Math 7-9

Systems Change
Math 7-9 > Factors > Operations

Factor Connections

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Operations specify how quantities can be combined and transformed. There are four arithmetic Operations: addition, subtraction, multiplication, and division. Throughout the school years, students develop an understanding of how Operations work with different types of numbers, such as fractions, decimals, and integers.

Students typically begin by thinking about Operations as telling them which computations to do (such as finding the sum or difference of two numbers). However, it is critical that students also develop a conceptual understanding of Operations. This conceptual foundation supports students in estimating approximate computations, alongside quickly and accurately calculating using procedures.

Main Ideas

Students' skill with Operations is supported by these critical conceptual components:

  • Understanding the algebraic properties of the Operations involved in the problem: For instance, students should able to transform the harder sum 3+8+7 into the easier sum 3+7+8 (it's easy to see that 3+7 = 10, and then it's easy to add 8 to 10);
  • Understanding the Place Value system and decomposition: For instance, a student could also transform 3+8+7 into 3+7+1+7 (making it easier to add up to 10, before adding 1 and 7); and
  • Understanding how relationships in a real world situation can be expressed by Operations (i.e., modeling).

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