In grades 3 through 5, math concepts have a very broad range of mathematics topics. However, these are the math concepts that students should understand by the end of the fifth grade based on the National Council of Teachers of Mathematics standards.

When it comes to **Numbers and Operations** concepts these are
the concepts that students study. They learn place values using the
base ten system as represented in whole numbers and decimals. Students
recognize parts of fractions as units of whole numbers, along with
finding locations on number lines. They use common fractions, decimals
and percents in models and other forms in 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 be able to mentally compute multiplication and
division problems, such as 20 x 40. Students develop fluency in arithmetic
computations in whole numbers and fractions. They learn to estimate
using mental computations, along with using calculators and pencil/paper.

In the area of **Geometry** concepts they learn to classify and
develop an understanding of two and three dimensional objects, such
as: squares, rectangles, cones, spheres, cylinders, etc. They also
study the polygons as they relate to lines that are parallel and perpendicular.
Additional areas of geometry and shapes will be the focus on 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

Third through fifth grade students also learn how to construct geometric shapes to find the area and volume of objects, 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 that students will explore are the distance between given points on a straight line, along with points on horizontal and vertical lines.

In the mathematical concept area of **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 begin to develop an understanding of expressions and equations.

The concept area of **Measurement** is focused on the using standard
and non-standard units of measurement to determine the relationships
between different objects. This also be 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 length, mass, volume, size, and angles of different objects to using formal and informal units of measure. Students explore the concepts of the metric system as they learn to convert U.S. customary units of measurement into the metric system. They learn to apply estimation skills for determining the shape, volume, area, and mass of different objects.

In the concept area of **Data Analysis and Probability**, students
use appropriate language to explain their findings in experiments
and simulations. They learn how to develop questions that will help
them find the differences between tow samples in a population.

Students use data on tables to **plot the data on line plots, bar
graphs, and line graphs**. This will then be used to draw conclusions
and predictions from data that was collected in observations, experiments,
and surveys. They develop mathematical theories for explaining events
that will result in a likely or unlikely outcome. They interpret data
that is represented on graphical plots to make predictions of likely
outcomes.

When it comes to **Problem Solving**, students develop 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.

In the concept are of **Representation**, students will learn
to collect and organize data. Then use the data to solve problems.
Answers are presented as models that are physical and social. They
are able to draw graphs, charts, tables, and other forms to explain
how they solved a problem.

For **Connection** concepts students learn to make connections
to real world applications and other subject content areas. This includes
making connections with other concepts in mathematics.

Students learn to **Communicate** their mathematics ideas in the
form of sentences, drawings, posters, and multimedia applications.
This be used to ascertain their level of understanding as they explain
mathematical concepts to other students and teachers.

Students use logical Reasoning and Proof to explain their mathematical findings and problem solving techniques.

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.