In 5th grade math concepts cover a broad range of mathematics topics. These are the math concepts that students must understand after completing fifth grade based on the National Mathematics Standards.

**Numbers and Operations** concepts fifth grade students learn
include place value represented in whole numbers and decimals. Students
apply and recognize parts of fractions as units of whole numbers,
along with finding fraction locations on a number line. They use common
fractions, decimals, and percents in numerical models and physical
models to represent whole numbers.

Students learn to locate and plot numbers less than 0 on a number line using negative whole numbers, fractions, decimals, and percents. They use addition and multiplication in problem solving situations that involve reciprocal functions in subtraction and division. Other mathematical operations include the distributive laws in multiplication and addition. They must be able to mentally compute multiplication and division problems, such as 10 x 50 and 50 ÷ 10. Students develop fluency in arithmetic computations using whole numbers and fractions. They learn to estimate mental computations, and check with calculators and pencil/paper.

**Geometry **concepts include classifying and developing an understanding
of two and three dimensional objects, such as: squares, rectangles,
pyramids, cubes, cones, spheres, cylinders, etc. They also study how
polygons relate to parallel and perpendicular lines. Additional areas
of geometry and shapes are the focus of transformations and symmetry
of shapes as they are flipped, rotated, and turned. Further explorations
are in the development tessellations, congruence, and similarities
of geometric shapes. They learn to make connections of geometric shapes
to everyday objects.

Fifth grade students also learn how to construct geometric shapes to find their area and volume, using mathematical formulas. These include squares, prisms, rectangles, cones, circles, spheres, cylinders, etc. They also spend time learning how to apply geometric shapes to real world applications, along with connections to of content subject areas. Additional concepts in this area include the distance between given points on a straight line, along with points on horizontal and vertical lines.

**Algebra** students develop representations of patterns and functions
using words, tables, graphs, and models. They explore and computer
whole numbers using the commutative, associative, and distributive
properties. In addition, they learn to apply variables to mathematical
problems to the second variable level. They develop a basic understanding
of expressions and equations.

**Measurement** concepts focus on using customary standard and
non-standard units of measurement and determine the relationships
between varieties of objects. This is also connected with geometry
as they learn how to measure the area, volume, and mass of different
geometric shapes. They learn how to measure all aspects of circles,
prisms, and pyramids.

Students apply measurement applications to the conversion of U.S. customary units of measurement into the metric system. They develop a basic understanding of meter, liter, and grams; including their variables. They learn to apply estimation skills for determining the shape, volume, area, and mass of different objects.

**Data Analysis and Probability** concepts focus on using appropriate
language to explain findings in mathematical experiments and simulations.
They learn how to develop questions that help find the differences
between two or more samples in a population.

Students use data tables to construct line plots, bar graphs, and line graphs. They use data to draw conclusions and predictions collected in observations, experiments, and surveys. They develop mathematical theories for explaining events that will result in likely or unlikely outcomes. They interpret data that are represented on graphical plots to make predictions of likely outcomes.

**Problem Solving** for fifth grade students focuses on the development
of problem solving strategies to help them develop a fundamental understanding
of mathematics. Students use word problems and other real world simulations
in problems solving situations.

**Representation** concepts focus on students learning to collect
and organize data, then using the data to solve problems. Answers
are presented as models that are numerical, written, physical, and
social. They are able to draw graphs, charts, tables, and other forms
to explain how they solved a problem.

**Connection** concepts are designed for fifth grade students
to demonstrate how to make connections to real world applications
and other subject content areas. This includes making connections
with other concepts in mathematics.

**Communicate** their mathematics ideas in the form of sentences,
drawings, posters, and multimedia applications is another concept
that students need to master. This is used to ascertain their level
of understanding as they explain mathematical concepts to other students
and teachers.

**Reasoning and Proof **concepts are used to explain mathematical
findings and problem solving techniques. This is necessary so that
they develop skills on how to present logical arguments to math situations.

All of these mathematical concepts are used to develop a well rounded base knowledge of mathematical ideas and language as students' progress to higher levels of mathematics.