Units of Measurement

📏 Units of Measurement

Part 1 of 5 — Measuring Length

Topics in This Part

🔑 Key Idea: A measurement tells you how much of something there is — how long, how heavy, how much liquid, or how much time. To measure, you need two parts: a number and a unit (like "$5$ centimeters"). This lesson builds up the units you need and shows how to switch between them.

What Is a Unit?

A unit is a standard amount that everyone agrees on, so a measurement means the same thing to everybody.

If you said a desk is "$4$ long," nobody knows what you mean — $4$ what? Pencils? Hands? Steps? A unit fixes that:

• "$4$ feet long" → everyone pictures the same length.
• "$4$ pounds heavy" → everyone pictures the same weight.

There are two main systems of units you will use:

💡 Both systems measure the same real things (length, weight, volume). They just use different units — like how "dog" and "perro" are two words for the same animal.

Metric Length: mm, cm, m, km

Metric length units are built on tens, which makes them easy. From smallest to largest:

The key relationships to memorize:

$1 \text{ cm} = 10 \text{ mm} \qquad 1 \text{ m} = 100 \text{ cm} \qquad 1 \text{ km} = 1000 \text{ m}$

🔑 The "bigger holds more smaller" idea: It takes $10$ little millimeters to fill up $1$ centimeter, and $100$ centimeters to fill $1$ meter. The bigger the unit, the fewer you need to cover the same distance.

Concept Check 🎯

Customary Length: in, ft, yd, mi

The U.S. customary length units don't all jump by tens — you have to memorize each one. From smallest to largest:

The key relationships to memorize:

$1 \text{ ft} = 12 \text{ in} \qquad 1 \text{ yd} = 3 \text{ ft} \qquad 1 \text{ mi} = 5280 \text{ ft}$

⚠️ Watch out: A foot is $12$ inches, not $10$. The customary system isn't based on tens, so the numbers ($12$, $3$, $5280$) just have to be learned.

Unit Facts Drill 🧮

Fill in each blank using the length facts above.

1) $1$ meter $= \,?$ centimeters 2) $1$ foot $= \,?$ inches 3) $1$ kilometer $= \,?$ meters

Choosing the Right Unit 🔽

Pick the unit that makes the most sense for measuring each thing. (A good measurement uses a unit that gives a "comfortable" number — not too huge, not too tiny.)

Wrapping Up Part 1

You now know the two systems and their length units:

• Metric: mm → cm → m → km, where $1\text{ cm}=10\text{ mm}$, $1\text{ m}=100\text{ cm}$, $1\text{ km}=1000\text{ m}$.
• Customary: in → ft → yd → mi, where $1\text{ ft}=12\text{ in}$, $1\text{ yd}=3\text{ ft}$, $1\text{ mi}=5280\text{ ft}$.

🔑 The big pattern for the whole lesson: Bigger units take more small units to fill them. We'll use that fact in Part 4 to convert between units. Next up: measuring weight and liquids.

⚖️ Units of Measurement

Part 2 of 5 — Weight & Liquid Volume

Topics in This Part

🔑 Key Idea: Weight tells you how heavy something is. Liquid volume (also called capacity) tells you how much liquid a container holds. Each has its own metric and customary units.

Mass & Weight

Metric weight units (smallest to largest):

$1 \text{ kg} = 1000 \text{ g}$

Customary weight units (smallest to largest):

$1 \text{ lb} = 16 \text{ oz} \qquad 1 \text{ ton} = 2000 \text{ lb}$

💡 The short way to write pound is lb (from the old Latin word libra). The short way to write ounce is oz.

Concept Check 🎯

Liquid Volume (Capacity)

Metric liquid volume (smallest to largest):

$1 \text{ L} = 1000 \text{ mL}$

Customary liquid volume (smallest to largest):

The customary "ladder" of liquid units:

$1 \text{ c} = 8 \text{ fl oz} \qquad 1 \text{ pt} = 2 \text{ c} \qquad 1 \text{ qt} = 2 \text{ pt} \qquad 1 \text{ gal} = 4 \text{ qt}$

🔑 Memory trick — "G-Q-P-C": A Gallon holds 4 Quarts, each quart holds 2 Pints, each pint holds 2 Cups. Going up the ladder, the containers get bigger.

Quick Facts Drill 🧮

Fill in each blank using the unit facts above.

1) $1$ liter $= \,?$ milliliters 2) $1$ gallon $= \,?$ quarts 3) $1$ kilogram $= \,?$ grams

Matching Units to Objects 🔽

Choose the best unit to measure each thing.

⏰ Units of Measurement

Part 3 of 5 — Time, Money & Reading Scales

Topics in This Part

🔑 Key Idea: Length, weight, and volume aren't the only things we measure. We also measure time and money — and we measure anything by reading a tool like a ruler or scale correctly.

Units of Time

Time has its own ladder of units. Notice the numbers are not based on tens:

$1 \text{ min} = 60 \text{ sec} \qquad 1 \text{ hr} = 60 \text{ min} \qquad 1 \text{ day} = 24 \text{ hr}$

⚠️ Don't mix these up: An hour is $60$ minutes, and a day is $24$ hours. These are special "clock numbers," not the round metric $1000$.

Concept Check 🎯

Units of Money

In the U.S., money is measured in dollars and cents. The big fact:

$\$1 = 100 \text{ cents}$

The common coins are each worth a number of cents:

💡 Money is actually metric-like: a dollar splits into $100$ cents, just like a meter splits into $100$ centimeters. The word cent even means "hundred" (think century $=100$ years).

Quick example: $3$ quarters $= 3 \times 25 = 75$ cents. Add $2$ dimes $= 2 \times 10 = 20$ cents, for $75 + 20 = 95$ cents total.

Counting Money 🧮

Find the total value in cents.

1) $4$ quarters $= \,?$ cents 2) $2$ dimes and $1$ nickel $= \,?$ cents 3) $2 $= \,?$ cents

Reading a Ruler

A ruler is just a number line for length. To read it correctly:

1. Line up the start of the object with the $0$ mark (not the very edge of the ruler).
2. Count the whole units the object passes.
3. Read the small tick where the object ends.

On a centimeter ruler, the longest lines are the centimeters, and the $9$ little ticks between them split each centimeter into millimeters ($1\text{ cm}=10\text{ mm}$).

⚠️ Most common mistake: starting at the metal edge or at the "$1$" instead of the $0$. Always begin counting from $0$, or your answer will be off.

Reading Check 🎯

🔁 Units of Measurement

Part 4 of 5 — Converting Units

🔑 The One Big Rule for Grade 4: When you go from a bigger unit to a smaller unit, you multiply. (Think: it takes more small units to cover the same amount, so the number gets bigger.)

Bigger → Smaller Means Multiply

To convert a measurement, ask: how many small units fit in one big unit? Then multiply by that number.

$\text{(number of big units)} \times \text{(small units in one big unit)} = \text{small units}$

Worked Example: feet → inches

Convert $5$ feet to inches. Since $1 \text{ ft} = 12 \text{ in}$:

$5 \text{ ft} = 5 \times 12 = 60 \text{ in}$

Worked Example: meters → centimeters

Convert $3$ meters to centimeters. Since $1 \text{ m} = 100 \text{ cm}$:

$3 \text{ m} = 3 \times 100 = 300 \text{ cm}$

💡 Sanity check: The number got bigger ($5 \to 60$, $3 \to 300$). That's exactly what should happen — you're now counting in smaller pieces, so it takes more of them.

A Conversion Toolbox

Here are the "multiply by" facts you'll use most. To go from the big unit to the small unit, multiply by the number in the last column.

🔑 To convert a larger unit into a smaller one, multiply by the matching number above.

Concept Check 🎯

Convert It 🧮

Use the toolbox. To go from a bigger unit to a smaller unit, multiply.

1) $7$ meters $= \,?$ centimeters 2) $3$ pounds $= \,?$ ounces 3) $5$ liters $= \,?$ milliliters 4) $2$ hours $= \,?$ minutes

Two-Column Conversion Tables

In Grade 4 you'll often build a small table. To make a table of yards → feet, multiply each yard amount by $3$ (since $1\text{ yd}=3\text{ ft}$):

Notice each row follows the same rule: multiply the yards by $3$. Tables like this make conversions fast and let you spot the pattern.

💡 The number you multiply by never changes for a given pair of units — it's the same $3$ in every row. Find that number once, then reuse it.

Finish the Table 🔽

Complete this gallons → quarts table. Remember $1$ gallon $= 4$ quarts, so multiply each gallon amount by $4$.

🧩 Units of Measurement

Part 5 of 5 — Word Problems & Mastery Check

You can now name units, choose the right one, read tools, and convert bigger units into smaller ones. Let's put it together with real-world problems and a final quiz.

Quick Reference

🔑 Problem-solving plan: (1) Find out which units appear. (2) Make sure they match — convert the bigger unit to the smaller unit (multiply) if needed. (3) Then add, subtract, or compare.

Worked Word Problem

Maya has a ribbon $2$ meters long. She cuts off $75$ centimeters. How many centimeters of ribbon are left?

Step 1 — Match the units. The ribbon is in meters but the cut is in centimeters. Convert meters to centimeters (bigger → smaller, so multiply):

$2 \text{ m} = 2 \times 100 = 200 \text{ cm}$

Step 2 — Now subtract, since both amounts are in centimeters:

$200 - 75 = 125 \text{ cm}$

✅ Answer: $125$ centimeters of ribbon are left. The key move was converting to a common unit first.

Word Problem Practice 🎯

Solve It 🧮

Convert to a common unit first, then answer in the unit shown.

1) A rope is $4$ feet long. How many inches is that? 2) A jug holds $2$ gallons. A pitcher holds $5$ quarts. How many quarts does the jug hold? (so you can compare) 3) Sam runs for $3$ minutes. How many seconds is that?

Exit Quiz ✅

Answer all three to finish the lesson.