National Math Standards Grades 6-8

Sixth graders should thoroughly understand basic concepts such as multiplication, division, basic geometry, ratios and fractions. Quick and accurate computation gives students the ability to move on to higher math concepts without spending a lot of energy on fundamental math.

In terms of the products that we looked at, The Quarter Mile Math program is a good choice for helping kids increase their speed and accuracy, so they can spend time conceptualizing rather than stressing over 12 X 9. Surprisingly, many students by the 6th grade have lost much of the speed they had in the 3rd or 4th grade in relation to multiplication and division, so refreshers can be helpful.

Many students take Algebra in the 7th or 8th grade, so the 5th or 6th grade is the perfect time to introduce pre-Algebra. Subjects to conquer before Algebra I include negative, positive and rational numbers, basic equation solving, ratios, proportions, percents, inequalities, the coordinate plane, area and volume, the right triangle, basic statistics and probability. To help with these subjects a comprehensive program such as Math Success or Microsoft Student may help. By Geometry, which some kids take in the 8th grade, a scientific calculator and graphing paper can come in handy.

In terms of the National Standards for Mathematics, the following areas are to be addressed between the 6th and 8th grade and accomplished by the end of the 8th grade. As your child advances, you can check off their successful areas. If a subject is not addressed in school or they are having difficulties, you may want to look to outside sources to ensure that your child meets the minimum standards before they struggle through a more complex course.

Understands numbers and ways of representing numbers as well as the relationship among numbers and number systems

• Works flexibly with fractions, decimals, and percents to solve problems
• Can compare and order fractions, decimals, and percents efficiently and find their locations on a number line
• Understands the meaning of percents greater than 100 and less than 1
• Understands and uses ratios and proportions to represent quantitative relationships
• Understands large numbers and recognizes and appropriately uses exponential, scientific and calculator notation
• Uses factors, multiples, prime factorization and relatively prime numbers to solve problems
• Understands the meaning of integers and can represent and compare quantities with them

Understands meanings of operations and how they relate to one another

• Understands the meaning and effects of arithmetic operations with fractions, decimals and integers
• Uses the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions and decimals
• Understands and uses the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems

Computes fluently and makes reasonable estimates

• Selects appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, or paper and pencil, depending on the situation, and can apply the selected methods
• Can develop and analyze algorithms for computing with fractions, decimals and integers and develops fluency in their use
• Develops and uses strategies to estimate the results of rational-number computations and judges the reasonableness of results
• Develops, analyzes and explains methods for solving problems involving proportions, such as scaling and finding equivalent ratios

Measurements

• Understands both metric and standard systems of measurement
• Understands relationships among units and can convert from one unit to another within the same system
• Understands, selects and uses units of appropriate size and type to measure angles, perimeter, area, surface area and volume

Understands patterns, relations, and functions

• Represents, analyzes and generalizes a variety of patterns with tables, graphs, words and symbolic rules
• Relates and compares different forms of representation for relationships
• Identifies functions as linear or nonlinear and contrasts their properties from tables, graphs or equations

Represents and analyzes mathematical situations and structures using algebraic symbols

• Conceptually understands different uses of variables
• Explores relationships between symbolic expressions and graphs of lines with attention to the meaning of intercept and slope
• Uses symbolic algebra to represent situations and to solve problems, particularly those that involve linear relationships
• Recognizes and generates equivalent forms for simple algebraic expressions and solves linear equations

Uses mathematical models to represent and understand quantitative relationships

• Models and solves contextualized problems using various representations, such as graphs, tables or equations

Analyzes change in various contexts

• Uses graphs to analyze the nature of changes in quantities in linear relationships
Models and solves contextualized problems using various representations, such as graphs, tables or equations

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

• Describes, classifies and understands relationships among types of two- and three-dimensional objects using defining properties
• Understands relationships among angles, side lengths, perimeters, areas and volumes of similar objects
• Creates and analyzes inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity and the Pythagorean relationship

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

• Uses coordinate geometry to represent and examine the properties of geometric shapes
• Uses coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides

Applies transformations and uses symmetry to analyze mathematical situations

• Describes sizes, positions and orientations of shapes under informal transformations such as flips, turns, slides and scaling
• Examines the congruence, similarity and line or rotational symmetry of objects using transformations

Uses visualization, spatial reasoning and geometric modeling to solve problems

• Draws geometric objects with specified properties, such as side lengths or angle measures
• Uses two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume
• Uses visual tools such as networks to represent and solve problems
• Uses geometric models to represent and explain numerical and algebraic relationships
• Recognizes and applies geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

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

• Formulates questions, designs studies and collects data about a characteristic shared by two populations or different characteristics within one population
• Selects, creates and uses appropriate graphical representations of data, including histograms, box plots and scatterplots

Sometimes parents are the ones who need a boost with a refresher course. The higher their kids advance in math, the harder it may be for them to help their kids with their homework. If the above concepts are confusing or you are not sure what they mean, you may want to look at a program that clearly defines math concepts and can update your math lingo. If your child is moving into subjects like Algebra, Geometry or higher, Microsoft Student is a good choice, not only does it offer definitions and articles, but you can often go to the exact page number and problem number of your students homework and get full explanations on how to do the problem. This is an excellent help for kids and the parents who are trying to help them.

It is always a good idea to speak with your child's math teacher; they may have excellent ideas on how you can help your kid succeed in an area that is challenging them. They may be able to suggest activities, provide extra work sheets or recommend products or websites that may be helpful.

In regards to websites, a good place to start is The Math Forum at www.mathforum.org, which hosts the popular "Dr. Math", a student center, forums and advice for parents.

Lastly, sometimes parents unintentionally transfer their math fears and insecurities onto their child. If you didn't like math when you were a kid or still struggle with math concepts, it is never too late to try again. You may find that learning math with the patience and experience of an adult easier, but if you still cannot overcome your math anxieties, try to find others to help, such as a private tutor, peer tutor or a good math program.

References

Houghton Mifflin, (1988). Pre algebra curriculum. Retrieved Mar. 16, 2006, from Curriculum Guide for Pre Algebra Web site: http://www.wtvl.net/honda/Curriculum%20Guide%20For%20Pre-algebra.htm.

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.