Solve problems involving length, time, or unit conversions. - ISEE Lower Level Quantitative Reasoning

SECTION 1

Why Do We Need Measurement Units?

Long ago, people needed ways to measure things. A farmer wanted to know how long a field was. A baker needed to know how much flour to use. But there was a big problem — everyone measured differently!

Some people used their feet to measure distance. Others used their arms! Imagine if your friend's foot was bigger than yours. You would get different answers for the same field. That's why people created standard units — measurements that are the same for everyone.

3000 BC • Ancient Egypt

Egyptians used the cubit — the length from elbow to fingertip — to build the pyramids.

1200s • The King's Foot

In England, a "foot" was based on the actual foot of the king. When the king changed, the measurement could change too!

1790s • The Metric System

France created the metric system with meters, liters, and grams. Most countries use it today.

Today • Two Systems Side by Side

The United States mainly uses customary units (inches, feet, pounds). On the ISEE, you'll see both systems!

Today, we still need to switch between different units. How many inches are in 3 feet? How many minutes in 2 hours? That's what unit conversion is all about. Let's learn how!

SECTION 2

Core Ideas About Measurement

Before we start converting, let's learn the big ideas. These four principles will help you solve any measurement problem on the ISEE.

Units Tell You What You're Counting

"12" means nothing by itself. 12 inches? 12 feet? 12 hours? Always check the unit!

Smaller Units Make Bigger Numbers

1 foot = 12 inches. When you change to a smaller unit, the number gets bigger. Think: more tiny pieces!

Bigger Units Make Smaller Numbers

24 inches = 2 feet. When you change to a bigger unit, the number gets smaller. Fewer big pieces cover the same distance.

Multiply or Divide — That's It!

To convert, you either multiply (going to smaller units) or divide (going to bigger units). That's the whole trick!

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KEY TAKEAWAY

Think of unit conversion like trading coins. If you trade 1 dollar for quarters, you get 4 quarters — a bigger number of smaller pieces. If you trade 100 pennies for dollars, you get 1 dollar — a smaller number of bigger pieces. The total value stays the same. That's exactly how unit conversion works!

SECTION 3

See the Conversion Connections

This diagram shows the most important conversions you need to know for the ISEE. Think of each arrow as a doorway between units. The number on the arrow tells you the "exchange rate."

The arrows show how many smaller units fit inside one bigger unit. For example, 12 inches fit inside 1 foot. So 1 foot × 12 = 12 inches.

Look at the diagram above. Each arrow shows the number you multiply by. To go from feet to inches, you multiply by 12. To go from inches to feet, you divide by 12. It's like using a doorway — multiply going one way, divide going back!

SECTION 4

The Conversion Facts You Need

On the ISEE, you need to have certain conversion facts memorized. Here are the key ones. Don't worry — there aren't too many!

LENGTH CONVERSIONS

1 foot = 12 inches • 1 yard = 3 feet = 36 inches

A foot is about the length of a ruler. A yard is about the length of a baseball bat.

TIME CONVERSIONS

1 minute = 60 seconds • 1 hour = 60 minutes • 1 day = 24 hours

Think of a clock! The second hand goes around once every minute. The minute hand goes around once every hour.

THE CONVERSION RULE

To go from BIG units to SMALL units → MULTIPLY To go from SMALL units to BIG units → DIVIDE

Example: 3 feet to inches → 3 × 12 = 36 inches (multiply because inches are smaller). 36 inches to feet → 36 ÷ 12 = 3 feet (divide because feet are bigger).

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ISEE Test Tip

If you're not sure whether to multiply or divide, ask yourself: "Should my answer be a bigger number or a smaller number?" Going to smaller units? Bigger number. Going to bigger units? Smaller number. Use this to check your work and eliminate wrong answer choices!

SECTION 5

A Closer Look at Each Type

Let's look at length conversions and time conversions side by side. This chart will be your best friend for ISEE problems!

Conversion Type	What to Remember	Example
Inches → Feet	Divide by 12	48 inches ÷ 12 = 4 feet
Feet → Inches	Multiply by 12	5 feet × 12 = 60 inches
Feet → Yards	Divide by 3	9 feet ÷ 3 = 3 yards
Yards → Feet	Multiply by 3	4 yards × 3 = 12 feet
Minutes → Hours	Divide by 60	120 minutes ÷ 60 = 2 hours
Hours → Minutes	Multiply by 60	3 hours × 60 = 180 minutes

Key conversion facts for the ISEE

This bar model shows how 1 yard, 3 feet, and 36 inches are all the same length. The smaller the unit, the more pieces you need.

Notice something cool in the diagram? The yellow bar (1 yard), the three blue bars (3 feet), and the pink boxes (36 inches) are all the exact same length. Only the number and unit change!

SECTION 6

Worked Example: Solving a Conversion Problem

Let's work through a problem together, step by step. This is exactly how you should think on test day!

Emma's soccer practice lasts 2 hours and 15 minutes. How many total minutes is that?

1
Step 1 — Identify What You Know

Emma's practice is 2 hours and 15 minutes. We need to find the total in minutes only. So we need to convert the 2 hours into minutes, then add the extra 15 minutes.
2
Step 2 — Convert Hours to Minutes

We know that 1 hour = 60 minutes. We have 2 hours. Since we're going from a big unit (hours) to a smaller unit (minutes), we multiply.

2 × 60 = 120 minutes
3
Step 3 — Add the Extra Minutes

Now add the 15 minutes that were already in minutes.

120 + 15 = 135 minutes
4
Step 4 — Check Your Answer

Does 135 minutes make sense? 2 hours is 120 minutes, and 15 more is 135. That's more than 2 hours but less than 2.5 hours. Yes, that makes sense!

Answer: 135 minutes

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ISEE Strategy

On the ISEE, always check whether the answer choices are in the same unit as the question asks for. Sometimes a problem asks for inches but gives you feet. Read carefully! Underline the unit the question wants.

SECTION 7

ISEE Strategies for Measurement Problems

Knowing the facts is great, but you also need smart strategies. Here are the best tricks for test day!

Strategy	When to Use It	Example
Check the units first	Every problem! Before you calculate.	"How many inches..." tells you the answer is in inches.
Estimate to eliminate	When you're unsure of your math.	5 feet ≈ 60 inches. If a choice says 500, it's way too big!
Bigger or smaller?	When you forget whether to multiply or divide.	Inches are smaller than feet, so there should be MORE of them.
Work backwards	When a problem gives you the answer unit and asks for the starting unit.	"A rope is 48 inches. How many feet?" Start with 48 and divide by 12.

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KEY TAKEAWAY

On the ISEE, you should never leave a question blank — there's no penalty for wrong answers! If you're stuck on a conversion problem, use estimation to cross out answers that are way too big or way too small. Then make your best guess from what's left. Even eliminating one or two wrong answers gives you a much better chance!

SECTION 8

Beyond Basic Conversions

You're building skills now that will help you for years to come! Here's how today's topic connects to what you'll learn later.

What You Learn Now	What Comes Next
Inches, feet, yards	Metric system: meters, centimeters, kilometers
Minutes and hours	Speed and rate problems (miles per hour)
Multiply and divide to convert	Using ratios and proportions for conversions
One-step conversions	Multi-step conversions (inches → yards in one problem)

How today's skills build into future math

For now, focus on memorizing the key facts and practicing the multiply-or-divide decision. On the ISEE Lower Level, most conversion problems use whole numbers and one or two steps. You've got this!

SECTION 9

Practice Problems

Time to practice! Try each problem on your own first. Remember: check the units, decide whether to multiply or divide, and always answer every question!

Question 1: CONCEPTUAL

Which of the following is the longest?

A. 1 foot
B. 10 inches
C. 1 yard
D. 2 feet

Show answer (C)

The correct answer is C. 1 yard = 3 feet = 36 inches. Let's compare: A is 1 foot (12 inches). B is 10 inches. C is 1 yard (36 inches). D is 2 feet (24 inches). Since 36 inches is the greatest, 1 yard is the longest.

Question 2: BASIC CALCULATION

How many inches are in 4 feet?

A. 16
B. 36
C. 48
D. 52

Show answer (C)

The correct answer is C. Since 1 foot = 12 inches, multiply: 4 × 12 = 48 inches. A (16) is wrong because it uses 4 × 4. B (36) is inches in a yard, not in 4 feet. D (52) might come from adding 4 + 48. Always multiply the number of feet by 12.

Question 3: INTERMEDIATE

A movie lasts 1 hour and 45 minutes. How many total minutes is the movie?

A. 45
B. 95
C. 105
D. 145

Show answer (C)

The correct answer is C. First convert 1 hour to minutes: 1 × 60 = 60 minutes. Then add the extra 45 minutes: 60 + 45 = 105 minutes. A (45) forgets to include the hour. B (95) incorrectly adds 50 instead of 60. D (145) puts the 1 in front of 45 instead of converting properly.

Question 4: APPLIED

Tom has a piece of rope that is 6 feet long. He cuts off 30 inches. How many inches of rope does Tom have left?

A. 30
B. 42
C. 54
D. 66

Show answer (B)

The correct answer is B. First, convert 6 feet to inches: 6 × 12 = 72 inches. Then subtract the 30 inches he cut off: 72 − 30 = 42 inches. A (30) just repeats what was cut off. C (54) might come from using 7 × 12 − 30. D (66) subtracts only 6 from 72 instead of 30.

Question 5: CRITICAL THINKING

Maya starts doing homework at 4:15 PM and finishes at 5:30 PM. She then reads for 45 minutes. How many total minutes did Maya spend on homework and reading?

A. 75
B. 105
C. 120
D. 150

Show answer (C)

The correct answer is C. First, find the homework time: from 4:15 to 5:15 is 60 minutes, and from 5:15 to 5:30 is 15 more minutes, so homework = 75 minutes. Then add reading time: 75 + 45 = 120 minutes. A (75) only counts the homework time and forgets the reading. B (105) may incorrectly calculate the homework time as 60 minutes. D (150) might add an extra 30 minutes somewhere.

SUMMARY

Lesson Summary

Summary

In this lesson, you learned how to solve unit conversion problems involving length and time. The key facts to remember are: 1 foot = 12 inches, 1 yard = 3 feet, 1 hour = 60 minutes, and 1 minute = 60 seconds.

When converting from big units to small units, multiply — your number gets bigger. When converting from small units to big units, divide — your number gets smaller. On the ISEE, always read the question carefully to check which unit the answer should be in, use estimation to eliminate wrong choices, and never leave a question blank. You've got this!