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California 2007 U.S. Fifth grade (average age 10 years old ) mathematics standards:

Link to California standards

Number Sense

1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers:
1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.
1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.
1.3 Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication.
1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 23 x 3).
1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals:
2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.

2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.
2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.
2.4 Understand the concept of multiplication and division of fractions.
2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Algebra and Functions

1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results:
1.1 Use information taken from a graph or equation to answer questions about a problem situation.
1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.

1.3 Know and use the distributive property in equations and expressions with variables.
1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.
1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid.

Measurement and Geometry

1.0 Students understand and compute the volumes and areas of simple objects:
1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rec 1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects.
1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm3], cubic meter [m3], cubic inch [in3], cubic yard [yd3]) to compute the volume of rectangular solids.
1.4 Differentiate between, and use appropriate units of measures for, two-and three-dimensional objects (i.e., find the perimeter, area, volume).

2.0 Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:
2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software).
2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems.
2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.

Statistics, Data Analysis, and Probability

1.0 Students display, analyze, compare, and interpret different data sets, including data sets of different sizes:
1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ.
1.2 Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets.

1.3 Use fractions and percentages to compare data sets of different sizes.
1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph.
1.5 Know how to write ordered pairs correctly; for example, ( x, y ).

Mathematical Reasoning

1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and apply them in other circumstances.

Florida 2007 U.S. Fifth grade mathematics standards:

Link to Florida standards

MA.5.A.1.1 Describe the process of finding quotients involving multi-digit dividends using models, place value, properties and the relationship of division to multiplication.

MA.5.A.1.2 Estimate quotients or calculate them mentally depending on the context and numbers involved.
MA.5.A.1.3 Interpret solutions to division situations including those with remainders depending on the context of the problem.
MA.5.A.1.4 Divide multi-digit whole numbers fluently, including solving real-world problems, demonstrating understanding of the standard algorithm and checking the reasonableness of results

MA.5.A.2.1 Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties.
MA.5.A.2.2 Add and subtract fractions and decimals fluently and verify the reasonableness of results, including in problem situations.
MA.5.A.2.3 Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding.
MA.5.A.2.4 Determine the prime factorization of numbers.

MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces.

MA.5.G.3.2 Describe, define and determine surface area and volume of prisms by using appropriate units and selecting strategies and tools

MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations.
MA.5.A.4.2 Construct and describe a graph showing continuous data, such as a graph of a quantity that changes over time.

MA.5.G.5.1 Identify and plot ordered pairs on the first quadrant of the coordinate plane.
MA.5.G.5.2 Compare, contrast, and convert units of measure within the same dimension (length, mass, or time) to solve problems.
MA.5.G.5.3 Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement.
MA.5.G.5.4 Derive and apply formulas for areas of parallelograms, triangles, and trapezoids from the area of a rectangle.

MA.5.A.6.1 Identify and relate prime and composite numbers, factors and multiples within the context of fractions.
MA.5.A.6.2 Use the order of operations to simplify expressions which include exponents and parentheses.
MA.5.A.6.3 Describe real-world situations using positive and negative numbers.
MA.5.A.6.4 Compare, order, and graph integers, including integers shown on a number line.
MA.5.A.6.5 Solve non-routine problems using various strategies including “solving a simpler problem” and “guess, check, and revise.”

MA.5.S.7.1 Construct and analyze line graphs and double bar graphs.
MA.5.S.7.2 Differentiate between continuous and discrete data and determine ways to represent those using graphs and diagrams

Oregon 2007 U.S. Fifth grade mathematics standards:

Link to Oregon standards

It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations.
5.1 Number and Operations and Data Analysis: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.
5.1.1 Use fraction models to represent the addition and subtraction of fractions with unlike denominators.
5.1.2 Use decimal models, place value, and number properties to add and subtract decimals (to the thousandths).
5.1.3 Select and use appropriate strategies to estimate fraction and decimal sums and differences.

5.1.4 Develop fluency with efficient procedures for adding and subtracting fractions and decimals and justify why the procedures work.
5.1.5 Solve problems involving the addition and subtraction of fractions and decimals.
5.1.6 Use ordered pairs on coordinate graphs to specify locations and describe paths.
5.1.7 Construct and analyze double bar, line, and circle graphs to solve problems involving fractions and decimals.

5.2 Number and Operations and Algebra: Develop an understanding of and fluency with division of whole numbers.
5.2.1 Apply understanding of models for division (e.g., equal-sized groups, arrays, area models, equal intervals on the number line) and the relationship of division to multiplication to solve problems.
5.2.2 Apply concepts of place value and the properties of operations to solve problems involving division.
5.2.3 Select and use appropriate estimation strategies for division (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers.

5.2.4 Develop and use accurate, efficient, and generalizable methods to find quotients for multi-digit division problems.
5.2.5 Develop fluency with efficient procedures for dividing whole numbers and justify why the procedures work on the basis of place value and number properties.
5.2.6 Determine the most appropriate form of the quotient and interpret the remainder in a problem situation.

5.3 Geometry, Measurement, and Algebra: Describe and relate two-dimensional shapes to three-dimensional shapes and analyze their properties, including volume and surface area.
5.3.1 Identify and classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).
5.3.2 Find and justify relationships among the formulas for the areas of triangles and parallelograms.
5.3.3 Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular- and square-based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or vertices as well as types of faces.
5.3.4 Recognize volume as an attribute of three-dimensional space.

5.3.5 Determine volume by finding the total number of same-sized units of volume that fill a three-dimensional shape without gaps or overlaps.
5.3.6 Recognize a cube that is one unit on an edge as the standard unit for measuring volume.
5.3.7 Determine the appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume.
5.3.8 Decompose three-dimensional shapes and find surface areas and volumes of triangular and rectangular prisms.
5.3.9 Identify and measure necessary attributes of shapes to use area , surface area, and volume formulas to solve problems (e.g., to find which of two gift boxes needs the most wrapping paper or has the greater volume?).

Australia , China , Japan, Malaysia, New Zealand, Singapore, and other APEC countries

Link to math standards for 9 APEC members (the Asia-Pacific Economic Cooperation group). Note that some have rather large PDF files.