National Math Standards for Middle School

Number and Operations Standard

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

• Work flexibly with fractions, decimals, and percentages to solve problems.

• Understand and use ratios and proportions to represent quantitative relationships.

Understand meanings of operations and how they relate to one another.

• Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

Compute fluently and make reasonable estimates.

• Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.

• Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results.

• Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Algebra

Represent and analyze mathematical situations and structures using algebraic symbols.

• Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

• Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.

Use mathematical models to represent and understand quantitative relationships.

• Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Geometry

Use visualization, spatial reasoning, and geometric modeling to solve problems.

• Use two-dimensional representations of three-dimensional objects to visualize and solve problems, such as those involving surface area and volume.

• Use geometric models to represent and explain numerical and algebraic relationships.

• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement.

• Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

Apply appropriate techniques, tools, and formulas to determine measurements.

• Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

• Solve problems involving scale factors, using ratio and proportion.

• Solve simple problems involving rates and derived measurements for such attributes as velocity and density.

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

• Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Select and use appropriate statistical methods to analyze data.

• Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

Problem Solving

• Solve problems that arise in mathematics and in other contexts.

• Apply and adapt a variety of appropriate strategies to solve problems.

Communication

• Organize and consolidate mathematical thinking through communication.

• Communicate mathematical thinking coherently and clearly to peers, teachers, and others.

• Analyze and evaluate the mathematical thinking and strategies of others.

• Use the language of mathematics to express mathematical ideas precisely.

Connections

• Recognize and apply mathematics in contexts outside of mathematics.

Download Microsoft Active Accessibility.