NCTM Principles and Standards for School Mathematics Supported by KaAMS

Number and Operations Standard for Grades 6-8

…        understand and use ratios and proportions to represent quantitative relationships;

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

Algebra Standard for Grades 6-8

…        relate and compare different forms of representation for a relationship;

…        model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Geometry Standard for Grades 6-8

…        understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;

…        use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume;

Measurement Standard for Grades 6-8

…        understand both metric and customary systems of measurement;

…        understand relationships among units and convert from one unit to another within the same system;

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

…        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 Standard for Grades 6-8

…        formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population;

…       select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Problem Solving Standard for Grades 6-8

…        solve problems that arise in mathematics and in other contexts;

…        apply and adapt a variety of appropriate strategies to solve problems;

Reasoning and Proof Standard for Grades 6-8

…        select and use various types of reasoning and methods of proof.

Communication Standard for Grades 6-8

• organize and consolidate their mathematical thinking through communication
• communicate their 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 Standard for Grades 6-8

• recognize and use connections among mathematical ideas;
• understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
• recognize and apply mathematics in contexts outside of mathematics.

Representation Standard for Grades 6-8

…        use representations to model and interpret physical, social, and mathematical phenomena.