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## Algebra Topics - Introduction to Word Problems

Algebra topics -, introduction to word problems, algebra topics introduction to word problems.

## Algebra Topics: Introduction to Word Problems

Lesson 9: introduction to word problems.

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## What are word problems?

Johnny has 12 apples. If he gives four to Susie, how many will he have left?

12 - 4 = 8 , so you know Johnny has 8 apples left.

## Word problems in algebra

You can tackle any word problem by following these five steps:

- Read through the problem carefully, and figure out what it's about.
- Represent unknown numbers with variables.
- Translate the rest of the problem into a mathematical expression.
- Solve the problem.
- Check your work.

We'll work through an algebra word problem using these steps. Here's a typical problem:

## Step 1: Read through the problem carefully.

With any problem, start by reading through the problem. As you're reading, consider:

There are a few important things we know that will help us figure out the total mileage Jada drove:

- The van cost $30 per day.
- In addition to paying a daily charge, Jada paid $0.50 per mile.
- Jada had the van for 2 days.
- The total cost was $360 .

## Step 2: Represent unknown numbers with variables.

## Step 3: Translate the rest of the problem.

Let's take another look at the problem, with the facts we'll use to solve it highlighted.

$30 per day plus $0.50 per mile is $360.

$30 per day and $.50 per mile is $360

$30 ⋅ day + $.50 ⋅ mile = $360

Now we have our expression. All that's left to do is solve it.

## Step 4: Solve the problem.

We can start by getting rid of the 60 on the left side by subtracting it from both sides .

## Step 5: Check the problem.

$30 per day and $0.50 per mile

## Problem 1 Answer

Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1.

## Step 1: Read through the problem carefully

So is the information we'll need to answer the question:

## Step 2: Represent the unknown numbers with variables

## Step 3: Translate the rest of the problem

Let's look at the problem again. This time, the important facts are highlighted.

## Step 4: Solve the problem

- f is already alone on the left side of the equation, so all we have to do is calculate the right side.
- First, multiply 1/2 by 8 . 1/2 ⋅ 8 is 4 .
- Next, add 4 and 25. 4 + 25 equals 29 .

That's it! f is equal to 29. In other words, the cost of a family pass is $29 .

## Step 5: Check your work

- Let's work on the right side first. 29 - 25 is 4 .
- To find the value of s , we have to get it alone on the left side of the equation. This means getting rid of 1/2 . To do this, we'll multiply each side by the inverse of 1/2: 2 .

So now we're sure about the answer to our problem: The cost of a family pass is $29 .

## Problem 2 Answer

Let's go through this problem one step at a time.

- The amount Flor donated is three times as much the amount Mo donated
- Flor and Mo's donations add up to $280 total

Here's the problem again. This time, the important facts are highlighted.

The important facts of the problem could also be expressed this way:

Mo's donation plus Flor's donation equals $280

Mo's donation plus three times Mo's donation equals $280

We can translate this into a math problem in only a few steps. Here's how:

m plus three times m equals $280

It will only take a few steps to solve this problem.

- To get the correct answer, we'll have to get m alone on one side of the equation.
- To start, let's add m and 3 m . That's 4 m .
- We can get rid of the 4 next to the m by dividing both sides by 4. 4 m / 4 is m , and 280 / 4 is 70 .

We've got our answer: m = 70 . In other words, Mo donated $70 .

If our answer is correct, $70 and three times $70 should add up to $280 .

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## 5 Easy Steps to Solving Word Problems

## Why Are Word Problems Difficult for Children?

Why can word problems be so confusing and scary? There are a few possible reasons.

- Word problems are often introduced to us at an age before our skills of abstract thinking are fully developed. However, a student’s imagination is a great asset to use in understanding word problems!
- Word problems are sometimes simply included as the “harder problems” at the end of homework assignments and the student is never really taught how to approach them.
- It is sometimes ignored that a student’s math and reading ability come into play when word problems are assigned. But if the second grade math student is still only reading on a first-grade level, he will have difficulty solving word problems even if he is otherwise good at math! It can thus be helpful to assess both a student’s math and reading ability to set him up for success. The tutoring service provided by masterygenius.com is a great option since both math and reading skills can be addressed.

## A quick tip before we get started…

So what are the five easy steps to solving word problems? Let’s take a look!

## Five Easy Steps to Solving Word Problems (WASSP)

- Write (or draw) what you know.
- Ask the question.
- Set up a math problem that could answer the question.
- Solve the math problem to get an answer.
- Put the answer in a sentence to see if the answer makes sense!

Let’s look at an example word problem to demonstrate these steps.

## 1. Write (or draw) what you know.

## 2. Ask the question.

The student could write, “How many cookies can each of Matt’s friends have?”

## 3. Set up a math problem that could answer the question.

- It can be a good idea to teach students “clue” words or phrases in problems which can identify what math operation may be needed. However, this should not be the student’s only skill for deciding what math operation to use, because these “clue” words can sometimes be confusing. For example, the phrases “how many in all” and “how many more” seem very similar to a student, but the first phrase indicates addition and the second phrase indicates subtraction!
- It is good for a student to also be able to reason what math operation is needed based on understanding the scenario itself (which is a better builder of true critical thinking skills). This is why the first two steps (write what you know and ask the question) are so important. The student that has a true understanding of the scenario will be better equipped to reason what math operation is needed.

Dividing 12 cookies among 3 friends means 12 is divided by 3.

## 4. Solve the problem.

12 cookies ÷ 3 friends = 4 cookies per friend

## 5. Put the answer in a sentence to see if the answer makes sense.

“Each of Matt’s friends can have four cookies.”

What if the student had decided this was a multiplication problem?

12 cookies × 3 friends = 36 cookies per friend

If the student then writes a sentence using the answer, he may realize the answer can’t be right.

“Each of Matt’s friends can have 36 cookies.”

## Practice the Five Easy Steps for Word-Problem Success!

Step 5 ( Put the answer in a sentence) can help the student decide whether the answer makes sense.

Now your student is ready for word-problem success!

## IMAGES

## VIDEO

## COMMENTS

Step 1: Read through the problem carefully. The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it. Let's look at the problem again. The question is right there in plain sight: A single ticket to the fair costs $8.

Step 1: Visualize the Problem. The first step is to visualize the problem. See if you can picture what is going on. Draw pictures if that will help you. Pinpoint or highlight the important parts ...

Key Words for Solving Word Problems The hardest part of solving a word problem is actually understanding the problem and determining the operation (or operations) that needs to be performed. Listed below are a few of the most commonly used key words in word problems and the operations that they signal.