National Math Standards Grades 3-5

By Pamela S. Stevens

Children from the 3rd through the 5th grade cover a variety of subjects, ranging from multiplication to fractions to decimals.

Here is a rough guideline, parents may find helpful:

3rd Grade

By the 3rd grade, kids will begin to think of numbers in sets or groups and be able to apply numbers to situations. For example, they will learn to count by sets such as by 3s, 5s, 7s and so on as well as by groups of 10s or 100s. They should be able to formulate basic equations from word problems or everyday life situations. They will learn how to count money and change, understand place values, be able to use measuring devices and tell time and begin geometry.

In terms of geometry, they will be able to recognize and name three-dimensional shapes and learn about symmetry. They will also learn how to interpret charts and graphs. Of the programs we looked at, The Quarter Mile Math Level 1 or Young Einstein Mathematics include hundreds of drills and can be used to increase speed, accuracy and math confidence in basic skills.

4th Grade

In the 4th grade, kids learn about fractions, multiply whole numbers efficiently, can estimate, can apply a variety of measuring units and add/subtract decimals. They will do word problems and learn about the function rule. In geometry, they start to work with points, lines and rays as well as learn about transformation, congruency and the coordinate system.

5th Grade

By the 5th grades, kids are able to work with large numbers, decimals, improper fractions and mixed numbers and can compare equivalencies such as fractions and percents. They will begin to work with angles and sliding, flipping and turning of two-dimensional shapes and learn to identify three-dimensional shapes from their two-dimensional representations. They will learn to determine the mean, median and mode of data sets and make predictions based on probability. The program Math Arena includes games that incorporate slides, flips and turns. Mighty Math Calculating Heroes includes a good activity area that helps with comparing 2D representations of 3D objects.

These are the National Standards as outlined by the National Council of Teachers of Mathematics for 3rd through 5th graders. Your child should have all of these concepts mastered by the end of the 5th grade.

Understands numbers, ways of representing numbers, relationships among numbers and number systems

• Understands the place-value structure of the base-ten number system and can represent and compare whole numbers and decimals
• Recognizes equivalent representations for the same number and generates them by decomposing and composing numbers
• Understands fractions as parts of unit wholes, as parts of a collection, as locations on number lines and as divisions of whole numbers
• Uses models, benchmarks and equivalent forms to judge the size of fractions
• Recognizes and generates equivalent forms of commonly used fractions, decimals and percents
• Explores numbers less than 0 by extending the number line and through familiar applications
• Describes classes of numbers according to characteristics such as the nature of their factors

Understands meanings of operations and how they relate to one another

• Understands various meanings of multiplication and division
• Understands the effects of multiplying and dividing whole numbers
• Identifies and uses relationships between operations such as division as the inverse of multiplication to solve problems
• Understands and uses properties of operations, such as the distributivity of multiplication over addition.

Computes fluently and makes reasonable estimates

• Has developed a fluency with basic number combinations for multiplication and division and uses these combinations to mentally compute related problems
• Can add, subtract, multiply and divide whole numbers
• Develops and uses strategies to estimate the results of whole-number computations and to judge the reasonableness of results
• Develops and uses strategies to estimate computations involving fractions and decimals in situations relevant to students' experience
• Uses visual models, benchmarks and equivalent forms to add and subtract commonly used fractions and decimals
• Selects appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools

Measurements

• Understands such attributes as length, area, weight, volume, and size of angle and selects the appropriate type of unit for measuring each attribute
• Understands the need for measuring with standard units and is familiar with standard units in the customary and metric systems
• Can perform simple unit conversions, such as from centimeters to meters, within a system of measurement
• Understands that measurements are approximations and how differences in units affect precision
• Can evaluate what happens to the measurements of a two-dimensional shape such as its perimeter and area when the shape is changed

Understand patterns, relations, and functions

• Describes, extends and makes generalizations about geometric and numeric patterns
• Can represent and analyze patterns and functions, using words, tables and graphs

Represents and analyzes mathematical situations and structures using algebraic symbols

• Identifies such properties as commutativity, associativity and distributivity and uses them to compute with whole numbers
• Grasps the idea of a variable as an unknown quantity using a letter or a symbol
• Can express mathematical relationships using equations

Uses mathematical models to represent and understand quantitative relationships

• Models problem situations with objects and use representations such as graphs, tables or equations to draw conclusions

Analyzes characteristics and properties of two- and three-dimensional geometric shapes and develops mathematical arguments about geometric relationships

• Identifies, compares and analyzes attributes of two- and three-dimensional shapes and develops vocabulary to describe the attributes
• Classifies two- and three-dimensional shapes according to their properties and develops definitions of classes of shapes such as triangles and pyramids
• Investigates, describes and reasons about the results of subdividing, combining and transforming shapes
• Explores congruence and similarity
• Makes and tests conjectures about geometric properties and relationships and develops logical arguments to justify conclusions

Specifies locations and describes spatial relationships using coordinate geometry and other representational systems

• Describes location and movement using common language and geometric vocabulary
• Makes and uses coordinate systems to specify locations and to describe paths
• Finds the distance between points along horizontal and vertical lines of a coordinate system

Applies transformations and uses symmetry to analyze mathematical situations

• Predicts and describes the results of sliding, flipping and turning two-dimensional shapes
• Describes a motion or a series of motions that will show that two shapes are congruent
• Identifies and describes line and rotational symmetry in two- and three-dimensional shapes and designs

Uses visualization, spatial reasoning and geometric modeling to solve problems

• Builds and draws geometric objects
• Creates and describes mental images of objects, patterns and paths
• Identifies and builds a three-dimensional object from a two-dimensional representations of that object
• Identifies and draws a two-dimensional representation of a three-dimensional object
• Use geometric models to solve problems in other areas of mathematics, such as number and measurement
• Recognizes geometric ideas and relationships and applies them to other disciplines and to problems that arise in the classroom or in everyday life

Formulates questions that can be addressed with data and collects, organizes and displays relevant data to answer them

• Designs investigations to address a question and considers how data-collection methods affect the nature of the data set
• Collects data using observations, surveys and experiments
• Represents data using tables and graphs such as line plots, bar graphs and line graphs
• Recognizes the differences in representing categorical and numerical data

At this level, most parents are still able to help their kids with their homework and projects, although it may be helpful to review basic math terminology (Math Success is a good program to help parents review). What is important at this math stage is to make sure that kids have a solid foundation to build upon. After mastering basic skills and concepts, kids can begin to apply math to real life situations and scientific applications.

References

Internet 4 Classrooms, (n.d.). Mathematics performance skills. Retrieved Mar. 16, 2006, from I4C Web site: http://www.internet4classrooms.com.

National Council of Teachers of Mathematics, (n.d.). Number and operations standard. Retrieved Mar. 16, 2006, from Principles and Standards for School Mathematics Web site: http://standards.nctm.org/document/appendix/numb.htm.

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