cons of calculator use are discussed in this Education World article:

Educators Battle Over Calculator Use: Both Sides Claim Casualties

Updated January 2008