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Instructor Overview

Students write an expression for the length of a train, using variables to represent the lengths of the different types of cars.

Key Concepts

  • A numerical expression consists of a number or numbers connected by the arithmetic operations of addition, subtraction, multiplication, division, and exponentiation.
  • An algebraic expression uses letters to represent numbers.
  • An algebraic expression can be written to represent a problem situation. Sometimes more than one algebraic expression may represent the same problem situation. These algebraic expressions have the same value and are equivalent.
  • The properties of operations can be used to make long algebraic expressions shorter:
    • The commutative property of addition states that changing the order of the addends does not change the end result:
      a + b = b + a.
    • The associative property of addition states that changing the grouping of the addends does not change the end result:
      (a + b) + c = a + (b + c).
    • The distributive property of multiplication over addition states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together:
      a(b + c) = ab + ac.

Goals and Learning Objectives

  • Write algebraic expressions that describe lengths of freight trains.
  • Use properties of operations to shorten those expressions.