Possible National Math Standards Alignment for Gummi Bear Engineering

Although this list is not meant to be exhaustive, it demonstrates that there are a variety of standards to which gummi bear engineering lends itself.

Number and Operation Standards

Grades 3-5

• explore numbers less than 0 by extending the number line and through familiar applications; (SailCar)

Algebra

Grades 3-5

• represent and analyze patterns and functions, using words, tables, and graphs.
• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
• investigate how a change in one variable relates to a change in a second variable;
• identify and describe situations with constant or varying rates of change and compare them.

Grades 6-8

• represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
• identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
• model and solve contextualized problems using various representations, such as graphs, tables, and equations.
• use graphs to analyze the nature of changes in quantities in linear relationships.

Geometry Standard

Grades 3-5

• identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes; (Skyscraper)
• make and use coordinate systems to specify locations and to describe paths; (Bear-a-pult)
• build and draw geometric objects; (Skyscraper)

Grades 6-8 (for any cost analysis extension)

• draw geometric objects with specified properties, such as side lengths or angle measures;
• use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume;
• recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Measurement

Grades 3-5

• understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute;
• carry out simple unit conversions, such as from centimeters to meters, within a system of measurement;
• develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms;
• develop strategies to determine the surface areas and volumes of rectangular solids

Grades 6-8

• 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;
• develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes;
• solve simple problems involving rates and derived measurements for such attributes as velocity

Data Analysis and Probability

Grades 3-5

• collect data using observations, surveys, and experiments;
• represent data using tables and graphs such as line plots, bar graphs, and line graphs;
• use measures of center, focusing on the median, and understand what each does and does not indicate about the data set;
• propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.

Grades 6-8

• select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
• find, use, and interpret measures of center and spread, including mean and interquartile range;
• discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.
• make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit;
• use conjectures to formulate new questions and plan new studies to answer them.

Reasoning and Proof

• Make and investigate mathematical conjectures

Communication

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

Connections

• Recognize and apply mathematics in contexts outside of mathematics