SECTION 1
Why Do We Need a Plan?
People have been solving math problems for thousands of years. But here is something interesting: the best problem solvers are not always the fastest at arithmetic. They are the best at organizing information before they even start calculating. Throughout history, mathematicians have developed strategies for breaking problems into smaller, more manageable pieces.
~300 BC • Euclid's Elements
~825 AD • Al-Khwarizmi's Algorithm
1945 • Pólya's Problem-Solving Steps
Today • Standardized Test Strategy
The big question these thinkers all tried to answer is the same one you face on the SSAT: How do I turn a confusing problem into a clear path to the answer? That is exactly what this lesson will teach you.
SECTION 2
Core Principles of Problem Solving
Before you do any math, you need a game plan. Think of it like packing for a trip. You would not throw everything in your closet into a suitcase. You would figure out where you are going, what the weather is like, and then pack only what you need. Problem solving works the same way.
Read the Whole Problem
Identify What You Need to Find
Pull Out the Key Facts
Choose Your Operations
Check Your Answer
KEY TAKEAWAY
SECTION 3
Seeing the Problem-Solving Process
The diagram below shows the five-step process as a flowchart. Notice how you start at the top by reading the problem, then move down step by step. If your answer does not make sense at the end, the arrow loops you back to check your work.
This flowchart is your mental checklist. On the SSAT, you will not have time to draw it on paper for every question. But after practicing, these steps will become automatic. You will naturally read the question, spot the key facts, pick the right operation, and check your work — all in under a minute.
SECTION 4
Translating Words into Math
One of the trickiest parts of word problems is figuring out which math operation to use. Certain signal words (words that hint at an operation) hide inside the sentences. Learning to spot them is like learning a secret code.
ADDITION SIGNALS
Look for words like: sum, total, altogether, combined, in all, increased by, more than
SUBTRACTION SIGNALS
Look for words like: difference, fewer, less than, remaining, left over, decreased by, how many more
MULTIPLICATION SIGNALS
Look for words like: times, each, per, every, of, double, triple, product
DIVISION SIGNALS
Look for words like: split, share equally, divided by, per, ratio, average, out of
Watch Out!
SECTION 5
Sorting Relevant from Extra Information
SSAT problems often include numbers or facts that you do not need. They are there to test whether you can tell the difference between relevant information (facts that help you answer the question) and extra information (facts that do not connect to the question). Let's look at a sample problem and sort its details.
Sample Problem
Here is a quick test you can use for any fact in a problem: ask yourself, "Does this number or detail connect to the question?" If the answer is no, set it aside. If the answer is yes, write it down and figure out how it fits into your solution path.
SECTION 6
Worked Example: Full Problem Walkthrough
Problem
Step-by-Step Solution
- 1
Step 1 — Read and Find the Question
The question asks: "How far will the train have traveled by 11:30 AM?" So we need to find a distance.Goal: find the distance traveled - 2
Step 2 — Identify Relevant Information
Relevant: speed = 60 miles per hour, departure time = 9:00 AM, arrival time = 11:30 AM. Extra: the train has 8 cars — this does not affect distance.Key facts: 60 mph, 9:00 AM to 11:30 AM - 3
Step 3 — Choose Operations
To find distance, we use: distance = speed × time. First we need to figure out how much time passed. From 9:00 AM to 11:30 AM is 2 hours and 30 minutes, which equals 2.5 hours.Time = 2.5 hours - 4
Step 4 — Solve
Distance = 60 × 2.5. We can break this into easier pieces: 60 × 2 = 120 and 60 × 0.5 = 30. Then 120 + 30 = 150.Distance = 150 miles - 5
Step 5 — Check
Does 150 miles make sense? At 60 mph, you travel 60 miles in one hour and 120 miles in two hours. Half an hour more adds 30 miles. So 120 + 30 = 150 miles. ✓ It checks out.Answer confirmed: 150 miles
Notice how we never used the fact that the train has 8 cars. That detail was extra information placed there to distract you. On the SSAT, always be on the lookout for numbers that have nothing to do with the question.
SECTION 7
Common Mistakes and How to Avoid Them
Even strong math students lose points by falling into common traps. Here is a comparison of what can go wrong and how to stay on track.
| Common Mistake | Why It Happens | How to Fix It |
|---|---|---|
| Using extra information in your calculation | You grab every number in the problem without asking if it connects to the question | Before calculating, label each fact as "relevant" or "extra" |
| Choosing the wrong operation | You do not look for signal words or think about what the question is really asking | Reread the question and match key words to operations (see Section 4) |
| Answering a different question than what was asked | You solve for one thing when the question asks for something else (e.g., finding total cost when the question asks for change) | Underline the actual question. After solving, reread it to make sure you answered it. |
| Skipping the check step | You rush to the next problem without verifying your answer is reasonable | Take 5 seconds to ask: is this answer too big, too small, or about right? |
Four common mistakes and their fixes
KEY TAKEAWAY
SECTION 8
Connecting to Harder Problem Types
The planning strategy you just learned works for every kind of SSAT math problem. As problems get harder, the planning step becomes even more important. Here is how the same five steps apply to more advanced problem types you will encounter.
| Problem Type | Basic Version (This Lesson) | Advanced Version (What's Next) |
|---|---|---|
| Arithmetic word problem | One or two operations, one piece of extra info | Three or more operations, multiple extra details |
| Geometry problem | Find area using given length and width | Find area of a combined shape where you must first calculate a missing side |
| Rate / distance / time | Single trip at one speed | Two legs of a trip at different speeds; find average speed |
| Data interpretation | Read one value from a chart | Compare multiple values and calculate percent change |
How planning applies to basic and advanced SSAT problems
No matter how complex a problem gets, your first move is always the same: find the question, gather the relevant facts, ignore the rest, and choose your operations. The more you practice this habit now, the more naturally it will come when the problems get tougher.
SECTION 9
Practice Problems
Try each problem on your own before reading the answer. For every problem, start by identifying the question, pulling out the relevant facts, and choosing your operations.
Question 1: CONCEPTUAL
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Question 2: BASIC CALCULATION
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Question 3: INTERMEDIATE
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Question 4: APPLIED
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Question 5: CRITICAL THINKING
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SUMMARY
Lesson Summary
Summary
Every SSAT word problem can be tackled with a clear five-step process: read the whole problem, find the question, pull out the key facts while ignoring extra information, choose the right operations using signal words, and check that your answer makes sense. This process works whether the problem involves arithmetic, geometry, rates, or data.
Remember that wrong answer choices are often built from common mistakes like using extra numbers or picking the wrong operation. By following your plan, you avoid those traps. Practice sorting information and choosing operations on simple problems first. As this becomes a habit, you will be ready to apply it to the trickiest problems the SSAT throws at you.