Lesson 1: Use a Problem Solving Strategy

New Concept

Learn a systematic, 7-step strategy to confidently translate any word problem into a solvable equation. This approach builds skills for tackling various number problems by breaking them down into manageable parts, turning challenges into clear solutions.

What’s next

Next, we'll walk through this 7-step strategy with interactive examples. Then, you'll apply it yourself in a series of practice problems.

Property

Start with a fresh slate and begin to think positive thoughts. If we take control and believe we can be successful, we will be able to master word problems. Word problems are a learnable skill, just like driving a car or cooking a meal.

Examples

• Instead of thinking 'I'll never get this,' try thinking 'I can read the problem carefully and identify what it's asking.'

• Instead of saying 'I'm bad at word problems,' remind yourself 'I have learned many new math skills that will help me succeed now.'

Property

1. Read the word problem to understand all the words and ideas.
2. Identify what you are looking for.
3. Name what you are looking for by choosing a variable.
4. Translate the words into an algebraic equation.
5. Solve the equation using good algebra techniques.
6. Check the answer to make sure it makes sense in the context of the problem.
7. Answer the question with a complete sentence.

Examples

• A hat is on sale for 15 dollars, which is one-third the original price. What was the original price? Let $p$ be the original price. The equation is $15 = \frac{1}{3}p$. Multiply by 3 to get $p = 45$. The original price was 45 dollars.

• The number of oranges was 4 more than twice the number of lemons. If there were 16 oranges, how many lemons were there? Let $L$ be the number of lemons. The equation is $16 = 2L + 4$. Solving gives $12 = 2L$, so $L=6$. There were 6 lemons.

Property

In number problems, you are given clues about one or more numbers and you use these clues to build an equation. When a problem involves two or more numbers, define them in terms of the same variable.

Examples

• The sum of a number and five is 18. Find the number. Let the number be $n$. The equation is $n + 5 = 18$. Subtracting 5 from both sides gives $n = 13$. The number is 13.

• The difference of three times a number and four is 11. Find the number. Let the number be $x$. The equation is $3x - 4 = 11$. Adding 4 gives $3x = 15$, so $x=5$. The number is 5.

Property

Consecutive integers are integers that immediately follow each other. If we define the first integer as $n$, the next consecutive integer is $n + 1$. The one after that is one more than $n + 1$, so it is $n + 1 + 1$, or $n + 2$.

$n$ = 1st integer

$n + 1$ = 2nd consecutive integer