Identifying Relevant Information — Identify relevant information and choose a strategy. - SHSAT Math

SECTION 1

Why This Skill Matters

Word problems have been part of math for thousands of years. Ancient civilizations wrote their math challenges as little stories, not as plain equations. The skill of identifying relevant information — figuring out which numbers and facts actually matter — has always been the first step to solving them.

1650 BCE • The Rhind Papyrus

Ancient Egyptian scribes wrote math problems as word stories about bread, beer, and land. Solvers had to pick out the key numbers from the story.

800 CE • Al-Khwarizmi's Algebra

The mathematician Al-Khwarizmi showed how to translate word problems into equations. His name gave us the word "algorithm" — a step-by-step strategy.

1900s • Standardized Testing Begins

Tests like the SHSAT started using multi-step word problems to measure how well students can sort useful facts from extra details and choose a plan.

Today • The SHSAT Challenge

On the SHSAT, you have limited time. Problems often include extra information designed to distract you. Knowing what to ignore is just as important as knowing what to use.

Here is the big question this lesson answers: when you read a word problem packed with numbers and details, how do you decide which facts to use and which strategy will get you to the answer fastest?

SECTION 2

Core Principles of Identifying Relevant Information

Before you do any math, you need a game plan. These four core principles will guide you through every multi-step word problem on the SHSAT.

Read for the Question First

Always find out what the problem is asking before you look at the numbers. The question tells you what kind of answer you need.

Sort Given vs. Extra

Given information is any fact you need to reach the answer. Extra information is there to distract you. Circle or underline only what connects to the question.

Identify Hidden Steps

Multi-step problems don't hand you the answer in one move. Look for intermediate values — numbers you must calculate before you can find the final answer.

Choose Your Strategy

Decide if you should work forwards (from given facts to the answer), work backwards (from the answer choices), or set up an equation. Pick the method that fits the problem.

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KEY TAKEAWAY

Think of a word problem like cleaning out your backpack before a trip. You dump everything out, decide what you actually need, and leave the rest behind. The "stuff you need" is relevant information. The "stuff you leave behind" is extra information. Your plan for packing is your strategy.

SECTION 3

Visualizing the Process

The diagram below shows the step-by-step process you should follow every time you face a multi-step word problem. Start at the top and work your way down. Notice how the very first step is reading the question, not crunching numbers.

The 5-Step Problem-Solving Flow. Steps 1 through 3 focus on understanding and filtering. Steps 4 and 5 focus on execution. Most mistakes happen when students skip straight to Step 5.

Notice the flow splits your work into two phases. The first phase (Steps 1–3) is about understanding. The second phase (Steps 4–5) is about doing the math. Rushing through the first phase is the number-one reason students get tricked by extra information on the SHSAT.

SECTION 4

The Math Behind Strategy Choice

Multi-step word problems usually boil down to a few basic operations combined together. The trick is figuring out which operations to use and in what order. Here are the most common setups you will see.

TOTAL COST PATTERN

Total = (Number of items) × (Price per item) + Extra fees

This pattern appears in shopping, ticket, and pricing problems. The extra fees part (like tax or shipping) is the hidden step many students miss.

RATE × TIME PATTERN

Distance = Rate × Time

Use this for speed, work-rate, or production problems. If a problem gives you two of these three values, you can find the third. Remember: Rate = Distance ÷ Time, and Time = Distance ÷ Rate.

PART-WHOLE PATTERN

Part = Fraction (or Percent) × Whole

Fraction and percent problems follow this pattern. If the problem says "⅓ of the students," then Fraction = ⅓ and Whole = total number of students.

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Strategy Tip

When you read a problem, look for signal words. Words like "each," "per," and "every" usually mean multiplication. Words like "left over," "remaining," and "difference" usually mean subtraction. Words like "total," "altogether," and "combined" usually mean addition.

SECTION 5

Sorting Relevant from Extra Information

Let's look at a sample problem and practice sorting its facts. Read this problem carefully:

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Sample Problem

Maria has 3 brothers and 2 sisters. She bought 5 notebooks at $4 each and 3 pens at $2 each. She paid with a $50 bill. The store has been open for 12 years. How much change did Maria receive?

The diagram below sorts every piece of information from this problem into two categories: relevant (you need it) and extra (you can ignore it).

The left column shows the four facts that connect to finding Maria's change. The right column shows three facts that are true but useless for solving this problem. On the SHSAT, extra information often looks important because it involves real numbers.

How did we sort these? We used a simple test: Does this fact help me answer the question? The question asks about change from a purchase. To find change, you need the total cost and the amount paid. Brothers, sisters, and the store's age have nothing to do with money, so they are extra.

SECTION 6

Worked Example

Let's walk through a full SHSAT-style problem from start to finish using our 5-step flow.

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Problem

A school club is selling candy bars to raise money. They bought 120 candy bars for $0.75 each. They sell each candy bar for $1.50. The club has 15 members and their advisor is 34 years old. If they sell all the candy bars, how much profit does the club make?

Full Solution

1
Step 1 — Read the Question

The question asks: How much profit does the club make? Profit means the money earned from sales minus the money spent to buy the items.
2
Step 2 — List All Facts

Here are all the facts in the problem: 120 candy bars, cost $0.75 each, sell for $1.50 each, 15 members, advisor is 34 years old, and they sell all the bars.
3
Step 3 — Cross Out Extras

"15 members" does not affect costs or sales. "Advisor is 34 years old" has nothing to do with money. Cross both out. We keep: 120 bars, $0.75 cost each, $1.50 selling price each.

Relevant: 120 bars, $0.75 cost, $1.50 price
4
Step 4 — Choose a Strategy

We need profit. Profit = Revenue − Cost. Revenue = number sold × selling price. Cost = number bought × buying price. So we will multiply twice, then subtract.
5
Step 5a — Calculate Total Cost

Total Cost = 120 × $0.75

Total Cost = $90.00
6
Step 5b — Calculate Total Revenue

Total Revenue = 120 × $1.50

Total Revenue = $180.00
7
Step 5c — Calculate Profit

Profit = $180.00 − $90.00

Profit = $90.00
8
Step 5d — Check

Does this make sense? Each candy bar earns $1.50 − $0.75 = $0.75 profit. Multiply $0.75 × 120 = $90. ✓ Our answer matches.

SECTION 7

Comparing Problem-Solving Strategies

Not every strategy works equally well for every problem. The table below compares three common strategies so you know when to use each one.

Strategy	How It Works	Best For	Watch Out For
Work Forward	Start with given values, calculate step by step until you reach the answer.	Problems where you know starting values and need a final total.	Losing track of intermediate results. Write each step down!
Work Backward	Start with the answer choices (or the end result) and reverse the operations.	Problems where the answer choices are simple numbers or the final value is given.	Reversing operations incorrectly (e.g., adding when you should subtract).
Set Up an Equation	Use a variable (like x) to represent the unknown. Translate the words into math.	Problems with an unknown value connected to other values by clear relationships.	Setting up the equation incorrectly. Re-read the problem after writing the equation.

Three SHSAT strategies compared

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KEY TAKEAWAY

Choosing a strategy is like choosing a route to school. There might be three different ways to get there. All of them work, but one might be faster depending on traffic. On the SHSAT, the fastest strategy saves you precious minutes. If a problem gives you answer choices with small numbers, try working backward. If it gives you lots of starting information, work forward.

SECTION 8

Connecting to Harder Problems

The skills you are learning now — sorting information and choosing a strategy — are the same skills used in more advanced math. The table below shows how what you learn today connects to tougher problems you will see later.

Skill You're Learning Now	How It Shows Up Later
Sorting relevant vs. extra information	In algebra, word problems get longer. You may see a full paragraph with 8–10 facts and only need 3 of them.
Identifying hidden intermediate steps	In systems of equations, you solve for one variable first, then use it to find another — the same "hidden step" idea.
Choosing the best strategy	In high school, you will choose between graphing, substitution, and elimination for systems. Strategy choice becomes even more important.
Checking your answer	In proofs and formal math, verifying results is a required step, not just a good habit.

From SHSAT skills to advanced math

Think of these SHSAT word problems as training for your math brain. Every time you practice sorting information and picking a strategy, you are building habits that will make algebra, geometry, and beyond feel more manageable.

SECTION 9

Practice Problems

Try these five problems. For each one, first identify the relevant information and cross out the extras. Then choose your strategy before you calculate.

Question 1: CONCEPTUAL

A problem says: "Jake is 12 years old. He ran 3 miles in 24 minutes. His dog weighs 40 pounds. What was Jake's average speed in miles per hour?" Which pieces of information are relevant to answering the question?

Show answer

The relevant facts are: Jake ran 3 miles in 24 minutes. These are the only values you need because the question asks for speed, and speed = distance ÷ time. Jake's age (12) and the dog's weight (40 pounds) are extra information — they are real numbers, but they have nothing to do with speed. Always ask yourself: does this fact connect to what the question is asking?

Question 2: BASIC CALCULATION

A store sells T-shirts for $12 each and hats for $8 each. The store is on Main Street and has been open for 5 years. Priya buys 4 T-shirts and 2 hats. How much does she spend in total?

Show answer

First, cross out the extras: the store's location (Main Street) and how long it has been open (5 years) don't affect cost. The relevant facts are: T-shirts cost $12 each, hats cost $8 each, Priya buys 4 T-shirts and 2 hats. Strategy: multiply then add. Cost of T-shirts = 4 × $12 = $48. Cost of hats = 2 × $8 = $16. Total = $48 + $16 = $64.

Question 3: INTERMEDIATE

Marcus earns $9.50 per hour at his part-time job. He works 4 hours on Saturday and 6 hours on Sunday. He spends $15 on lunch during the weekend and saves $20 for a gift. His supervisor has worked at the store for 7 years. How much money does Marcus have left after lunch and the gift?

Show answer

Extras: The supervisor's 7 years is irrelevant. Relevant: $9.50/hour, 4 hours Saturday, 6 hours Sunday, $15 lunch, $20 gift. Strategy: work forward — find total earnings, then subtract expenses. Total hours = 4 + 6 = 10. Total earnings = 10 × $9.50 = $95.00. Total spending = $15 + $20 = $35. Money left = $95 − $35 = $60.00.

Question 4: APPLIED

A rectangular garden is 15 feet long and 8 feet wide. The gardener wants to put a fence around the entire garden. Fencing costs $6 per foot. The garden has 24 tomato plants and 10 pepper plants inside. The gardener's truck can carry 200 pounds. How much will the fencing cost in total?

Show answer

Extras: 24 tomato plants, 10 pepper plants, and the truck's 200-pound capacity have nothing to do with fencing cost. Relevant: length = 15 ft, width = 8 ft, fencing costs $6 per foot. This is a two-step problem. Step 1: Find the perimeter (total fence length). Perimeter = 2 × (15 + 8) = 2 × 23 = 46 feet. Step 2: Find the cost. Cost = 46 × $6 = $276. The total fencing cost is $276.

Question 5: CRITICAL THINKING

A movie theater charges $10 per adult ticket and $6 per child ticket. On Friday, 45 adults and 30 children bought tickets. On Saturday, 60 adults and 50 children bought tickets. The theater has 200 seats and was built in 2005. The popcorn machine makes 50 bags per hour. What was the total ticket revenue for both days combined?

Show answer

There is a lot of information here! Extras: 200 seats, built in 2005, and 50 bags of popcorn per hour do not affect ticket revenue. Relevant: $10/adult, $6/child, Friday counts (45 adults, 30 children), Saturday counts (60 adults, 50 children). Strategy: calculate each day's revenue, then add. Friday revenue = (45 × $10) + (30 × $6) = $450 + $180 = $630. Saturday revenue = (60 × $10) + (50 × $6) = $600 + $300 = $900. Total revenue = $630 + $900 = $1,530. You could also find total adults (45 + 60 = 105) and total children (30 + 50 = 80) first, then calculate (105 × $10) + (80 × $6) = $1,050 + $480 = $1,530. Either strategy works!

SUMMARY

Lesson Summary

Summary

In this lesson, you learned the 5-step process for tackling multi-step word problems on the SHSAT. The key is to read the question first, then list all facts, cross out extras, choose a strategy (work forward, work backward, or set up an equation), and finally solve and check your answer.

Remember: extra information is designed to distract you. Always test each fact by asking, "Does this help me answer the question?" Common problem patterns include Total Cost (multiply then add), Rate × Time = Distance, and Part = Fraction × Whole. Look for signal words (each, per, total, remaining) to decide which operation to use. The more you practice this process, the faster and more accurate you will become on test day!