Lesson 4: Exponents and Order of Operations

Getting Started

Most math problems are shown is a form that is called a mathematical expression. A mathematical expression is simply a math sentence that includes at least two numbers and one or more operators (+,−,×,÷). The image that follows shows several examples of expressions.

In working with expressions, you've learned the rules and steps for solving problems for each of the four operations: addition, subtraction, multiplication, and division. There are also rules for the order in which the operations should be performed. This process is called the order of operations. The order of operations is a set of rules that defines the order in which to complete operations when solving a mathematical expression.

This may be review for you, but it's a good idea to practice order of operations further to make sure you know the correct way to solve multi-operation problems. Being able to correctly and confidently use the order of operations is an important skill in problem solving, including the higher math levels you'll explore in coming years. You will revisit the skill later in this level when you are introduced to algebra concepts.

Stuff You Need

3-hole drilled card stock (kit)
colored pencils
glue or glue stick
Interactive Notebook
number cards (kit)
scissors
symbol cards (kit)

Ideas to Think About

Why are mathematical notations useful in writing math expressions?
What does an exponent indicate should be done mathematically?
How does the order of operations lead to the correct answer for a problem?

Things to Know

Mathematical expression: a math sentence that includes at least two numbers and one or more operators (+,−,×,÷)
Order of operations: a set of rules that define the order in which to complete operations when solving a mathematical expression
An exponential expression contains two parts — a base and an exponent.
The base of an exponential expression is a factor, and the exponent indicates how many times to use that base as a factor.
A notation is a shorthand way of writing something. For example, 3⁴ is a shorter way to write 3 × 3 × 3 × 3.

Skills

Write and evaluate numerical expressions involving whole-number exponents
Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations)

Introducing the Lesson

Your child has most likely been introduced in previous levels to the order of operations, but this concept bears repeated practice, especially as the child prepares for higher levels of math work. The order of operations, which includes computation with exponents, is used extensively in algebra, geometry, and other related math courses. The goal is to have your child be able to use these skills with confidence and fluency as she prepares for these coming concepts.