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.