Wachusett Regional School District
Wachusett Mountain

District Frameworks - Mathematics

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Standard IV

Mathematical Connections

It is important that students see the relations and connections among mathematical ideas and that they view mathematics as an integrated whole. Students need to experience and understand that in using mathematics to solve or explore problems they may draw on any of several areas of mathematics. Important or interesting problems do not come with labels such as "geometry," "algebra," or "probability."

While mathematical content as presented in the NCTM Standards and these Standards is divided into distinct standards, topics, and clusters, these descriptions serve only as an aid in identifying appropriate content for students in K-12. The content need not be presented to students in the way the descriptions are organized.

Also it is important for students to understand that mathematics is related to other subjects they study such as art, music, social studies, health, and physical education, for example. They need to learn that mathematics is one way of learning about the world, and it is connected, not isolated, from other ways of learning. In addition, these connections will help students use their strengths and interests to branch out to subjects with which they feel less comfortable. A proficient mathematics student who thinks of him or herself as someone who "can't draw" may be engaged in and helped to explore art through the study of tessellation in mathematics class. A history buff who thinks he or she can't do mathematics may gain a new view of mathematics and his or her ability in mathematics by analyzing data from a questionnaire on family histories.

In grades K-4 the study of mathematics shall include opportunities to make connections so that students will:

  • Link conceptual and procedural knowledge;  
  • Relate various representations of concepts or procedures to one another; 
  • Recognize relationships among different topics in mathematics; 
  • Use mathematics in other curriculum areas; 
  • Use mathematics in their daily lives.

In grades 5-8, the mathematics curriculum shall include the investigation of mathematical connections that students will:

  • See mathematics as an integrated whole; 
  • Explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations; 
  • Use a mathematical idea to further their understanding of other mathematical ideas; 
  • Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business; 
  • Value the role of mathematics in our culture and society.

In grades 9-12, the mathematical curriculum shall include investigation of the connections and interplay among various mathematical topics and their applications that all students will:

  • Recognize equivalent representations of the same concept; 
  • Relate procedures in one representation to procedures in an equivalent representation; 
  • Use and value the connections among mathematical topics; 
  • Use and value the connections between mathematics and other disciplines.


In the adult basic education classroom, curriculum design shall include approaches to making mathematical connections which allow the learner to:

  • view mathematics as an integrated whole that is connected to past learning, the real world, adult life skills, and work-related settings; 
  • explore problems using appropriate technology and describe results using a variety of mathematical models or representations including graphs, concrete, verbal, and algebraic models or representation; 
  • apply mathematical thinking and modeling to solve problems that arise in other disciplines, and in the real world, including work-related settings.