In Your Child's Classroom Emphasis on Real-World Problem Solving The math your fifth-grader is learning emphasizes real-world math applications and problem solving.

Computational skills are imbedded into the activities but are not taught in isolation as they may have been when you went to school.

A successful lesson engages students to problem solve and use mathematical reasoning to do tasks that engage students. Students work in groups to solve real-world problems such as figuring out how much paint would be needed to paint the classroom.

Wendy Miller, North Carolina's 2006 Teacher of the Year, explains that your child will be building on material that's been previously introduced so that she can master it. "Fifth-graders will experience a spiraling and challenging curriculum," she says. "There will be a blend of understanding math concepts and applying skills to solve real-world problems. The fifth-grade classroom should provide students an opportunity to use problem-solving strategies to solve authentic tasks."

Your child may figure the sale price of an item when a store advertises that it's 60% off. She might keep track of her grade- point average or figure the square footage of carpet needed for the classroom. She may work in groups to cooperatively find a solution to math problems. She may also 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. She'll engage in activities that require her to think about numbers and number relationships.

Kathy Rank, Ohio's 2005 Teacher of the Year, notes: "Students will spend more time exploring concepts through activities and will learn to justify their thinking as they write about mathematical operations. I want students to discover mathematical concepts and relationships, and learn to picture those concepts in their minds as they learn to recognize the connections between math and the world."

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 In fifth grade your child works with very large numbers (in the billions) and very small ones (in the thousandths), decimals and fractions. Your child continues to build on the "number sense" he has learned in previous years. 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.

Your child will work with place value. She'll learn that in the number 7980.76, the 9 has a value of 9 hundreds and the 6 has a value of 6 one hundredths. In a lesson about place value, she may be asked to compare similar numbers (such as 56,008 and 56,080) on a number line or with the symbols for greater than (>), less than (<) and equals (=). Your child will learn to convert decimals and fractions as she learns to order and compare different types of numbers.

Fifth-grade students also may learn about negative numbers by placing them on a number line. Students will relate negative numbers to real-world situations, such as a loss of money or below-zero temperatures.

Learning to estimate In fifth grade, your child works with estimation and rounding of whole numbers and decimals, which will help him with addition, subtraction, multiplication and division of large numbers. She learns different estimation strategies to determine whether a solution is reasonable. Students will apply these strategies as they estimate the amount of money needed for a shopping trip or the population of a city.

Learning computation skills Your fifth-grader adds, subtracts, multiplies and divides with decimals, fractions and whole numbers. By the end of the year, he will typically be multiplying three-digit numbers by two-digit numbers (42 x 638) and dividing five-digit numbers by one, two, three-digit numbers (64459/3) with and without remainders. He will also be adding and subtracting five-digit numbers. He solves word problems using strategies to determine the operations needed. For example:

John has $13.56. He needs to buy binders for school. If each binder is $3.50, how many binders can he buy? How much change will he have? (Answer: He can buy three binders and will have $3.06 in change.)

The properties of multiplication learned in earlier grades become increasingly important as students progress in their mathematical thinking.

• Commutative property: When two numbers are multiplied together the order does not change the product. 6 x 3 = 3 x 6 = 18
• Associative property: When three or more numbers are multiplied, the product is the same regardless of the order of multiplication. (3 x 2) x 4 = 24 3 x (2 x 4) = 24
• Distributive property: The sum of two numbers multiplied by a third number is equal to the sum of the numbers being added multiplied by the third number. 2 x (6 + 3) = 2 x 6 + 2 x 3
• Property of one: The product of one and another number is the number itself. 7 x 1 = 7
• Zero property: The product of zero and another number is zero. 8 x 0 = 0

Algebra In algebra, mathematical relations are explored by using letters or symbols to represent numbers. Your child will use algebraic thinking to solve real-world problems using tables and graphs.

Your fifth-grader learns to take information from a graph or equation to answer questions about a problem. For example, a graph could show the number of chaperones needed for a field trip as one chaperone for every five students. Your child would be asked to look at the graph and tell how many chaperones would be needed if X number of students were going on the trip.

Your fifth-grader will use and solve for an unknown variable that stands for a number in an equation. For example:

5N + 2 = 12, the N is the unknown variable and N = 2.

She will solve problems in which she has to write the equation and graph the resulting information on a grid. To graph the equation she needs to find the ordered pairs, which are any two numbers used to give the location of a point on a graph. For example, your child may be asked to solve the following:

An ice cream cone costs $2. Write an equation showing the cost of buying one or more ice creams and graph the ordered pairs on a grid. The equation would be 2 x i = p (i = number of ice creams; p= price.) So, if you bought one ice cream the ordered pair would be (1, 2), two ice creams (2, 4), and so on.

Geometry In geometry, studying points, lines, shapes and figures provides students with an understanding of the structure of space and spatial relations. Your fifth-grader learns about the characteristics and relationships among points, lines, line segments, rays, planes and shapes. She measures right, acute and obtuse angles using a protractor. She will also learn the properties of equilateral, right, scalene and isosceles triangles.

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 polygons Your child learns about polygons, the closed figures formed by line segments. She will construct and measure polygons with up to 10 sides. She will use the formula a=lw to find the area of a polygon and will begin to use a formula to find the volume of a prism. She will be able to, label the diameter and radius of a circle, and find its area and circumference.

Exploring graphs Your child continues 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. Your child will be placing points on the graph with a horizontal and vertical value. Graphing is a skill your child will use in other subjects, such as science and social studies to present and understand information.

Measurement Your child continues to work to measure with accuracy, using metric and U.S. standard units. He knows whether to use a ruler, scale, thermometer or clock to measure length, width, height, temperature, weight, capacity and depth. He measures objects such as desks, books and doors, and solves problems involving elapsed time in hours, minutes and seconds. He will also measure and convert temperatures in degrees Fahrenheit and Celsius.

Data and Probability Your child interprets and compares information from circles, line and bar graphs. She generates survey questions, collects responses and then creates an appropriate graph to display the data. She can interpret and explain the data and identify 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.

Your child will predict the possible outcomes of an event, such as tossing the dice, displaying the results and comparing them to his predictions.

State Math Tests Your child may take a state-level math test at the end of fifth-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 February 2008