## 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*.

- The commutative property of addition states that changing the order of the addends does not change the end result:

# Goals and Learning Objectives

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

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