Word Problems: Why Students Struggle and How to Build Understanding

Word Problems: Why Students Struggle and How to Build Understanding

Word problems are often the moment when students begin to feel stuck in their math class. Not because the math is too advanced, but because word problems require a different skill set than computation alone.

Many students can solve equations once they’re written. The challenge is figuring out what equation to write in the first place.

Word problems usually test translation (turning words into an equation) more than they test a student’s ability to solve the problem.

A Simple Strategy That Helps Students Stop Guessing

A Helpful Strategy that we use with our students.

1. Define the variable
   
   

2. Translate the story into an equation
   
   

3. Solve
   
   

4. Check your answer in context
   
   

What to Look For When Helping Your Student with Their Homework,
If your child says “I don’t know where to start” (instead of “I can’t solve it”), the issue is usually translation, not math ability. Below are some examples that you can try out with your student.

Example 1: “Money Left Over” Problems

A student starts with $92. After buying notebooks, they have $20 left. If they bought 6 notebooks, how much did each notebook cost?

Common Student Thought:
“Do I divide first… or subtract first?”

Step 1: Define the Variable

Let x = cost of one notebook

Step 2: Translate the Situation

Total = spent + left

Spent = number × cost

92=6x+20

Translation:
The +20 is what’s left over. The 6x is what was spent.

Step 3: Solve

92−20=6x

+20 +20

------------------

(Divided by 6) 72=6x (Divided by 6)

------------------

x=12

Step 4: Check

6 notebooks at $12 = $72
$92 − $72 = $20 left

✅ Check Rule:
Your answer must make the story true — not just the equation.

Example 2: Fractions Embedded in Context

A student donates one-half of their sticker collection and then receives 8 new stickers. They now have 22 stickers. How many stickers did they have originally?

Common Student Thought:
“Where does the one-half go?”

Step 1: Define the Variable

Let x= original number of stickers

Step 2: Translate the Actions

After donating half, they keep 12​x. Then they add 8.

12​x + 8 = 22

Translation:
The fraction applies to the original amount x, not the final 22.

Step 3: Solve

12​x + 8 = 22

-8 -8

—------------------------

(2x) 12​x = 14 (X2)

—------------------------

X = 28

Step 4: Check

Half of 28 is 14.
14 + 8 = 22 ✅

Why This Matters Later:
Colleges often reteach this kind of reasoning in support math courses because students weren’t taught how to model multi-step situations.

Why These Problems Feel Hard (Even When the Math Isn’t)

Both examples rely on the same core skills:

1. Define variables clearly
   
   

2. Translate language into relationships
   
   

3. Build an equation before solving
   
   

Key Idea:
When students have a repeatable process, confidence rises, because they’re no longer guessing.

How Mountain Scholars Tutoring Supports This Skill

Mountain Scholars Tutoring focuses on:

• Breaking math down into understandable steps

• Teaching students how to approach problems, not just memorize answers

• Building independence so students don’t rely on constant help

• Helping students see that math is learnable

We specialize in working with students who feel behind and students who are already excelling. If you are ready to work with us, Book Your Strategy Call Here