Mathematical and computational thinking in K–2 builds on prior experience and progresses to recognizing that mathematics can be used to describe the natural and designed world(s).  

• Decide when to use qualitative vs. quantitative data.  

• Use counting and numbers to identify and describe patterns in the natural and designed world(s).  

• Describe, measure, and/or compare quantitative attributes of different objects and display the data using simple graphs.  

• Use quantitative data to compare two alternative solutions to a problem.  

Mathematical and computational thinking in 3–5 builds on K–2 experiences and progresses to extending quantitative measurements to a variety of physical properties and using computation and mathematics to analyze data and compare alternative design solutions.  

• Decide if qualitative or quantitative data are best to determine whether a proposed object or tool meets criteria for success.  

• Organize simple data sets to reveal patterns that suggest relationships.   

• Describe, measure, estimate, and/or graph quantities (e.g., area, volume, weight, time) to address scientific and engineering questions and problems.   

• Create and/or use graphs and/or charts generated from simple algorithms to compare alternative solutions to an engineering problem. 

Mathematical and computational thinking in 6–8 builds on K–5 experiences and progresses to identifying patterns in large data sets and using mathematical concepts to support explanations and arguments.  

• Use digital tools (e.g., computers) to analyze very large data sets for patterns and trends.  

• Use mathematical representations to describe and/or support scientific conclusions and design solutions.  

• Create algorithms (a series of ordered steps) to solve a problem.  

• Apply mathematical concepts and/or processes  (e.g., ratio, rate, percent, basic operations, simple algebra) to scientific and engineering questions and problems.  

• Use digital tools and/or mathematical concepts and arguments to test and compare proposed solutions to an engineering design problem.