Math in fifth grade is a time to master the concepts acquired to this point. Students also learn to apply these concepts and mechanics to more complex numbers. They study and learn the language of math as well as the actual computations. They learn to actively use these concepts and their math vocabulary in solving real world problems. They use strategies to decide which steps to take and in what order, deciding how to best use the tools they now have.
Numbers in fifth grade math go from very large to very small. Students take fractions and decimals down to the thousandths and integers up to a billion. Students are taught to order these numbers and in doing so, learn to convert decimals and fractions. Negative numbers are introduced situations where negative numbers may occur are discussed. Geographical locations below sea level and temperatures below freezing are negative numbers the students will be able to relate to.

Students in fifth grade refine their rounding and estimation skills. New estimation strategies are introduced to compare answers and to ensure a reasonable solution. These estimation skills also help to give the student reassurance that an answer to a difficult problem is correct.
In this grade, students learn to find factors of numbers and also to determine if a number is prime or composite. They build on the properties of multiplication they have already learned. They learn to multiply fractions and decimals. Word problems are increasingly complex with multiple steps required to solve them. They learn that when 2 numbers less than zero are multiplied, the answer is a number smaller than either of the 2 original numbers. Other operations include an introduction to algebraic equations using letters or symbols to represent numbers in equations. Fifth grade students also learn how to extrapolate information from a chart or graph.
In geometry, students learn to measure circumference. Problems needing real world solutions are addressed using perimeter, area and volume equations. Students learn more about spatial relations by studying the characteristics and relationships among points, lines, rays, shapes and planes. New tools such as protractors and compasses are introduced.
Children learn to measure accurately and creatively. They can measure items that are out of reach by measuring a similar item they can reach or by measuring the part they can reach and multiplying to get a result. They learn to make a determination as to whether an estimated result or accurate solution needs to be reached. Time is measured in increments both smaller, seconds, and larger, centuries. Students can use calendars, schedules and planners to solve real time problems. Temperature can be converted from Fahrenheit to Celsius.
Fifth graders use graphs and charts to provide information they can interpret and compare. They are also creating graphs and charts. They create a grid with 4 sections and plot points with ordered pairs of whole numbers on the horizontal xaxis and vertical yaxis.
Predicting possible outcomes and graphing probabilities are tasks a fifth grader complete in the course of the school year. The students may work on projects that generate survey questions and interpret the data to identify the mode, median, mean and range.
By the end of the school year, the fifth graders have learned that the principles of math they have been accumulating since first grade or even kindergarten will be useful in every aspect of their lives. They have learned to analyze a problem and use their skills and learned strategies to break it into smaller divisions to make solving it easier. After achieving a solution, they can defend their answers and support them with evidence.