Number Theory and Order of Operations


(taken from “Big Ideas by Dr. Small”):

  1. Thinking of numbers as factors or multiples of other numbers provides alternative representations of those numbers.
  2. Classifying numbers as factors and/or multiples of other numbers, or as primes or composites, provides additional information about those numbers.
  3. Just as multiplication and division are intrinsically related, so are factors and multiples.
  4. There is a specific order in which the operations are to be carried out.


GOAL #1: I can represent numbers as factors and multiples of other numbers.

GOAL #2: I can identify numbers as prime or composite.

GOAL #3: I know the difference between a perfect square and a square root.

GOAL #4: I can use the order of operations to simplify mathematical expressions.


  • Generate multiples and factors, using a variety of tools and strategies (e.g., identify multiples on a hundreds chart; create rectangles on a geoboard) (Sample problem: List all the rectangles that have an area of 36 cm2 and have whole-number dimensions.);
  • Represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper);
  • Explain the relationship between exponential notation and the measurement of area and volume (Sample problem: Explain why area is expressed in square units [units2] and volume is expressed in cubic units [units3];
  • Solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);
  • Evaluate expressions that involve whole numbers, including expressions that contain brackets, using order of operations;