# Order of Operations

### Unit 1.2

## The basics ... in a way that is engaging and fun for students.

**The Order of Operations **

**Note: **The order of operations is the law of the land in mathematics. It is always important.

**Big Idea**

The order of operations is how we perform arithmetic, how we combine values, and how we embed and compress numeric expressions.

**Key Knowledge**

Group operations are performed first. Then, exponents are treated. After that, multiplication and division are done from left to right. While the order in which multiplication is performed does not matter, the same is not true for division. Be aware of the different ways in which division can be written. The last operations are addition and subtraction, which are done from left to right.

Functions have an input and an output. The notation shows which is the input.

**Pro-Tip**

#### (for students)

Read carefully!

**Here are some screen shots of the lesson.**

## To download a printable copy of the homework, please click here.

## In part two students will be introduced to some formulas they will be using in Algebra as well as to function notation.

**The Order of Operations and Function Notation**

**Note: **The order of operations is the law of the land in mathematics. It is always important.

In this section students will practice the order of operations by evaluating formulas and learning how function notation works.

**Big Idea**

The order of operations is how we perform arithmetic, how we combine values, and how we embed and compress numeric expressions.

**Key Knowledge**

Group operations are performed first. Then, exponents are treated. After that, multiplication and division are done from left to right. While the order in which multiplication is performed does not matter, the same is not true for division. Be aware of the different ways in which division can be written. The last operations are addition and subtraction, which are done from left to right.

Functions have an input and an output. The notation shows which is the input.

**Pro-Tip**

#### (for students)

Read carefully!

When dealing with function notation, the letter *f* is just a name, and when something like *f *^{-1} is seen, this is not an exponent but instead means inverse. More on this later!

## Here are a few screen shots of the PowerPoint.

## To download a printable copy of the practice problems below, please click here.

## This is an application of exponents and the order of operations combined ... scientific notation.

**Teaching Scientific Notation**

**Note: **Students will be asked, on Cambridge IGCSE exams, to calculate, without a calculator, things like and write their answer in scientific notation. There are easy ways to handle this type of problem if students learn that scientific notation uses exponents as a way to write long numbers concisely.

**Big Idea**

Scientific notation is just arithmetic. Using what has been learned before about how when terms are like we can multiply and sometimes even add before dealing with exponents, the problems presented with scientific notation are easily accessible.

**Key Knowledge**

It is convention that a number written in scientific notation has a single digit, followed by a decimal point and a decimal expansion, which is multiplied by a power of 10.

**Pro-Tip**

#### (for students)

When dealing with addition of numbers in scientific notation, it is best to rewrite the expressions so they are like terms.

To quickly and accurately remember how to manipulate the numbers in scientific notation, remember that 10 to the power of a positive number is large, where 10 to the power of a negative number is small (because of division). This can help remind students which way to “move,” the decimal point.

### Below are a few screen shots of the PowerPoint.