# Writing Numerical Expressions Worksheets

Math is a universal language it can be interpreted and written by people of the planet that speak and write in over 6,500 written and spoken language. Math is something that is truth that bonds all those people and allows them to communicate ideas. In English we communicate through the written use of words and sentences. Numerical expressions are the foundation that we use to communicate ideas through math. Being able to convert between numerical expressions and written language is difficult and requires plenty of practice to become proficient with. When you truly break down a math sentence you will find they that are quite predictable and follow a seasoned pattern. This series of lessons and worksheets will help us learn how to interpret and write numerical expressions.

### Aligned Standard: Grade 5 Operations - 5.OA.2

- Breaking Down Expressions Step-by-step Lesson- Start off with a very basic expression and see how it develops into an answer for you.
- Guided Lesson - I tried to give you a huge range of problems, from the very simple to those using parentheses.
- Guided Lesson Explanation - I write this as if students understand the steps of PEMDAS.
- Practice Worksheet - The practice problems are the next step up in difficulty.
- Matching Worksheet - Match the math sentence to the integers and operations that they represent.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

The use of parentheses is what stumps everyone. Don't forget that they are your first concern.

- Homework 1 - 16 more than the quotient of fourteen divided by four.
- Homework 2 - Write this as a math statement: Seven less than the quotient of twelve divided by five.
- Homework 3 - This mixes what is expected of you.

### Practice Worksheets

These are great for students that need to put some extra time in.

- Practice 1 - Find the final value of the following problem.
- Practice 2 - They get a little more confusing. Here is an example: Fifty-eight times the addition of sixty-seven and eighty-two.
- Practice 3 - Convert the integers to words and vice versa.

### Math Skill Quizzes

The operations almost always include multiplication or a set of parentheses. I am a little biased towards those because I see students struggle with them.

- Quiz 1 - Make math sentences from all the information that you are given.
- Quiz 2 - Reverse what was done on the last quiz. Start with the words and make number sentences from them.
- Quiz 3 - A mixed review quiz. A nice way to see where you sit with all these problems.

### How to Write Numerical Expressions or Equations as Sentences

Much like sentences and phrases in language, math has very similar counterparts. A phrase is a group of words that give of an idea or concept. In math we have expressions that can be just a number, variable, symbol, or mixture of these three. Numerical expressions do not include the of the = symbol. Mathematical equations function much like sentences in language. An equation connects multiple expressions with the help of an equals sign. Writing numerical expressions from scratch are where students often get lost. It is not easy to convert math expressions or equations into complete thoughts. It can be a bit tricky to articulate the data which is presented in both math equations and expressions. So, when we are writing a word problem, we need to be familiar with the terminology that is used in defining a particular action that is taking place in that equation.

When taking we are trying to bring a math expression to words, it makes sense to examine all that is being presented to you. You need to look for clues that are presented to you. It is not difficult to recognize the numbers or variables that are involved. Where the difficulty comes is understanding how those numbers and variable interact. In this case we are attempting to understand the math operations (addition, subtraction, multiplication, or division) that are taking place. Much like when we are tackling word problems, there are keywords and phrases that are often used to describe these relationships (operations).

The Commonly Used Keywords and Phrase – There are a number of often used keywords and phrases that indicate specific math operations. Here is a good list of them to get you started.

**Addition - **Sums are processed through the operation of addition. Commonly used keywords and phrases include: added, additional, and, combined, in all, increase, more, raise, together, total of.

**Subtraction - **Difference are found through the operation of subtraction. Commonly used keywords and phrases to indicate this operation include: decrease, diminish, drop, fewer than, go down, left, less, lost, minus, reduce, take away.

**Multiplication - **Products are found through the operation of multiplication. Common words that are used include: area, by, for every, product, times, and multipliers (such as double, triple, quadruple...)

**Division - **One of the complicated operations to write and identify you will find that these keywords and phrases often indicate a quotient is at play: average, out of, part, per, ratio, split, shared.

Example: Write this expression in a sentence: 14 x 8 - 4

The first step is to identify the operations at work here and how they interact through PEMDAS. There are two operations a) the product of fourteen and eight. B) The difference of that product (a) and four. We can restate that as four less than the product. There are several ways that we can put this together to make a fluid sentence. A nice way to combine these might look like this: Four less than the product of fourteen and eight.